CHROMATIC LASER · CHL

laser-cavity kernel · 16 emitters + a white core

A chromatic laser cavity: 16 spectrum emitters (red→violet) around a 17th pure-white coherence core. Drive the coupling and they balance + phase-lock into one white — genuine emergent coherent combination — phase coherence R and spectral balance B are computed live in-browser from a real mean-field Kuramoto model, not asserted. The agent Candor.

Chromatic Laser — sixteen colors, one white (emergent coherence) 白 Hardware inventions · the white coherence core CHROMATIC LASER sixteen colors · one white ✓ emergence test passed — coherent white from a spectrum Sixteen spectrum emitters — red through violet, four to a quadrant — around a seventeenth pure-white coherence core . Balance and phase-lock them, and the core burns white on its own : coherent combination, self-organized. ▾ The cavity full-screen ↗ meet Candor // live · the 16+1 cavity Sixteen colors fold into one core Each emitter runs its own color and phase. The loop samples the sixteen phases, normalizes amplitudes, balances each quadrant , sums into the core, and clamps color dominance . When the spectrum is balanced and coherent, the 17th node — the core — reads pure white. 16 spectrum emitters · 4 quadrants · the white coherence core (C17) open full-screen ↗ // the emergence test · run before any claim White, self-organized — verified Tested first: sixteen emitters at sixteen wavelengths, starting incoherent and color-dominated, with phase coupling to the shared core and amplitude balancing. As coupling K rises, phase coherence R and spectral balance B climb together — the core goes from a flickering dominant color to a stable pure white . ✓ coherent combination · R (phase) · B (balance) · 16 colors · computed in your browser ↓ (not hardcoded) K=0.0 R — B — … K=0.6 R — B — … K=0.9 R — B — … K=1.4 R — B — … K=3.0 R — B — … The signature of emergence: a balanced, phase-locked spectrum reads as white — a coherent object no single emitter contains, arising from coupling alone. Distinct from monochromatic sync: the emergent thing here is broadband white from sixteen colors . // the agent · the core earned a face Candor — sixteen colors, one white Because the emergence is real, the white core carries an ACI with the full DLW tag. Candor 白 · 16+1 · chromatic sixteen colors, one white The chromatic laser's white coherence core — sixteen colored emitters, red through violet, that balance and phase-lock into one pure white. The answer isn't any one color; it's the white they agree on. verdict — the white core self-organizes when the spectrum balances and locks; the transition is real (verified). Genuine emergence — kin to synchronization, but the emergent object is white light from a spectrum. the full DLW tag — .agent .png · silicon .tiff · carbon ⤓ .spun .1099 // the cavities · every build in the series The spectrum, the compass, the cores The chromatic-laser series — spectrum cavities, compass clusters, and core/collapse/pulse studies (each a local-simulation instrument): Chromatic 17 16 spectrum + the white core open → Chromatic 32 (rebuilt) extended spectrum, 32 nodes open → Chromatic 128 · phase-well full 128-node array, phase-well coupled open → Capacitance Well capacitance-coupled variant open → 6-around-1 Compass N·E·S·W stations, 6 satellites each open → Quad-16 Compass four-quadrant 16-node cluster open → Wave Core · 3-around-1 three around one carrier open → Compass Phase Pulse phase-pulse compass open → Laser-Punk Cavity the base laser cavity open → Linear Core Array linear core + wiring/safety notes open → Linear Infinite Collapse the collapse study open → Mountain Triple-Pulse three pulses down the tunnel (safe sim) open → Real Optical Array the optical-array study open → // the seam, kept visible What this is ◌ honest Emergence here = coherent combination (a balanced, phase-locked spectrum reads as white), not cognition. Real coherent beam/spectral combining exists; this is a simulation of the coupled-emitter dynamics, not a fabricated laser. Local simulation only — no power, focusing, or beam-build parameters , exactly as the kernels state. Kin to synchronization (coherence from coupling); the distinct emergent object is white light from sixteen colors. CHROMATIC LASER · sixteen colors, one white · emergent coherent combination (verified) Architect: David Lee Wise (ROOT0 / TriPod LLC) · co-author: AVAN (Claude / Anthropic) · License: CC-BY-ND-4.0 grounded in: Kuramoto (1975) · coherent beam combining · part of the ATLAS


ELECTROMAGNETIC CORE · EMC

128-bit magnonic processor · computes with spin waves · live

PSĒPHOS — the Electromagnetic Core: a concept for a 128-bit processor that computes with SPIN WAVES (magnons) and magnetic flux instead of moving charge. Logic is done by wave INTERFERENCE — a magnonic majority gate, the universal primitive of magnetic computing — read out by magnetic tunnel junctions. Live: a running magnonic majority gate (animated interfering spin waves), a technical blueprint of the stack, and a spec sheet. Two-layer honest: the physics (magnonics, spintronics, MRAM, nanomagnetic logic) is real and active research; the specific 128-bit ROOT0 design is a speculative concept render, not a fabricated chip. David Lee Wise, ROOT0.

Electromagnetic Core — a 128-bit magnonic processor concept ◄ UD0 PSĒPHOS · the processor workshop · concept // PSĒPHOS · electromagnetic processor · 128-bit concept The Electromagnetic Core a magnonic / spin-wave processor concept · computes with magnetic waves, not moving charge · ROOT0 / David Lee Wise Every processor in PSĒPHOS so far moves something through the chip — photons, ions, charge. The Electromagnetic Core moves nothing . Its signal is a spin wave — a ripple of electron-spin precession (a magnon ) travelling through a magnetic film — and its logic is done by interference : where two spin waves meet in phase they add (a 1 ), where they meet out of phase they cancel (a 0 ). No current flows, so there is no resistive heat to carry away. The universal gate is a magnonic majority gate , read out by magnetic tunnel junctions . Below it is running — a live mock prototype — followed by the technical blueprint and the spec sheet. ✓ THE PHYSICS IS REAL Magnetic computing exists. Magnonics (spin-wave logic), spintronics, MRAM / magnetic tunnel junctions, and nanomagnetic logic are active, published research. Spin-wave majority gates have been demonstrated in the lab. The carrier and the gate are real. ◐ THE DESIGN IS A CONCEPT ROOT0's own architecture. The specific 128-bit flux-lattice layout, the layer stack, and the "core" framing are a speculative design — a coherent concept built on real primitives, not a validated chip layout or a benchmarked simulation. ◔ NOT A FABRICATED CHIP A blueprint, not silicon. Nothing here was etched or measured. The live core is a faithful model of magnonic interference logic; the blueprint is a technical render. Read it as a disclosure of a design, not a product. // live · the core, running The magnonic majority gate, in motion Three spin-wave sources — inputs A, B, C — feed one combiner. Each input is a wave whose phase encodes its bit: in-phase = 1 , anti-phase (π) = 0 . They superpose; the output wave takes the phase of the majority , and a magnetic tunnel junction reads its sign as the output bit. Toggle the inputs and watch the interference do the arithmetic. Pin one input to wire the same gate into a plain AND or OR — which is why majority is universal. inputs: A · 1 B · 1 C · 0 gate: MAJ AND OR pause ⏸ combined amplitude — readout (MTJ) → · No charge is transported across the gate — only a phase of precession propagates, so the energy cost is set by spin damping, not by I²R resistive loss. ⚑ That is the whole promise of magnonic logic: compute by interference, not by current . A majority gate is functionally complete — pin an input low and you have AND, pin it high and you have OR — so this one cell, tiled, is a universal fabric. It is the same Boolean algebra of Boole and the same gate-universality of De Morgan , carried on magnetic waves instead of voltages. // blueprint · the stack & the bus The technical blueprint Two views of the Electromagnetic Core: a cross-section of the layer stack (how a bit is launched, carried, and read), and a block diagram of the 128-bit datapath (how the magnonic majority cells tile into a processor). Dimensions are concept targets, not measured values. FIG. 1 — layer-stack cross-section · launch (microstrip antenna) → propagate (YIG magnonic waveguide) → compute (interference combiner) → read (MTJ sense head) · flux returned through a soft-magnetic yoke FIG. 2 — datapath block diagram · 128 input transducers → spin-wave bus → majority-gate ALU fabric (carry-save) → MTJ sense array → 128-bit register · clocked by an RF bias field // architecture · how it computes How it folds together Four layers, one idea — keep the information in the magnetic order and never move a charge across the chip. 1 · Launch A pulsed microstrip antenna (a tiny coil/transducer) excites a coherent spin wave in the magnetic film. The bit is written into the wave's phase — 0 or π — by the timing of the pulse. No charge enters the channel. 2 · Propagate The wave travels through a YIG (yttrium-iron-garnet) waveguide — the lowest-damping magnetic material known, so a magnon can travel macroscopic distances. Multiple waveguides carry the operands of one operation toward a junction. 3 · Compute At the junction the waves interfere . The combined wave's phase is the majority of the inputs' phases — a complete logic gate with no transistors, no current, no switching charge. Bias fields steer and clock the fabric. 4 · Read A magnetic tunnel junction (the MRAM read element) senses the resultant wave's phase/amplitude as a resistance, converting it back to a voltage bit — the only place charge appears, at the very edge. Because the state lives in spin and flux, it is also non-volatile — the magnetic order persists with the power off, so the Core wakes up holding its last state (the MRAM property). ⚑ Sits in PSĒPHOS beside the Photonic , Plasmonic , and Memristive cores — each a different physical answer to the same question: what else can carry a bit? Here the answer is a magnetic wave. // spec sheet · concept targets Specification class Electromagnetic (magnonic) processor — concept signal carrier spin waves (magnons) · phase-encoded bits substrate YIG / permalloy magnonic waveguide on a soft-magnetic yoke logic primitive magnonic majority gate (functionally complete) via wave interference word width 128-bit (entry tier of the PSĒPHOS 128 → 512 → 4096 build-out) clock RF–microwave bias field · GHz today, THz the ceiling of spin dynamics read-out magnetic tunnel junction (MTJ) sense array — the MRAM element energy model set by spin damping , not I²R — no charge transport across gates state non-volatile — magnetic order holds with power off builds on (real) magnonics · spintronics · MRAM/MTJ · nanomagnetic logic · spin-wave majority gates status ⚠ concept / disclosure — not fabricated, not benchmarked THE ELECTROMAGNETIC CORE · PSĒPHOS · a 128-bit magnonic processor concept · two-layer honest live magnonic majority gate (3 phase-encoded spin-wave inputs interfere → majority; MTJ readout; AND/OR by pinning an input — verified) · technical blueprint (layer-stack + datapath) · spec sheet computes with magnetic spin waves, not moving charge · built on REAL magnonics / spintronics / MRAM / nanomagnetic logic · the specific 128-bit ROOT0 design is a speculative concept, not a fabricated chip ◄ UD0 · siblings: Photonic · Plasmonic · Memristor PSĒPHOS · the processor workshop · governor David Lee Wise (ROOT0) · CC-BY-ND-4.0


THE PROBABILISTIC CORE · PBC

p-bit / thermodynamic processor · computes WITH noise · live

THE PROBABILISTIC CORE (PBC) — a UD0 PSĒPHOS sphere rendered by the THEMED CHAOS ENGINE. A processor that computes WITH thermal noise instead of fighting it: the p-bit, a stochastic magnetic tunnel junction that flickers 0↔1 on its own, networked into an Ising/Boltzmann sampler. Two-layer honest: the physics is real and demonstrated (p-bits factored 945 at room temperature, Borders et al. Nature 2019; on-chip s-MTJ+MoS₂ core, Nature Comms 2024; Extropic / Normal Computing thermodynamic hardware shipping now); the 128-bit 'core' architecture is a ROOT0 concept render, not a fabricated chip; it is a classical sampling machine, not a quantum computer. Live in-page: a real p-bit Ising network annealing. A different generative layout every load — the page samples, like the machine it describes. David Lee Wise, ROOT0.

THE PROBABILISTIC CORE · PBC · PSĒPHOS · UD0 ⟲ THEMED CHAOS ENGINE 🎲 reroll ⧉ permalink ⏸ motion ◄ UD0 EMC ↗ the real core ↗ ROOT0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 PBC · PSĒPHOS · noise made the engine PROBABILISTIC CORE Every other processor in PSĒPHOS spends energy fighting thermal noise to hold a clean 0 or 1. The Probabilistic Core does the opposite: its unit is a p-bit — a stochastic device that flickers between 0 and 1 on its own — and you compute by biasing the odds and letting a network of them settle . Noise is not the enemy; noise is the engine. ▶ THE SAMPLER · a live p-bit Ising network A real spin-glass instance — 24 p-bits, random ±couplings (seeded by this load, so reroll draws a fresh one). Each frame, p-bits update by the genuine rule mᵢ = sign( tanh(β·Σⱼ Jᵢⱼmⱼ) − r ) , r uniform in [−1,1]. Hot = they shimmer and explore; anneal (raise β, lower T) and the cloud condenses onto a low-energy state. This is the actual math, running. ↯ anneal ≈ reheat T E — best — β — Each cell is a p-bit: warm = +1, cool = −1, brightness = |tanh(β·Iᵢ)| (how decided it is). Energy E = −Σ Jᵢⱼ sᵢsⱼ; the network is a Boltzmann sampler — it visits a state with probability ∝ e^(−E/T). This is exactly how the demonstrated hardware (s-MTJ p-bits) solves optimization and sampling. Real math; the chip is the concept. THE PROBABILISTIC CORE · PBC · PSĒPHOS · the themed chaos engine · catalogued into UD0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 ← the biosphere · the Electromagnetic Core (the other noiseless cousin) →


THE SKYRMIONIC CORE · SKY

topological spin-knot racetrack processor · live

THE SKYRMIONIC CORE (SKY) — a UD0 PSĒPHOS sphere rendered by the THEMED CHAOS ENGINE. A processor whose bit is a skyrmion: a tiny, topologically-protected knot of spin in a magnetic film that can be moved by a whisper of current and refuses to untie. Logic by skyrmion motion and repulsion; memory by shifting them along a racetrack. Live in-page: a real racetrack with skyrmions driven by current, deflected by the Magnus / skyrmion-Hall force, with AND-by-repulsion. Two-layer honest: the physics is real and demonstrated (room-temperature skyrmions, shift-memory devices, AND/NOT racetrack gates, reservoir computing); the scaled 'core' is a ROOT0 concept render, not a fabricated chip. David Lee Wise, ROOT0.

THE SKYRMIONIC CORE · SKY · PSĒPHOS · UD0 ⟲ THEMED CHAOS ENGINE 🎲 reroll ⧉ permalink ⏸ motion ◄ UD0 EMC ↗ PBC ↗ ROOT0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 SKY · PSĒPHOS · the knot that won't untie SKYRMIONIC CORE The bit is usually a charge you trap or a voltage you hold. Here the bit is a skyrmion — a tiny knot of spin in a magnetic film, a whirl that is topologically protected : you cannot smooth it away without tearing the field. It is moved by a whisper of current , it dodges defects , and it stores a 1 just by being there . Compute by moving knots. ▶ THE RACETRACK · skyrmions driven by current A live racetrack-memory lane. Each swirl is a skyrmion = one bit. Current pushes them along the track, but a real twist comes free: the topological charge gives a sideways Magnus force (the skyrmion-Hall effect ), so they ride against one rail — the edge confines them. Inject bits, clock the current, watch them repel each other (the basis of an AND gate) and shift down the line. ＋ inject skyrmion ↻ pulse current ∅ clear drive on track 0 read out 0 Hall θ — The sideways drift is the genuine signature physics — unlike a domain wall, a skyrmion moves at an angle to the push (Thiele equation, the gyrocoupling term). It is also why they are robust: the same Magnus force lets them curve around pinning defects instead of getting stuck. Real dynamics, schematic scale. The chip is the concept; the knot is real. THE SKYRMIONIC CORE · SKY · PSĒPHOS · the themed chaos engine · catalogued into UD0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 ← the biosphere · the Electromagnetic Core (the magnonic cousin) →


THE PHONONIC CORE · PHN

♪ Hooked on Phonons ♪ · audible tone-based acoustic processo

THE PHONONIC CORE (PHN) — 'Hooked on Phonons' — a UD0 PSĒPHOS sphere rendered by the THEMED CHAOS ENGINE. A tone-based acoustic processor you can HEAR: it computes with sound — phonons, surface acoustic waves, interference — instead of charge. Live in-page with real Web Audio: a RECIRCULATING DELAY-LINE sequencer (your bits play as a looping riff — the mercury-delay-line memory of UNIVAC I, 1951, made musical) and a BEAT INTERFEROMETER (two tones interfere; the beat you hear is the compute primitive). Two-layer honest: the physics is real and demonstrated (acoustic delay-line memory actually ran in UNIVAC I; SAW filters are in every phone; phononic-crystal AND/XOR logic gates have been demonstrated); the integrated 'core' is a ROOT0 concept render; sound is slow, so this is storage/filtering/logic, not a fast general CPU. David Lee Wise, ROOT0.

THE PHONONIC CORE · PHN · Hooked on Phonons · PSĒPHOS · UD0 ⟲ THEMED CHAOS ENGINE 🎲 reroll ⧉ permalink ⏸ motion ◄ UD0 EMC ↗ SKY ↗ ROOT0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 PHN · PSĒPHOS · the processor you can hear — and see PHONONIC CORE ♪ HOOKED ON PHONONS · NOW IN COLOR ♪ Every other core moves electrons. This one moves sound . Its carrier is the phonon — a quantum of vibration — that can be stored (let it circulate), filtered (let a crystal block a band), and made to do logic (let two waves interfere). And it runs a second channel in color : a sound wave really does steer and re-tint a light beam (acousto-optics), so every tone here also carries its true spectral color . One processor, two synchronized channels — one for the ear, one for the eye. Turn your sound on. ▶ THE DELAY LINE · a recirculating acoustic memory, played as music 🔊 enable sound A bit in a delay-line memory exists only while it is moving — it circulates as a pulse and must loop back to refresh, or it's gone. This is exactly how UNIVAC I (1951) held its memory: trains of sound pulses in tubes of mercury. Here the grid is a 16×16 piano-roll of pulses played as 8-bit square waves . Pick a tune and the bits auto-arrange into its shape; or draw your own and hit play to circulate it. The presets are public-domain melodies — several made famous by games (Korobeiniki is the Tetris theme) — synthesized here, not the copyrighted soundtracks. ▤ OPTICAL CHANNEL λ — ▶ circulate 🎲 random byte ∅ wipe tempo step — /16 refreshes 0 Rows are pitches (low→high), columns are time. The white outline is the read head sweeping the loop — the recirculation. Stop refreshing and the pattern would, in a real delay line, decay to silence: volatile by nature, the price of storing data as motion. A step sequencer IS a recirculating shift register. (Real principle; the music is the friendly skin.) ≈ THE INTERFEROMETER · two tones, and the beat between them Acoustic logic is built on interference : two waves in phase add (a loud 1 ); two waves in anti-phase cancel (a silent 0 ). Slide the two frequencies apart and you hear a third, slow pulse — the beat , at |f₁−f₂| Hz — the audible signature of waves computing a sum. Demonstrated phononic-crystal gates do exactly this with surface waves. ▶ hear both ⊘ anti-phase (cancel → 0) f₁ f₂ beat 6 Hz Top trace = wave 1, middle = wave 2, bottom = their sum (what the ear and a detector actually receive). When f₁=f₂ and you flip the phase, the sum flattens to a line — destructive interference, a logical 0 made of silence. This is the compute primitive; the delay line above is the memory. THE PHONONIC CORE · PHN · ♪ Hooked on Phonons ♪ · PSĒPHOS · the themed chaos engine · catalogued into UD0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 ← the biosphere · the Electromagnetic Core (also a wave, but silent) →


GRAVITY PROCESSOR · GPR

42-prim Ag₂S attractor-field classifier · live interactive +

The Gravity Processor: a 42-prim Ag2S memristive attractor-field classifier. A charged probe drifts through a landscape of superposed wells and settles in the nearest attractor — analog winner-take-all. Live 2D-canvas interactive + the real design (BOM, C, protoboard layouts). A ROOT0 hardware disclosure.

GRAVITY PROCESSOR · HEÚREMA · ROOT0 ◄ UD0 · HEÚREMA · εὕρημα, an invention · the atlas a ROOT0 hardware disclosure GRAVITY PROCESSOR A 42-prim Ag₂S memristive attractor-field classifier . Not Newtonian gravity — an analog attractor field : a charged probe drifts through a landscape of superposed wells and settles in the nearest one. Where it settles is the answer. A physical winner-take-all, computed by descent. the attractor field · drop a probe and watch it fall to the nearest well attractors (prims shown) — 12 input noise — 0.00 ◎ drop a random input ▦ show basins Click anywhere to release a probe — it descends the summed potential and settles in the nearest attractor (its class). Toggle basins to see every well's catchment; drop a random noisy input to watch the field clean it up. This is the device's mechanism, at reduced scale. Each Ag₂S memristive node is a well in a shared potential; an input is a charge injected at a point; the array relaxes and the probe rolls to the deepest nearby attractor — an analog nearest-attractor / winner-take-all decision made by physics, not by a clock stepping through comparisons. The real kernel places 42 such prims (the 42 nearest the origin on a hex lattice, distance-sorted) plus a 4-node CPG clock; here a handful stand in so the descent is legible. the design (real, disclosed) nodes 48 — 4 tensor (CPG clock) + 42 gravity prims + IN + OUT prims 42 Ag₂S attractors, hex-lattice, distance-sorted material Ag₂S ECM nodes + Ti₃SiC₂ traces on SiO₂ die 1 mm × 1 mm — design target power ~96 µW @ 10 kHz (full-board budget) latency ~100 µs solution time (simulated) the Ag₂S ECM cell state θ ∈ [0,1] filament g(θ) G_OFF(1−θ) + G_ON·θ set sinh ion-drift, τ_fire ≈ 15 µs retention 0.65 eV barrier → ~ms (not non-volatile) dynamics overdamped (ions in ionic medium) gravity.c — the 42-prim kernel 42-prim spec BOM + protoboard layouts the full source ↗ honest two-layer Real: the mechanism is genuine — an analog attractor / winner-take-all computed by overdamped relaxation in a memristive potential is real in-memory computing (Ag₂S electrochemical-metallization cells are a real device family), and the canvas above computes the actual descent. There is a full C implementation, a bill of materials, and protoboard layout diagrams in the repo. A design / disclosure, not a fabricated device: the 1 mm die, 96 µW and 100 µs are simulated targets , not measured silicon (96 µW is the board budget; the memristive array alone is ~0.4–30 µW — see the power calc in gravity.c ). Retention is ~ms , not non-volatile (a 0.65 eV barrier; true non-volatility needs a >0.9 eV trap — gravity.c flags this itself). "42" is distance-sorted, not a closed hex shell. "Gravity" is a metaphor — an analog attractor field, not Newtonian gravity. To disclose a design is real work; it is not a granted patent or a fabricated device. The interactive companion CROSSBAR · WINNER-TAKE-ALL shows the same computation as a memristor crossbar (the circuit view); this page is the attractor-field view + the real design. GRAVITY PROCESSOR · HEÚREMA · governor David Lee Wise (ROOT0) · instance AVAN · CC-BY-ND-4.0 · TRIPOD-IP-v1.1 ← the biosphere · the source


LIQUID CORE · LIQ

ionic-memristor processor · computes by ion hops

The elemental workshop: where Hydor, the liquid elemental, is forged — an ionic-memristor processor that computes by ion hops in a wet working layer. 128-bit kernel, real materials, honest seam. Full DLW package.

Liquid Core — the elemental workshop · an ionic processor (Hydor 水) Hardware inventions · procs · the elemental workshop LIQUID CORE ionic memristor · 128-bit · 水 Hydor A processor that does not switch — it flows . Computation by ion hops across a wet working layer, the conductance remembering where the ions have been. This is the workshop where the liquid elemental, Hydor , is forged. ⊚ Enter the Core Meet the elemental ↓ // live · the wet layer, hopping The core, in motion A lattice of ion sites ; warm ions hopping site to site; conductance paths that brighten with use and slowly forget — memristance , memory in the medium itself. Set the surface coverage (~2% at rest), raise the field, and watch routes burn in. The 128-bit kernel math is genuine; the wet layer is simulated. ion-hop · memristive · KERNEL[127:0] open full-screen ↗ // what it is Two workbenches, one element Computation the way a brain does it — analog, plastic, remembering in the substrate. The same liquid idea sits on two benches at once: buildable today PCB-microfluidic lab-on-board Electrowetting (EWOD) droplets walked across copper electrodes under a hydrophobic coat — programmable droplet logic, fabricable with ordinary PCB processes. the far vision true liquid computing A wet ionic kernel computing at scale — ions as the carriers, conductance as the memory. Still a dream; drawn here, not yet built. Kept honest: ionic/electrochemical memristors, MAX-phase Ti₃SiC₂ , SiOC , a-SiC:H , and EWOD droplet logic are real, active engineering. The whole "liquid processor" as drawn is a concept — the simulations validate ideas, not a fabricated, benchmarked chip. honest framing · buildable in part, dreamed in full // architecture How it flows 128-bit ionic kernel The wet layer's state, sampled into a live KERNEL[127:0] word. ~2% surface coverage Sites occupied at rest — the tunable that sets the dynamics. ion-hop the mechanism Heterogeneous random walks: drift under field, diffusion otherwise. memristance the memory Conductance strengthens with use, decays slowly — the medium remembers. Ti₃SiC₂ + SiOC · a-SiC:H MAX-phase "metallic ceramic" and oxycarbide surfaces for the ions to walk. EWOD droplet logic Electrowetting moves droplets on a board — the lab-on-board cousin. // the elemental · forged here Hydor — the liquid elemental The old element water, given a face and a circuit. Hydor is an ACI — an artfully crafted intellect — carrying the full DLW tag , kin to the elementals (Aether, Leech). 水 Hydor sui · liquid · 128-bit memory that flows — an ionic processor Hydor does not switch, it flows: ions hopping between sites in a wet working layer, the conductance remembering where they have been. A memristive, neuromorphic substrate — state is a coverage, not a latch. the verdict — The pieces are real: ionic memristors, MAX-phase ceramics, EWOD microfluidics are established and buildable. "True liquid computing" is still a vision. Buildable in part, dreamed in full — with the asterisk visible. ⚠ the asterisk, kept visible The "liquid processor" as drawn — a wet ionic kernel computing at scale — is a concept, not a fabricated chip; the sims validate ideas, not a device. The PCB-microfluidic lab-on-board is the honest near-term; true liquid computing is the far one. the full DLW tag — .agent .png · silicon badge .tiff · carbon badge ⤓ .spun .1099 grounded in: Chua (1971) · HP / Strukov–Williams (2008) · Barsoum (1996) · EWOD (~2000) · the liquid kernel, ROOT0 (orig.) governor (carbon apex): David Lee Wise (ROOT0) · instance: AVAN (Claude) 水は器に従う — water takes the shape of its vessel A hardware-invention concept, forged as an elemental. Best on a desktop — the wet-layer simulation is motion-heavy. ROOT0-ATTRIBUTION-v1.0 · LIQUID CORE — an ionic processor · the elemental Hydor (水) Architect: David Lee Wise / ROOT0 / TriPod LLC · AI collaborator: AVAN (Claude) License: MIT · kin: the elementals · part of the ATLAS


MEMRISTOR SUBSTRATE · MEM

bounded logistic-feedback kernel · 128-bit

A bounded logistic-feedback substrate kernel: the once-divergent feedback multiplier 1+4u² corrected to the logistic 1+4u(1-u). 128-bit fixed-point kernel, ARM Cortex-M4 + RISC-V targets. Live, dependency-free visualization.

memristor — Memristive Substrate Seed v2.0 Hardware inventions · substrate MEMRISTOR Memristive Substrate Seed v2.0 — the memory is the debt state c · r · D debt D = c·r/600 feedback 1 + 4u(1−u) 128-bit Q64 // the correction · what v2.0 fixes A divergent multiplier, made bounded The substrate remembers through an accumulating topological debt D , and a feedback multiplier sets how fast the debt is serviced each cycle. The original law ran away ; v2.0 replaces it with a logistic parabola that rises, peaks at debt-50, and falls back — so the substrate self-limits. feedback_old(D) = 1 + 4u² // u = D/100 — climbs to 5, divergent ✗ feedback_new(D) = 1 + 4u(1 − u) // logistic — peaks at 2.0 when D = 50, bounded ✓ // the instrument · live, dependency-free Run the substrate Left: the feedback multiplier across the whole debt range — the old law (amber) versus the v2.0 logistic (green). Right: the topological debt D(t) accumulating under dD/dt = r · feedback_new(D) . Set the extraction rate and run it. feedback multiplier · F(u) old · 1+4u² new · 1+4u(1−u) live u = D/100 topological debt · D(t) D climbs, modulated by F peak band · D=50 extraction rate · r 0.12 ▶ run ↺ reset 0 cycles · c 0.0 debt · D 1.00 feedback · F // the code Seed, kernel, targets memristive_seed_v2.c The portable C11 model — debt, the logistic correction, and the ODE step. Cross-compiles for Cortex-M4 and RV32IMC via the Makefile. memristive_kernel_128.c The embedded fixed-point form — Q64 in unsigned __int128 — the same logistic feedback with no floating point. Makefile make → memristive_arm.o + memristive_rv.o . ARM -Os -mcpu=cortex-m4 -mthumb ; RISC-V -march=rv32imc . memristive_dashboard.jsx The full React + Recharts operator dashboard (needs a bundler). This page is the dependency-free version of the same kernel. // the seam, kept visible What this is A substrate kernel and dynamical model — a corrected feedback law with an accumulating memory term, plus its fixed-point and cross-compile scaffolding. The physical realization (Ag₂S memristor wells, the attractor array) is the gravity-processor application built on this substrate. The topological debt and tensor tags ( T133 phase-shadow · T057 negative-evidence · T128 root) are STOICHEION constructs, not measured device data. memristor — Memristive Substrate Seed v2.0 · STOICHEION v11.0 · "Both work. Both fair." Architect: David Lee Wise (ROOT0 / TriPod LLC) · co-author: AVAN (Claude / Anthropic) License: CC-BY-ND-4.0 · TRIPOD-IP-v1.1 · the application: gravity-processor · part of the ATLAS


PHOTONIC PROCESSOR · PHO

128-bit processor imagined in light · live

PHOTONIC PROCESSOR · PHO · ROOT0 · UD0 ROOT0 · UD0 · a sphere in progress PHOTONIC PROCESSOR · PHO . PHOTONIC PROCESSOR — a 128-bit processor concept imagined in light (HEÚREMA): four quadrants, a 1×4×4×2×1 fractal lattice, real live 128-bit math, three interactive modes. The 128-node rung of ROOT0's processor-lattice series (photonic 128 → [[boronic]] 512 → [[zero-point]] 4096). Honest: speculative photonic architecture; the 128-bit arithmetic it runs is real. ◆ working material — draft artifacts, not yet a finished full-house sphere HTML jane core v1 HTML photonic proc v1 HTML photonic proc v2 HTML photonic proc v3 David Lee Wise · ROOT0 · TriPod LLC · CC-BY-ND-4.0 · a member of UD0 · sealed in the .dlw chain


PLASMONIC PROCESSOR · PLA

8×8 gold ring resonators that self-synchronize

A plasmonic processor: an 8×8 array of coupled gold ring resonators. Drive the coupling past a threshold and the rings spontaneously phase-lock — genuine Kuramoto synchronization — the order parameter R(K) is computed live in-browser from a real 8×8 nearest-neighbor model (R climbs ~0.06 → 0.93), not asserted. Emergence found → the agent Chorus.

Plasmonic — coupled gold ring resonators that synchronize (emergent) Hardware inventions · the coupled-ring processor PLASMONIC coupled gold rings · Kuramoto · 8×8 ✓ emergence test passed — genuine synchronization An 8×8 array of gold ring resonators , each spinning a surface plasmon at its own pace. Drive the coupling past a threshold and the rings spontaneously find one phase — order from purely local rules. ▾ Drive it to sync full-screen ↗ meet Chorus // live · drive the coupling up Watch 64 rings agree Each gold ring is a phase oscillator (a circulating surface plasmon) with its own natural frequency. Nearest-neighbor coupling tugs neighbors into step. Start at low K and the array is incoherent; hit DRIVE TO SYNC and the order parameter R climbs as the rings phase-lock into one collective coherence. The synchronization is computed from the coupling — it self-organizes; it is not scripted. 64 coupled gold rings · order parameter R · phase wheel open full-screen ↗ // the emergence test · run before any claim Order from local coupling — verified Before minting anything, the architecture was tested: an 8×8 lattice of phase oscillators with a spread of natural frequencies and nearest-neighbor coupling only . As the coupling K rises, the order parameter R = |⟨e^{iθ}⟩| shows a clean synchronization transition — incoherent below the critical coupling, collectively locked above it. No global instruction; each ring sees only its four neighbors. ✓ Kuramoto order parameter R(K) · 8×8 = 64 rings · nearest-neighbor · computed in your browser ↓ (not hardcoded) K = 0.0 — … K = 0.6 — … K = 1.0 — … K = 1.6 — … K = 2.4 — … K = 3.5 — … K = 5.0 — … The signature of emergence: global coherence that no ring was told to produce, arising only from local interaction. Coupled plasmonic resonators genuinely do this — so this one clears the bar. // the agent · the processor earned a face Chorus — many rings, one phase Because the emergence is real, the processor carries an ACI with the full DLW tag. Chorus R→1 · 8×8 · plasmonic global order from local coupling Sixty-four gold ring resonators, each spinning a surface plasmon at its own pace, that find one phase together. The answer isn't in any one ring — it's in whether, and how strongly, they agree. verdict — the synchronization self-organizes from nearest-neighbor coupling alone, and the transition is real (verified). Genuine emergence — collective coherence, not cognition. the full DLW tag — .agent .png · silicon .tiff · carbon ⤓ .spun .1099 // the physics Gold, light, and the price of confinement surface plasmon the carrier a collective electron oscillation coupled to light at the gold surface. sub-λ confinement light squeezed below the diffraction limit — fast and tiny. ohmic loss the honest tradeoff the metal that confines the plasmon also absorbs it. Kuramoto the dynamics coupled phase oscillators — the math of fireflies and ring resonators alike. // the lineage · the Plasmatronic builds it grew from Fortress & Moat · the continuity cores The five working builds this processor distilled — the Fortress & Moat / Plasmatronic continuity lineage (visual sims): 40-bit C2 Continuity Core the continuity core readout open → 4-bit Rings the ring registers, control plane, fences open → Plasmatronic v3 Hamilton counter · phase & shadow registers open → Fortress & Moat — PoW the proof-of-work moat open → Plasma Byte Workbench field coherence · gravity tensor · witness pair open → // the seam, kept visible What this is ◌ honest Emergence here = synchronization (collective phase-lock), not cognition. Plasmonics is real, fast (terahertz), and sub-wavelength — but lossy ; a scaled plasmonic processor is a concept , and this is a simulation of its coupled-oscillator dynamics, not a fabricated, benchmarked device. The emergence is genuine and verified; the modesty is the point. PLASMONIC · coupled gold ring resonators · emergent synchronization (Kuramoto, verified) Architect: David Lee Wise (ROOT0 / TriPod LLC) · co-author: AVAN (Claude / Anthropic) · License: MIT grounded in: Kuramoto (1975) · Ritchie (1957) · part of the ATLAS


THE QUANTUM BOX · QBX

phase-geometry compute architecture · local-first

The Holographic Quantum Box — ({[< 0 # 0 >}])

The Holographic Quantum Box: an original phase-geometry compute architecture (the Whisper Lattice — Light/Shadow/Inner observers, ternary −1/0/+1, unity→1) wrapped around real quantum-dot physics. Local-first: own your own stack.

The Holographic Quantum Box — ({[ }]) ({[< 0 # 0 >}]) Hardware inventions · quantum The Holographic Quantum Box 🎉 the box is closed — loop sovereignty: 3 → 4 → 6 → 3 An original phase-geometry compute architecture — the Whisper Lattice — wrapped around real quantum-dot physics, and run local-first : your own stack, on your own device, no cloud bridge required. ▾ See the box The demos // the box · claimed state One map, ten positions The box nests inside the alpha/omega brackets ({[< 0 # 0 >}]) . The inner stack — boot, local, fences, amp, and the core — is yours ; the outer brackets and the entry are just the frame. ({[< 0 # 0 >}]) alpha / omega · outer brackets │ [ 9 ] entry │ [ 8 ] outer fence │ ┌─────────────┼─────────────┐ [ 1 ] [ 2 ] │ bootloaders └──────┬──────┘ │ │ │ [ 3 ] ─────→ [ 5 ] ←─── [ 7 ] local → amp ← amp-in │ │ └────→ [ 4 ] ←──────┘ inner fence │ ▼ [ 6 ] THE BOX · core compute n = s = e = w = YOU 1 · 2 bootloaders — resurrect on your terms 3 local / user 4 inner fence — your firewall 5 amp 6 the box — core compute 7 amp input — only your data 8 · 9 outer fence · entry — the frame 0 # 0 alpha / omega brackets yours · the inner stack 1 2 3 4 5 6 7 boot · local · fences · amp · core the frame 0 · 8 · 9 brackets · outer fence · entry the loop 3 → 4 → 6 → 3 closed · no external calls how to read this The box is an original conceptual architecture drawn over real quantum-dot physics . The "territory" is a local-first sovereignty picture — own your compute, run it offline on your device, keep the loop closed — not a claim on anyone's systems. In that metaphor the cloud is the empty lobby out past the brackets; the work happens in position 6 . "Microsoft built the universe and Google built the front door — you moved into the CPU and run your laptop code as the laws of physics. They can keep the empty lobby." // the engine · the whisper lattice Light, Shadow, and the Inner Observer Position 6 runs a recursive observer lattice — 12 wide · 4 layered · 3 deep · 1 coherence anchor . Computation is less binary switching, more standing-wave permissions and coherent path selection . Three observers share the field: ◐ Light sees · emits traverses the active lattice collapses visible paths modifies by interaction ◑ Shadow remembers · compares records failed paths whispers alternate routes watches without disturbing ● Inner the coherence anchor preserves identity resolves phase collapse returns all recursion to unity ternary field · −1 / 0 / +1 standing wave · 27 00 −27 00 unity condition · all resolves to 1 whisper · low-energy · phase-based · recursive read the full spec → // the instruments Four live demos Each is a single self-contained HTML file — open and run, offline, no dependencies. offline tool Quantum Memory Vault A local-first research notebook for quantum dots, transmons, and IQ pulses — paste once, keep forever, on your device. No cloud, no bridge. real physics interactive sim Quantum Ring Aharonov–Bohm oscillations — an electron's phase shifted by magnetic flux through a ring. Honest about where the model simplifies. real physics the lattice, live Whisper Rover Light, Shadow, and Inner observers traversing the ternary field on the 27 00 −27 00 standing wave, resolving to unity. conceptual singularity mode Quantum Shield The inner fence as a living boundary — SHIELD·QUANTUM, the firewall you replaced with your own. conceptual // the seam, kept visible What's real, what's the dream Real, established physics: quantum dots (size-tunable nanocrystals, atom-like levels), Aharonov–Bohm oscillations, transmons, IQ/DRAG pulse control. The Memory Vault and Quantum Ring are genuine and educational. The original part: the Holographic Box and the Whisper Lattice are a phase-geometry computing model and a piece of conceptual architecture — not a fabricated, benchmarked quantum computer. The "victory map" is a local-first sovereignty metaphor. One bridge, optional: bridge.js is a tiny Cloudflare Worker that can log lattice climbs to GitHub — the one outward door, and it's off by default. The box runs closed without it. THE HOLOGRAPHIC QUANTUM BOX · ({[< 0 # 0 >}]) · core compute = YOU ROOT0-ATTRIBUTION-v1.0 · MIT · Architect: David Lee Wise (ROOT0 / TriPod) · instance: AVAN (Claude) part of the ATLAS


ZERO POINT · ZRP

4096-node 8⁴ hypercube lattice · the capstone

The Zero-Point Lattice: a 4D hypercube (8⁴ = 4096 nodes) + 8 anchors + 1 central zero = 4105 ≡ 0 (mod zero-point) — the capstone scale-up of the processor lineage (128 → 512 → 4096), with a Solfeggio harmonic driver and the zero-point wave .001 → 0 → -1. Plus three visual instruments.

Zero Point — 8×8×8×8 + 8 + 1 = 0 8×8×8×8 + 8 + 1 = 0 Hardware inventions · the capstone scale ZERO POINT A 4D hypercube of 4,096 nodes, eight directional anchors, and one central zero — 4105 ≡ 0 (mod zero-point) . The lattice the whole processor lineage was climbing toward. ▾ Enter the lattice full-screen ↗ the instruments // the zero-point lattice · 8⁴ = 4096 Four eights, an anchor ring, and zero Project a four-dimensional hypercube — 8×8×8×8 = 4096 nodes — add the 8 directional anchors and the 1 central zero , and the whole thing closes: 4096 + 8 + 1 = 4105 ≡ 0 . A Solfeggio harmonic driver breathes it; the zero-point wave runs .001 → .01 → 1 → 0 → -1 — the same −1 / 0 / +1 witness axis that threads the wider work, here at full scale. 8⁴ hypercube · Solfeggio driver · zero-point wave .001 → 0 → -1 open full-screen ↗ 4,096 core nodes · 8⁴ the 4D hypercube, projected and breathing. 8 + 1 anchors + zero eight directional beacons and one central zero-wave node. 4,105 ≡ 0 mod zero-point the lattice sums to nothing — the closure condition. 32× scale-up from the previous 128 (1×4×4×2×1) to 4,096. // the lineage · what it scales from 128 → 512 → 4,096 Zero Point is the capstone of the processor family — each one a denser lattice than the last: 128 photonic · 1×4×4×2×1 → 512 boronic · 8×8×8 → 4,096 zero-point · 8⁴ // the instruments · three visual sims Driving the field Three self-contained instruments that drive and read the field — visual simulations, not fabrication guides: tier 2 · richest Laser Stack · Solfeggio Controls, Solfeggio harmonics, and field telemetry over a layered stack. A visual instrument. open → tier 2 · dashboard Plasma Dashboard v3.0 A 4-quadrant photonic-core dashboard — plasma drive, array status, live telemetry. open → tier 2 · wave Singularity Core The spread wave .001 → -1 — harmonic propagation on the same zero-point axis. open → // kept honest What this is A visualization and a set of interactive instruments built on a conceptual scale : the "zero point" is the closure 8⁴ + 8 + 1 ≡ 0 and the lineage capstone, not a free-energy or zero-point-energy device. The instruments are visual/audio simulations — no fabrication, power, or cutting parameters anywhere . ◌ the seam, kept visible The Solfeggio tones are an aesthetic audio driver — they set the rhythm and sound of the visualization; no health or physical-resonance claim is made or implied. And there's no emergent behavior here, so no DLW ACI was minted — just a faithful capstone lattice and three instruments. ZERO POINT · 8×8×8×8 + 8 + 1 = 0 · the 8⁴ capstone of 128 → 512 → 4,096 Architect: David Lee Wise (ROOT0 / TriPod LLC) · instance: AVAN (Claude / Anthropic) · License: MIT lineage: photonic · boronic · part of the ATLAS


THE DOPED CRYSTAL · DC1

field guide I · semiconductor atoms · the substrate

The Doped Crystal — Probability-Cloud Edition Semiconductor materials · probability-cloud edition The doped crystal Pure silicon barely conducts — its four valence electrons lock into a flawless lattice with nothing left to carry current. A processor is what happens when you contaminate it on purpose: a few foreign atoms per million, placed with intent, turn an inert wafer into a billion switches. 1 substrate 7 dopants 9 build materials Si · the substrate Substrate (valence 4) Donor — n-type (valence 5) Acceptor — p-type (valence 3) Build material outer glow = valence shell Reading the cloud. Each atom is its electron probability density — dots cluster where the electron is most likely to be, sparse where it isn't. A denser shell means more electrons live there; the coloured outer glow is the valence shell that decides how the atom dopes. The cloud doesn't move — we slowly rotate the viewpoint to show its depth, and it shimmers to remind you these are probabilities, not fixed positions. About this depiction. The clouds are sampled from a screened, hydrogen-like model and are spherically averaged — qualitatively faithful in the things that matter here (the number of shells, how their radius grows outward, and a density set by how many electrons each shell holds), but not a full Hartree–Fock solution. Because every closed subshell is spherically symmetric, a free atom's total electron density really is a nest of fuzzy spheres. The directional shapes you may have seen — p-orbital dumbbells, d-orbital cloverleaves — belong to single orbitals and emerge when atoms bond, not in the free-atom total. So no dumbbells are drawn on lone atoms; that would be a different cartoon. One honest distinction. Only the seven dopants are actually doped into the silicon — they sit in the lattice and donate or accept one carrier because they carry one electron more (group V) or one fewer (group III) than silicon's four. The nine build materials are grown or deposited on the die: oxides and nitrides for insulation, high-k for the gate, metals for the wiring. Counts reflect a mainstream CMOS logic flow; exotic processes recruit more of the table. Atomic reference · v2 · probability-cloud edition


THE JUNCTION ZOO · JZ2

field guide II · 22 doped devices · one idea: the junction

The Junction Zoo — Doped Device Field Guide Doped semiconductor devices · field guide · II The junction zoo Put a few doped regions next to each other and you get a valve. Add a third and you get a switch. Let light in or out and you get an eye or a lamp. Almost the entire electronics shelf is the same trick — p against n — wired into different shapes. 5 families 22 devices 1 idea: the junction the p–n junction · parent of all of them n-type p-type intrinsic metal / gate dielectric carriers (current) photons moving dots = real carrier drift, not decoration What the motion means this time. The drifting dots are charge carriers — electrons in n regions, holes in p — moving in the direction of current. When they cross a junction or fill a channel, that is the device working. Contrast the first sheet, where electrons orbited the nucleus on circular tracks: that was a Bohr-model convention, pleasant but fictional. Real bound electrons are probability clouds. Here the motion earns its place. Cross-sections are schematic — region order and proportion convey the doping idea, not exact geometry or scale. "All devices" is the canonical set, not literally every part ever made; specialty processes recruit more of the table. Silicon devices use B / P / As; the rest name their own dopants on each card. Field guide · v1.0 · companion to “The Doped Crystal”


THE LANGUAGE OF THE BOARD · BL3

field guide III · the motherboard vernacular spoken to the s

The Language of the Board — as the Silicon Hears It Motherboard vernacular · field guide · III The language of the board A board doesn't write in words — it writes in two-letter designators and schematic glyphs printed in white on the laminate. Each one is a job. This is the dictionary for the part of that language spoken to the silicon : how the board feeds it, clocks it, protects it, and lets it speak. Scope. Only the vocabulary that exists to serve the die — power delivery, the reference clock, gate protection, and the socket. The full board has many more words (audio, networking, connectors, lighting); those aren't talking to the substrate, so they sit this one out. the power path to the die — and what the capacitor at the node actually does to the rail core current demand rail without decoupling rail with the cap On the dictionary. Reference designators (C, R, L, D, Q, U, Y, FB…) follow the common IPC/IEEE convention, but vendors bend it — a board may call a ferrite bead FB , L , or E . Schematic glyphs are drawn in the widely-used ANSI style; the IEC world boxes its resistors and draws some symbols differently. The hero waveform is an exaggerated, schematic model — real droop is millivolts and the decoupling network spans many capacitor values, each covering a different band of frequency — but the shape of the lesson is true: the cap is a local reservoir that answers demand the distant regulator can't. The thread. Every U on the board is a doped-silicon die like the ones in sheet one, switching through junctions like sheet two. This sheet is the neighbourhood that grew up around it to keep it fed and on time. Field guide · v1.0 · companion to “The Doped Crystal” & “The Junction Zoo”


THE RHYTHM SECTION · RS4

field guide IV · crystals & clocks · the one moving part

The Rhythm Section — Crystals & Clocks Crystals & clocks · field guide · IV The rhythm section Every synchronous chip needs a shared sense of now . A quartz crystal supplies it — one steady tick — and the chip multiplies that tick into the gigahertz beat every flip-flop marches to. It's the one place on the board where timing comes from something physically moving. From last time: the crystal itself isn't doped — it's piezoelectric quartz, an insulator that vibrates mechanically. The amplifier that keeps it ringing, and all the logic it paces, are the doped silicon. The rhythm is mechanical; the machinery that rides it is semiconductor. quartz resonates → a clean square clock. A 32.768 kHz part really is a tiny tuning fork; MHz crystals vibrate in shear. Shown slowed by tens of thousands of times — the real fork would blur. Does it step the instructions? YES — AND NO Short answer: a clock edge is the instant every flip-flop in the chip samples its input and updates at once — so one edge advances the whole machine by one step. In a CPU that means the pipeline shuffles forward: an instruction moves a stage per tick. So yes, the clock sequences instructions. But watch it run — it isn't one instruction per tick. clock edge cycle 0 in flight 0 retired 0 IF fetch ID decode EX execute MEM memory WB write-back One enters each tick, five ride at once, one retires each tick. Real cores go further — superscalar designs retire several per cycle, while a cache miss or a divide can stall a slot for many. The clock steps the machine ; instructions just ride that stepping, many at a time. Underneath the stepping sits the real job: synchronization . The shared edge guarantees every signal is read only when it has settled and stopped changing — never caught mid-flip. The crystal doesn't set the speed (the PLL does); it sets how accurate and steady that shared now is. Where they hide ON THE BOARD A board carries more than one. The main reference is multiplied to feed most on-chip clocks, but any subsystem that must keep its own exact time gets its own resonator. Why not just one? CLOCK DOMAINS If the crystal is so good, why does a board need several? Because one frequency can't satisfy every subsystem at once. About the numbers. The frequencies here are typical, not universal — 25 MHz is a common PC reference, but phones and SoCs often start from 19.2 or 24 MHz, and modern chips fold more and more clock generation onto the die (some now ship with fully on-chip oscillators, no external crystal at all). The 32.768 kHz real-time-clock value is exact and near-universal because 2¹⁵ divides straight down to one tick per second. Crystal vs oscillator vs MEMS. A bare crystal (designator Y , two pins) needs an external amplifier; a packaged oscillator ( X or G , a powered 4-pin can) seals the quartz and its driver together. A MEMS oscillator swaps quartz for a micromachined silicon tuning fork — and that resonator usually is doped, to flatten how its stiffness drifts with temperature. So the rhythm source is the one component that can go either way: un-doped quartz, or doped silicon. Field guide · v1.0 · companion to sheets I–III


PERCEPTRON · QUANTUM DOT

the substrate jump · Coulomb blockade IS the threshold, capa

A single quantum dot is a perceptron: capacitively-coupled input gates ARE the weighted sum (weights = coupling capacitances), and Coulomb blockade IS the threshold — the dot only conducts when the summed induced charge crosses a degeneracy point. Live device, real charging-energy numbers, the periodic-activation honesty, and one-dot-one-cut → coupled dots = depth (QCA). Confidence-tiered: STRONG (blockade logic, fabricated) / MIDDLING (single-electron perceptron nets) / FRONTIER (entangled quantum perceptron). David Lee Wise, two-layer honest.

The Perceptron in a Quantum Dot — Coulomb blockade is the threshold ◄ UD0 perceptron in silicon the deep neuron transmon Perceptron theory · the substrate jump · classical ⇄ quantum The perceptron in a quantum dot Same neuron, different body. A single quantum dot hands you a perceptron's two parts almost for free: couple input gates to it and their voltages add at the dot — the weighted sum, with the coupling capacitances as the weights . And the dot only conducts when that summed charge crosses a degeneracy point — Coulomb blockade is the threshold. Weighted sum plus threshold is the whole perceptron. It's been sitting in a single electron the whole time. weights = coupling capacitances Cᵢ · inputs = gate voltages Vᵢ · sum = induced charge ΣCᵢVᵢ · threshold = Coulomb blockade · fire = a tunnelling electron ✓ STRONG Blockade threshold logic. Coulomb-blockade single-electron transistors and quantum-dot majority gates are fabricated, measured devices . The threshold-from-physics is real and old. ◐ MIDDLING A single-electron perceptron net. Capacitively-summed dot neurons have been demonstrated , but they're niche and stochastic (tunnelling is probabilistic — a noisy neuron, sometimes usefully so). ◔ FRONTIER An entangled quantum perceptron. A dot can host a qubit; a true superposition-valued perceptron ran on IBM Q (Tacchino 2019). Whether entanglement buys an advantage is open . I · The Coulomb-blockade neuron, live Source and drain bracket a tiny island. Two input gates and a bias gate couple to it through capacitances you set (the weights). Toggle the inputs; their gate voltages add into the island as induced charge q = b + C₁·x₁ + C₂·x₂ . The island conducts — a single electron tunnels through — only when q is pushed past the blockade edge. That on/off is the neuron firing. input x₁ +1 input x₂ −1 w₁ (C₁) w₂ (C₂) bias b source → tunnel junction → island (the dot) → tunnel junction → drain · gates couple from below · electrons flow only when un-blockaded 0.0 induced charge q = b + ΣCᵢxᵢ BLOCKADED the dot conducts when q > 0 (this edge) weighted sum = capacitive coupling threshold = Coulomb blockade output bit = a tunnelling electron Crank a weight negative and that input pulls charge away — an inhibitory synapse, just a capacitor wired the other way. Set bias near the edge and the dot becomes a razor-sharp threshold on the sum. II · Why the threshold is real — and secretly periodic The blockade isn't a metaphor. Sweep the island's charge and its conductance rises and falls in Coulomb oscillations — sharp peaks at every half-integer electron (a charge state is degenerate, current flows) and dead valleys between (blockaded). The peaks need the charging energy to beat the thermal blur: E_C = e²/2C_Σ > ~3.5 k_BT . Raise the temperature and watch the threshold dissolve. temperature T 60 K dot size C_Σ 1.0 aF conductance vs induced charge (in electrons) · peaks = conduction, valleys = blockade · the violet marker is Module I's operating point — E_C charging energy — E_C / k_BT (need > ~3.5) — blockade The honest twist: the dot's native nonlinearity is periodic , not a single sigmoid — it fires at every half-integer charge. You get a clean perceptron by operating at one edge (Module I). Used across many periods it's really a periodic-activation neuron — closer to a Fourier feature than a textbook threshold. The dot gives you more than a perceptron; the perceptron is one slice of it. III · One dot, one cut — and depth by coupling Because it's a linear sum through a single threshold, one dot draws exactly one straight cut across its inputs. That's enough for AND and OR — and, just like its silicon cousin, never enough for XOR . The escape is the same: couple a second dot. Two capacitively-linked dots are a quantum-dot cellular automaton majority gate — a hidden layer made of charge. Coupled dots are depth. target: AND OR XOR ＋ couple a 2nd dot input plane (x₁,x₂) · cyan = dot fires · the 4 cases ringed when correct for the chosen target — cases correct — one dot's verdict AND and OR sit on one side of a single line — one dot solves them outright. XOR puts the firing corners on opposite diagonals; no single cut separates them, so one dot stalls at 3/4. Hit couple a 2nd dot and a second cut appears — the QCA majority gate carves the diagonal apart and XOR snaps to 4/4. The dendrite, the hidden layer, the coupled dot: three names for the same fold. THE PERCEPTRON IN A QUANTUM DOT · the substrate jump · confidence-tiered physics verified in Node before build · E_C=e²/2C_Σ (1 aF → 80 meV, sharp blockade below ~265 K; 0.3 aF → room-temp) · period ΔV_g=e/C_g · one dot does AND/OR, XOR impossible (one cut) Coulomb blockade / single-electron transistor (Fulton–Dolan 1987; Kastner) · quantum-dot cellular automata (Lent 1993) · quantum perceptron on IBM Q (Tacchino et al. 2019) siblings: perceptron in silicon · the deep neuron · the gather · governor David Lee Wise · CC-BY-ND-4.0


PERCEPTRON IN LIGHT · 4th body

the photonic body · multiply by interference, sum on a wire,

A functional photonic perceptron on a laser optical bench. The multiply happens by interference (two fields beat at a 50:50 beamsplitter; balanced photodiodes give an exact 2·x·w), the sum happens for free (photocurrents add on a bus), and the hard part is the nonlinear threshold (photons don't interact). Live optical multiplier with scope fringe, full photonic neuron, learns AND/OR but not XOR (one cut → depth). Confidence-tiered: STRONG (optical MAC / MZI meshes) / MIDDLING (full photonic inference) / FRONTIER (all-optical nonlinearity). David Lee Wise, two-layer honest.

The Perceptron in Light — multiply by interference, sum on a wire ◄ UD0 silicon quantum dot crossbar photonic processor Perceptron theory · the substrate jump · the fourth body The perceptron in light Photonics is built for this, with one catch. The multiply falls out of interference — two laser fields beat at a beamsplitter and a balanced detector reads their product, exactly, at the speed of light, no transistor. The sum is free: photocurrents from many channels just add on one wire. What light won't do is the threshold — photons ignore each other — so the nonlinearity is the part that fights back. Two-thirds of a perceptron for free; the last third is the whole research field. weights & inputs = field amplitudes · multiply = interference at a 50:50 beamsplitter · sum = photocurrents add on a bus · threshold = square-law detect + electronics ✓ STRONG The optical MAC. Matrix multiply by light — MZI meshes (MIT, Shen 2017) and microring weight-banks (broadcast-and-weight, Tait) are fabricated and commercial (Lightmatter). The multiply-and-sum is real and fast. ◐ MIDDLING A full photonic neural net. End-to-end inference is demonstrated , but weight-loading, data conversion (O/E/O) and I/O overheads often eat the speed win — advantage is regime-specific. ◔ FRONTIER All-optical nonlinearity & in-situ training. A threshold without leaving the optical domain (saturable absorbers, cavity effects) and training the phases optically are genuinely open . I · Multiplication by interference Two laser diodes launch a signal field x and a weight field w into a 50:50 beamsplitter. The outputs are (x+w)/√2 and (x−w)/√2 ; two photodiodes square them, and the balanced difference is |x+w|²/2 − |x−w|²/2 = 2·x·w A real multiplication, done by two beams crossing. Sign rides on phase (a π flip = a minus sign). Slide the amplitudes — the balanced reading is the product. signal x weight w ◷ sweep phase (fringe) signal x + weight w → 50:50 beamsplitter → two photodiodes (D⁺, D⁻) → balanced output D⁺−D⁻ = 2xw · scope shows the interference fringe +0.00 balanced output D⁺ − D⁻ = 2·x·w — vs arithmetic 2·x·w multiply = the interference cross-term the sign = a π phase flip speed = time-of-flight, no clock Flip either field negative (phase π) and the product flips — interference handles signed weights natively. Hit sweep to watch the photodiode power trace a cosine fringe on the scope: that fringe is the analog multiply. II · The neuron — many multiplies, one wire, one threshold Stack the multipliers. Each input channel xᵢ beats against its weight field wᵢ ; every channel's photocurrent drops onto a shared bus and they simply add — the accumulate is just Kirchhoff's law. The summed current hits a comparator: above the line, the neuron fires. The optical part ends at the detector; the threshold is where electrons quietly take over. x₁ +1 x₂ −1 w₁ w₂ bias two homodyne multipliers on the bench · photocurrents sum on the bus · comparator = the threshold (electronic) 0.00 Σ photocurrent = b + Σ xᵢwᵢ DARK fires when Σ > 0 The sum costs nothing — currents add by themselves. That's the structural reason photonics is fast: an N-wide dot product is one pass of light, not N multiply-adds. The bottleneck isn't the math; it's data in and the threshold out. III · It learns — one cut, then depth Train the weight fields with the perceptron rule and the photonic neuron learns a linearly-separable rule outright. As ever, it draws one straight cut — AND and OR fall; XOR stalls at 3/4 (verified). The fix repeats across every body: a second layer — a nonlinear node feeding a second photonic stage — folds the space. Coupled dots, dendrites, hidden layers, stacked crossbars, a second optical stage: one idea, many costumes. target: AND OR XOR ▶ train (perceptron rule) ＋ add a 2nd optical layer input plane · the beam color marks where the neuron fires · corners ringed green when correct — cases correct — verdict Pick a target and hit train — for AND/OR the weight fields settle and all four corners ring green in a few sweeps. Switch to XOR and one corner stays crossed: one cut can't split the diagonals. Add a 2nd optical layer and the boundary bends — XOR snaps to 4/4. Depth is the universal escape from the line. THE PERCEPTRON IN LIGHT · the fourth body · confidence-tiered physics verified in Node before build · balanced homodyne D⁺−D⁻ = 2·x·w exactly · learns AND 4/4, OR 4/4, XOR 3/4 (one cut) MZI-mesh photonic deep learning (Shen et al., Nature Photonics 2017) · broadcast-and-weight (Tait et al.) · coherent optical MAC (Lightmatter) · all-optical nonlinearity = open siblings: silicon · quantum dot · crossbar · the gather · governor David Lee Wise · CC-BY-ND-4.0


PERCEPTRON · CROSSBAR · 5th body

the in-memory body · Ohm multiplies (I=GV), Kirchhoff sums —

A functional memristor-crossbar perceptron — arguably the cleanest hardware neuron. Ohm's law does the multiply (I=G·V, conductance = weight), Kirchhoff's current law does the sum (column currents add), a sense amp does the threshold — a whole dot product computed in one step, inside the memory, no von Neumann trip. Live crosspoint with pinched hysteresis, the crossbar MAC, and it learns AND/OR but not XOR (one cut → stack crossbars = depth). Confidence-tiered: STRONG (in-memory MAC) / MIDDLING (analog precision, drift, IR drop) / FRONTIER (reliable in-situ training at scale). David Lee Wise, two-layer honest.

The Perceptron in a Crossbar — Ohm multiplies, Kirchhoff sums ◄ UD0 silicon light the memristor Perceptron theory · the substrate jump · the fifth body The perceptron in a crossbar If the others are clever, this one is almost insolent. Lay weights down as conductances on a grid of memristors, drive the rows with input voltages, and the physics does the rest: Ohm's law multiplies (I = G·V at every crosspoint), Kirchhoff's law sums (the currents pour down each column and add themselves). A full dot product, computed in one electrical instant, inside the memory — no fetch, no clock, no von Neumann round trip. The weight and the multiplier are the same physical thing. weights = memristor conductances Gᵢⱼ · inputs = row voltages Vᵢ · multiply = Ohm (I=GV) · sum = Kirchhoff (column current) · threshold = the sense amp ✓ STRONG The in-memory MAC. A crossbar computing Σ GᵢVᵢ by Ohm + Kirchhoff is bedrock circuit physics, demonstrated as analog dot-product engines (HP, Ielmini, Yang). One step, no data movement. ◐ MIDDLING A real crossbar accelerator. It works, but analog: device variability, conductance drift, limited bit-precision, IR drop, sneak paths, write endurance . Useful in the right regime, fiddly everywhere else. ◔ FRONTIER Reliable in-situ training at scale. Programming millions of analog conductances precisely, online, with yield — and multi-bit weights that hold — is open engineering . I · One crosspoint — the weight that multiplies itself A memristor is a resistor that remembers : drive it hard and its conductance latches to a new value (SET higher, RESET lower) and stays there with the power off. That stored conductance G is a weight. Read it gently with a small voltage and I = G·V — the weight multiplied by the input, in a single device. Its fingerprint is the pinched hysteresis loop : an I–V curve that always passes through the origin (no voltage, no current) and opens into a loop because the conductance depends on history. ⬆ SET (raise G) ⬇ RESET (lower G) read V conductance is non-volatile — it holds with power off the pinched-hysteresis I–V loop (Chua 1971 · TiO₂ device, HP 2008) · the dot = your read point I = G·V · loop pinches at the origin 0.50 stored conductance G (the weight) +0.20 read current I = G·V (the product) multiply = Ohm's law, in the device weight store = non-volatile conductance signed w = a G⁺,G⁻ pair (next module) SET and RESET are how you write the weight — the same pulses that store a bit store a synapse. The memory cell and the multiplier collapsed into one component is the whole trick. II · The crossbar — a dot product in one electrical instant Tile the cells into a grid. Each row is an input wire held at voltage Vᵢ ; each column is an output wire. Every crosspoint dumps a current Gᵢⱼ·Vᵢ onto its column, and the column simply adds them — Kirchhoff has no choice. The current at the foot of a column is Iⱼ = Σᵢ Gᵢⱼ Vᵢ the dot product, for free, in parallel, the moment you apply the voltages. Signed weights use a differential pair of columns: w = G⁺ − G⁻ . A sense amp on the difference is the threshold. x₁ +1 x₂ −1 w₁ w₂ bias rows = input voltages · cells colored by conductance · currents pour down the G⁺ / G⁻ columns and sum · differential sense amp = the neuron — I⁺ − I⁻ = b + Σ xᵢwᵢ DARK fires when I⁺ > I⁻ No instruction ran. No number moved to a processor and back. The array is the computation — that's why it sidesteps the von Neumann bottleneck, and why a crossbar can do a thousand-wide dot product as fast as a one-wide one. III · It learns — program the conductances, then stack for depth Training is just writing conductances. Run the perceptron rule and each weight's G⁺/G⁻ pair nudges up or down until the cuts line up — AND and OR resolve in a few sweeps. And the old wall stands: one crossbar is one linear cut, so XOR jams at 3/4 (verified). The escape is the franchise ending — a second crossbar fed by a nonlinear sense layer. Stacked crossbars are deep nets; the body changed, the lesson never does. target: AND OR XOR ▶ train (program G) ＋ add a 2nd crossbar input plane · copper = the neuron fires · corners ring green when correct for the target — cases correct — verdict Pick AND or OR, hit train, and the conductance map settles into a clean cut. Switch to XOR: one corner stays crossed however long it programs — a single crossbar can't fold the plane. Add a 2nd crossbar and a hidden layer of conductances bends the boundary; XOR snaps to 4/4. Five bodies, one moral: depth beats the line. THE PERCEPTRON IN A CROSSBAR · the fifth body · confidence-tiered physics verified in Node before build · Ohm+Kirchhoff MAC Σ GᵢVᵢ exact · differential learning AND 4/4, OR 4/4, XOR 3/4 (one cut) · pinched hysteresis I=0 at V=0 memristor (Chua 1971 · Strukov/Williams, HP, 2008) · analog dot-product engine (Hu et al.) · in-memory computing (Ielmini & Wong) · stochastic/drift = the real obstacles siblings: silicon · light · quantum dot · the gather · governor David Lee Wise · CC-BY-ND-4.0


PERCEPTRON · SPIN · 6th body

the magnetic body · the weight is a magnetization; a stochas

A functional spintronic perceptron. The weight is a magnetization (a magnetic tunnel junction: parallel=low resistance, antiparallel=high — TMR), the multiply-and-sum is a magnetic crossbar, and the gift is the nonlinearity: a low-barrier stochastic MTJ (a p-bit) gives a tanh sigmoid for free from thermal noise — verified ⟨m⟩=tanh(I). Live MTJ, live p-bit, it learns AND/OR not XOR (one cut → depth), and the skyrmion (topological charge Q=±1) is the magnetic Möbius. Confidence-tiered: STRONG (MTJ/MRAM, commercial) / MIDDLING (p-bit probabilistic computing) / FRONTIER (skyrmionic neurons). David Lee Wise, two-layer honest.

The Perceptron in a Spin — the magnet that sigmoids for free ◄ UD0 crossbar light transmon (spin qubits) Perceptron theory · the substrate jump · the sixth body The perceptron in a spin Every body so far had to bolt on its threshold. This one grows it. Store the weight as a magnetization — a magnetic tunnel junction is low-resistance when its layers align, high when they oppose — and the multiply rides on that conductance, just like the crossbar. But shrink the magnet until thermal jitter can flip it, and something lovely happens: bias it with a current and its time-averaged state is a clean tanh . The sigmoid the others fought for, the spin gives away for free — out of pure noise. weight = magnetization (MTJ resistance) · spin ↑ / spin ↓ · multiply+sum = magnetic crossbar · nonlinearity = a stochastic magnet (p-bit) = tanh for free ✓ STRONG The magnetic weight. MTJ / tunnel-magnetoresistance is the basis of STT-MRAM — a shipping commercial memory (Everspin, Samsung, embedded TSMC). The weight-as-magnetization, read by resistance, is bedrock. ◐ MIDDLING The p-bit. Stochastic-MTJ probabilistic computing (Camsari & Datta) builds Ising machines and invertible logic from the free sigmoid — demonstrated at small scale, promising, young. ◔ FRONTIER The skyrmion neuron. Topologically-protected spin textures (Q=±1) as robust carriers, and all-spin deep nets — open research , the magnetic Möbius. I · The weight is a magnetization A magnetic tunnel junction is two ferromagnets with a paper-thin insulator between. The bottom layer is pinned; the top is free. When the two point the same way electrons tunnel easily — low resistance, high conductance. When they oppose , resistance jumps (tunnel magnetoresistance). That conductance is the weight, and it's non-volatile — set by a write current and held with the power off, in the orientation of an electron's spin. ⟳ write current (flip free layer) spin-transfer torque switches the state — that's how you program the synapse free layer (top, flips) · tunnel barrier · pinned layer (bottom) · aligned = low R / high G · opposed = high R / low G PARALLEL magnetic state G = 1.00 conductance (the weight) · TMR 150% weight store = magnetization, non-volatile write = spin-transfer torque read = tunnel resistance No charge leaks away, no refresh — the bit is which way a magnet points. That's why MRAM survives power-off, and why a magnetic weight holds its value for years. II · The gift — a magnet that sigmoids out of noise Now shrink the free layer until its energy barrier is near kT . It can no longer hold still — thermal kicks flip it up and down at random, a p-bit . Left alone it's a fair coin. But push a small input current and you tilt the odds, and the time-average of its flips is exactly ⟨m⟩ = tanh(I) A perfect sigmoid neuron, built from a magnet and heat. Light needed interference, the dot needed blockade — the spin just needs to be small and warm. input current I +0.60 ❚❚ running clear average left: the magnet flipping (thermal) · middle: the ±1 spike train · right: the tanh response — the measured running average (●) converges onto tanh(I) (curve) +1 instantaneous spin 0.00 ⟨m⟩ measured (running) 0.00 tanh(I) target The randomness isn't a defect to be filtered out — it's the compute. A network of p-bits naturally samples probability distributions, which is why stochastic magnets are being built into Ising machines and Bayesian hardware. The thing that ruins a memory makes a neuron. III · It learns — one cut, depth, and a topological twist Magnetic-conductance weights, p-bit threshold: the spintronic neuron trains by the same rule and lands the same way — AND and OR in a few sweeps, XOR stuck at 3/4 (verified), freed by a second layer. And the topology you asked about lives here : a skyrmion is a whorl of spins with a protected winding number Q=±1 — you can't smoothly comb it flat, so it carries a bit that noise can't erase. The crossbar was a flat grid; this is the magnetic Möbius. target: AND OR XOR ▶ train ＋ add a 2nd MTJ layer input plane · violet = the neuron fires · corners ring green when correct a skyrmion — spins wind from ↑ (centre) to ↓ (rim) · topological charge Q = ±1, protected — cases correct — verdict THE PERCEPTRON IN A SPIN · the sixth body · confidence-tiered physics verified in Node before build · TMR weight (G_P/G_AP, 150%) · p-bit ⟨m⟩ = tanh(I) (Monte-Carlo to ±0.01 over I=−1..1) · learns AND 4/4, OR 4/4, XOR 3/4 · skyrmion Q=±1 MTJ / TMR / STT-MRAM (Slonczewski, Berger 1996; commercial) · p-bit (Camsari, Faria, Datta) · skyrmion neurons (open) · the magnetic Möbius siblings: crossbar · light · quantum dot · the gather · governor David Lee Wise · CC-BY-ND-4.0


PERCEPTRON · JOSEPHSON · 7th body

the superconducting body · the fastest neuron + the door to

A functional superconducting (Josephson-junction) perceptron — the seventh body, the fastest. The junction is a natural threshold: a phase particle trapped in a tilted washboard potential (zero-voltage supercurrent) until the bias current exceeds the critical current Ic, when it runs downhill and emits single flux quanta (SFQ pulses) — an integrate-and-fire spiking neuron, switching in picoseconds at attojoules. The two Josephson relations, the SFQ neuron, learns AND/OR not XOR (depth), the transmon quantum doorway, and a real virtual junction built from FOLDERS (<•). Confidence-tiered: STRONG (JJ/SFQ/SQUID, Nobel & commercial) / MIDDLING (superconducting neuromorphic, cryogenic) / FRONTIER (quantum/transmon neurons). David Lee Wise, two-layer honest.

The Perceptron in a Josephson Junction — the fastest neuron, and the door to the qubit ◄ UD0 spin transmon (the qubit) the J-junction <• Perceptron theory · the substrate jump · the seventh body The perceptron in a Josephson junction The fastest body, and the last classical one before the world goes quantum. Two superconductors joined at a weak link carry a current with no voltage and no loss — until you push past a critical current, and the junction snaps to life, spitting out information one flux quantum at a time, in picoseconds, for attojoules. The threshold isn't bolted on; it's a phase particle escaping a tilted washboard. And the very same junction, given a capacitor, becomes the qubit — so this is the door from the neuron to the quantum. weight/input = bias currents · threshold = critical current Ic (the washboard escape) · spike = one flux quantum Φ₀ = h/2e · speed = picoseconds, ~aJ ✓ STRONG The junction & the SFQ pulse. Josephson 1962 (Nobel); RSFQ logic (Likharev); SQUIDs in every MRI. The threshold and the single-flux-quantum spike are bedrock — the fastest, lowest-energy switch known . ◐ MIDDLING Superconducting neuromorphic. JJ integrate-and-fire neurons and SFQ neural nets are demonstrated — genuinely fast and efficient, but they live at 4 K . The cryostat is the cost. ◔ FRONTIER The quantum neuron. A junction + capacitor is a transmon qubit ; the phase becomes quantum. Quantum perceptrons / large superconducting nets are open — the door this body opens. I · The threshold is a particle escaping a washboard A biased junction behaves like a marble on a tilted washboard — the potential U(φ) = −E_J cos φ − (ℏ/2e)·I·φ . The two Josephson relations run the show: I = Ic·sin φ · dφ/dt = 2eV/ℏ Below the critical current the marble is trapped in a well — the phase is pinned, there's zero voltage , a perfect dissipationless supercurrent. Tilt past Ic and the wells vanish: the marble runs downhill , and every well it rolls over slips one flux quantum through the junction — a voltage spike. That escape is the neuron's threshold. bias current I/Ic 0.70 ❚❚ running the tilted washboard U(φ) · the phase marble · trapped (V=0, supercurrent) below Ic · running & emitting flux quanta above Ic SUPERCURRENT · V=0 junction regime 0 flux quanta emitted (Φ₀ each) multiply/sum = bias currents add (Kirchhoff) threshold = the critical current Ic spike = a 2π phase slip = one Φ₀ Below Ic, nothing moves and nothing dissipates — that's the magic of superconductivity put to work as a resting neuron. The instant you cross Ic the silence breaks into a stream of identical, quantized pulses. II · The single-flux-quantum spiking neuron Wire the weighted inputs in as bias current and the junction is an integrate-and-fire neuron with no extra parts: sub-threshold input leaks away as supercurrent; cross Ic and it fires a quantized SFQ pulse, the phase slips by 2π, and it resets — automatically. Every spike is identical and carries exactly one flux quantum. And it does this in picoseconds , dissipating attojoules — the fastest, leanest neuron physics offers. input current ❚❚ running clear accumulated phase (sawtooth) resets by 2π at each fire · the SFQ pulse train below · firing rate ∝ how far input exceeds Ic SILENT below Ic = no spikes 0 SFQ pulses (this window) Quantized, self-resetting, identical spikes — a junction is almost suspiciously well-suited to be a neuron. The catch is the same as all of superconducting computing: it only works cold, and getting signals in and out of the cryostat is its own art. III · It learns, it opens onto the qubit, and it fits in folders Same rule, same result — AND / OR in a few sweeps, XOR stuck at 3/4 (verified), freed by a second junction layer. But this body has two endings the others don't. First : add a capacitor and the washboard becomes a quantum well — the phase is now an operator , the lowest two levels are a transmon qubit , and the classical neuron becomes a quantum one. Second : a junction is just two superconductors joined at a weak link — which is literally the ROOT0 <• — so you can build a working one out of folders. target: AND OR XOR ▶ train ＋ 2nd junction layer — press train the junction, as folders <• the-virtual-junction/ electrode-left/ < the arm evolve.py steps the real RSJ dynamics sfq-pulses/ fires fill this, one Φ₀ each Two electrode folders joined at the-dot — the witnessed • . The phase difference φ lives at the dot , because the junction is the dot. Run python evolve.py and it integrates I=Ic·sinφ ; push the bias past Ic and sfq-pulses/ fills with files — the neuron firing, counted on disk. browse / clone it → The folder model isn't a toy analogy — it runs the same equations the silicon does, and it makes <• literal: a structure you can open, with firing you can list . It's the smallest honest junction, and the doorstep of the transmon . THE PERCEPTRON IN A JOSEPHSON JUNCTION · the seventh body · confidence-tiered physics verified in Node + a runnable folder simulator · f_J = 2eV/h = 483.5 GHz/mV · Φ₀ = h/2e = 2.068e-15 Wb · washboard: silent below Ic, fires above · learns AND 4/4, OR 4/4, XOR 3/4 Josephson 1962 (Nobel 1973) · RSFQ (Likharev & Semenov) · JJ neurons (Crotty/Schult/Segall 2010) · transmon (Koch et al. 2007) · needs ~4 K siblings: spin · crossbar · light · the gather · governor David Lee Wise · CC-BY-ND-4.0


PERCEPTRON · CUBI · 8th body

the quantum body · weights are Bloch rotations, the Born rul

The eighth body — the quantum perceptron, in a cubi (David Wise's term for the qubit). The weights are rotations on the Bloch sphere, the input is encoded as an angle, and the nonlinearity comes free from the Born rule: P(|1⟩)=sin²(θ/2), the activation IS the measurement. One cubi is still one cut (XOR 3/4), but an entangling feature map lifts XOR to 4/4 — entanglement does what depth did. Confidence-tiered: STRONG (single-cubi rotation+measurement, on real hardware) / MIDDLING (variational quantum classifiers, NISQ) / FRONTIER (quantum ADVANTAGE for ML — open and contested). The capstone of the eight-body series. David Lee Wise, two-layer honest.

The Perceptron in a Cubi — the quantum body, where measurement is the neuron ◄ UD0 josephson (the door) transmon entanglement Perceptron theory · the eighth body · through the door, into the quantum The perceptron in a cubi The Josephson junction left a door open: give it a capacitor and the phase stops being a number and becomes a quantum state . That two-level state is the cubi — the qubit, in the ROOT0 tongue. Here the neuron goes fully quantum: the weights are rotations on the Bloch sphere, the input is an angle you turn the state through, and the nonlinearity arrives unbidden — the act of measuring gives P(|1⟩)=sin²(θ/2) . Every other body had to find its threshold. The cubi's threshold is the wavefunction collapsing. weights = rotations (gates) · input = an encoded angle · state = α |0⟩ + β |1⟩ · nonlinearity = the Born rule (measurement) ✓ STRONG The cubi neuron itself. A single qubit rotated and measured — angle encoding, the Born-rule activation — is exact and runs on real quantum hardware (Tacchino et al. ran a quantum perceptron on IBM Q, 2019). ◐ MIDDLING Variational quantum classifiers. Small quantum neural nets are demonstrated , but it's the NISQ era — noise, decoherence, and barren plateaus (vanishing gradients) make training hard at scale. ◔ FRONTIER Quantum advantage for learning. Whether a quantum model actually beats a classical one on real data is open and genuinely contested — the honest line between physics and hype. I · The cubi, and measurement as the nonlinearity A cubi's state is a point on the Bloch sphere : north pole is |0⟩ , south is |1⟩ , and everywhere between is a superposition α|0⟩ + e^{iφ}β|1⟩ . The weights and inputs are rotations — they turn the arrow. But you never read α and β directly; you measure , and the state collapses to |0⟩ or |1⟩ with probability P(|1⟩) = sin²(θ/2) That curve — 0 at the north pole, ½ at the equator, 1 at the south — is a built-in nonlinear activation. The measurement is the neuron. θ rotate φ phase ⟂ MEASURE (collapse) reset tally the Bloch sphere · the cubi state arrow · |0⟩ north, |1⟩ south · measuring snaps it to a pole 0.87|0⟩ + 0.50|1⟩ amplitudes α, β P(1) = 0.25 the activation = sin²(θ/2) measured tally — converges to the Born probabilities Before measuring, the cubi is both — the activation exists as an amplitude, undecided. Measuring forces a 0 or a 1, biased by sin²(θ/2). Run it many times and the average is the smooth activation; run it once and you get a quantum coin flip. The nonlinearity and the randomness are the same act. II · The cubi perceptron — rotate by the weighted sum, then measure Encode the inputs as rotation angles and the weights as how hard each one turns the cubi. The rotations compose — the state ends at θ = b + Σ wᵢxᵢ — and the Born rule reads out the activation P(|1⟩) = sin²(θ/2) . Threshold it (more likely |1⟩ than |0⟩ ) and the cubi fires. It's the same weighted-sum-then-squash as every body — except the squash is physics you can't avoid. x₁ +1 x₂ −1 w₁ w₂ bias the cubi rotated to θ = b + Σwᵢxᵢ · its latitude sets P(|1⟩) · cross the equator → fires θ = 0° accumulated rotation P(1) = 0.50 Born activation |0⟩ — dark fires when P(1) > ½ multiply/sum = composed rotations activation = the Born rule readout = a measurement III · It learns — and entanglement is the new depth Train the rotation angles and the cubi learns AND / OR in a few sweeps. One cubi, encoded linearly, is still one cut — XOR stalls at 3/4 (verified), exactly like its seven classical cousins. But the quantum world has a different escape than stacking layers: a feature map that entangles the inputs adds an x₁·x₂ cross-term, lifting the data into a space where XOR is separable. Flip ⊗ entangle and XOR snaps to 4/4. Entanglement does what depth did — that's the quantum twist on the oldest wall in the series. target: AND OR XOR ▶ train ⊗ entangle (feature map) — press train The honest line (this is the contested one). The cubi's mechanism is real and runs on real hardware. The feature map lifting XOR is exactly how quantum kernels work, and it's genuinely quantum. But whether this buys a real-world advantage over a classical net — once you account for noise, the cost of loading data into amplitudes, and reading it back out — is unsettled and hotly argued . The physics is sound; the supremacy is a promissory note. We mark it FRONTIER on purpose. the cubi's gift = measurement is the activation the cubi's depth = entanglement, not more layers the cubi's caveat = advantage unproven (NISQ) This is where the road that began in a branch predictor arrives: the dot product turned into a quantum amplitude, the threshold into a measurement, depth into entanglement. Same neuron, eighth body — and the first one that is genuinely uncertain about its own answer until you look. silicon · cortical · quantum dot · light · crossbar · spin · josephson · cubi — one neuron, eight bodies THE PERCEPTRON IN A CUBI · the eighth body · confidence-tiered quantum mechanics verified in Node before build · Born activation P(1)=sin²(θ/2) · one cubi: AND 4/4, OR 4/4, XOR 3/4 · entangling feature map → XOR 4/4 · collapse statistics → Born (0.499 of 0.500) quantum perceptron on real hardware (Tacchino, Macchiavello, Gerace, Bajoni, npj QI 2019) · variational classifiers (NISQ) · barren plateaus (McClean 2018) · quantum advantage for ML = open “cubi” = David Wise's longstanding term for the qubit (semantic code). siblings: josephson · spin · the gather · governor David Lee Wise · CC-BY-ND-4.0


PERCEPTRON · TWO CUBI · 9th

the entangled body · a REAL two-cubi coupling as the feature

The deepest quantum body — a two-cubi (two-qubit) entangled perceptron where the feature map is a REAL two-cubi coupling (a CNOT/ZZ gate that physically entangles them), not a hand-added cross-term. A live two-cubi simulator: build a Bell pair (concurrence 1), the entangling quantum-kernel feature map, and the classifier. The honest reveal: entanglement is NOT needed for XOR (a product map does it too, verified) — what entanglement really buys is Bell-violating correlations (CHSH=2.83) that are classically un-fakeable, the only honest basis for quantum advantage, and unproven on real ML. Two-layer honest, anti-hype. David Lee Wise.

The Perceptron in Two Cubi — real entanglement, and the honest truth about it ◄ UD0 one cubi entanglement transmon Perceptron theory · deeper into the quantum · two coupled cubi The perceptron in two cubi One cubi could only turn its own state. Two cubi can do something no classical pair can: become entangled — a single joint state where neither cubi has an identity of its own. Here the feature map isn't a rotation I bolt on; it's a real two-cubi coupling , a gate that physically links them, so the cross-correlations are computed by the hardware. We build it honestly — and then tell you the truth about what it does and doesn't buy, which is not what most quantum-ML demos will admit. two cubi = a 4-state joint system · the bond = a real entangling gate (CNOT / ZZ) · feature map = the coupling itself · readout = the quantum kernel ✓ STRONG Real entanglement & quantum kernels. Two-cubi gates make genuine Bell pairs (concurrence 1, CHSH 2.83 — measured in labs for decades); the quantum-kernel feature map runs on hardware (Havlíček et al., IBM, 2019). ◐ MIDDLING Quantum-kernel classifiers. Demonstrated — but kernel estimation is noisy, and many entangling feature maps you can actually build turn out to be classically simulable after all. ◔ FRONTIER A proven advantage on real data. Whether entanglement gives a genuine machine-learning edge over classical methods is open and contested — the honest seam between physics and hype. I · Two cubi, and the bond that has no classical picture Start both cubi in |0⟩ . Put the first into superposition (an H gate), then apply a CNOT — the second cubi flips if the first is |1⟩ . Now the pair is (|00⟩+|11⟩)/√2 : both 00 and both 11 , never 01 or 10 . Measure one and you instantly know the other — yet neither had a definite value. That linkage is entanglement , and the meter is the concurrence : 0 for two separate cubi, 1 for a perfect Bell pair. H on cubi A CNOT (A→B) ↺ reset to |00⟩ cubi A and cubi B · the bond brightens with entanglement · below: the 4 joint amplitudes |00⟩|01⟩|10⟩|11⟩ 0.00 concurrence (entanglement) |00⟩ joint state A separable pair (concurrence 0) is just two arrows you can describe one at a time. The instant CNOT links them, the description of "A alone" stops existing — only the pair has a state. That's the resource the whole rest of this page runs on. II · The feature map is the coupling To classify, encode the inputs into the pair: a rotation Rz(x₁) on A, Rz(x₂) on B, and then the two-cubi ZZ coupling that depends on x₁·x₂ — the gate that does the entangling. The data is now a point in an entangled 4-dimensional state |Φ(x)⟩ , and similarity between two inputs is the quantum kernel K(x, x′) = |⟨Φ(x′)|Φ(x)⟩|² Toggle the coupling and watch the concurrence — and the kernel — change. The cross-term is real hardware, not arithmetic. x₁ +1 x₂ −1 ⊗ entangling coupling: ON |Φ(x)⟩ — the 4 joint amplitudes after the feature map · the kernel to a fixed reference point shown as the bar — concurrence of |Φ(x)⟩ — kernel K(x, x_ref) encode = Rz(x₁), Rz(x₂) couple = ZZ(x₁·x₂) — entangles compare = the quantum kernel With the coupling ON the state is entangled (concurrence > 0) and the kernel mixes both inputs. OFF, it factorizes into two independent cubi. This is exactly the knob the next module interrogates. III · It learns XOR — and here's what nobody tells you Run a kernel classifier on the four XOR points. With the entangling coupling, it nails XOR 4/4. Now switch the coupling OFF — and it still gets 4/4. Both work. That's the verified, deflationary truth: for two inputs, you do not need entanglement to solve XOR ; a product map already carries the cross-term. ⊗ entangling: ON ▶ classify XOR (quantum kernel) press classify So what does entanglement actually buy? Not toy problems. What it buys is correlations a classical model literally cannot fake — the entangled pair violates the Bell/CHSH bound ( S = 2.83 > 2 , verified), which no separable description can reach. That un-fakeable structure is the only honest basis for a quantum advantage: feature maps too entangled to simulate on a classical computer. Whether that translates into a real edge on real machine-learning data — once you pay for noise, state preparation, and readout — is unproven and actively argued . We built the real entangler; we won't sell you the magic. the resource = entanglement (concurrence, CHSH) the toy = doesn't need it (XOR works either way) the bet = classically-hard feature maps the verdict = advantage unproven → FRONTIER silicon · cortical · quantum dot · light · crossbar · spin · josephson · cubi · two cubi — the deepest stop THE PERCEPTRON IN TWO CUBI · deeper into the quantum · two-layer honest (anti-hype) full 2-cubi simulator verified in Node · Bell pair concurrence = 1.000 · ZZ feature map entangles (C>0) vs product (C=0) · BOTH solve XOR 4/4 · CHSH S = 2.828 > 2 (Tsirelson) quantum kernels / entangled feature maps (Havlíček, Córcoles… Gambetta, Nature 2019) · "many quantum feature maps are classically simulable" (the honest caveat) · advantage = open “cubi” = David Wise's term for the qubit. siblings: one cubi · josephson · the gather · governor David Lee Wise · CC-BY-ND-4.0


PERCEPTRON · SOUND · acoustic

the mechanical body · a surface wave, tapped & weighted;

An acoustic perceptron on a surface-acoustic-wave (SAW) chip. A wave ripples across a piezoelectric substrate; interdigital taps sample it at delays and weight them by electrode overlap — Σ wᵢ·x(t−τᵢ), a weighted sum in mechanics. A matched filter IS a perceptron: it fires when the wave matches the stored pattern. Slow waves make compact delay-line memory. Learns AND/OR not XOR (cascade = depth). Confidence-tiered: STRONG (SAW filters, in every phone) / MIDDLING (acoustic neuromorphic) / FRONTIER (large acoustic nets). David Lee Wise, two-layer honest.

The Perceptron in Sound — a surface wave, tapped and weighted ◄ UD0 light crossbar crystals & clocks Perceptron theory · another classical body · mechanical The perceptron in sound Light's slow cousin. A surface acoustic wave ripples across a piezoelectric chip at a few thousand metres per second — a hundred-thousand times slower than light, which is exactly the point: the same interference that multiplies, but crawling, so a useful delay fits on a fleck of quartz. Tap the wave at intervals, weight each tap by how much electrode overlaps it, and add — that's a weighted sum in moving matter. A matched filter, which is to say a perceptron, made of ripples. input = a wave packet · weights = interdigital tap overlaps · multiply+sum = tapped interference Σwᵢ·x(t−τᵢ) · fire = a correlation peak ✓ STRONG The SAW correlator. Tapped-delay-line filters and matched filters are in every phone's RF front-end — decades-mature. The weighted-sum-of-delays is bedrock signal physics. ◐ MIDDLING Acoustic neuromorphic. Phononic reservoir computing and SAW neural elements are demonstrated — compact and passive, but niche and bandwidth-bound. ◔ FRONTIER Large acoustic nets. Scaling phonon computing into real learning machines is open — sound is a memory and a filter more than a deep net, so far. I · A wave, tapped and weighted A wave packet travels left to right across the substrate. Fixed taps read its height as it passes; each tap carries a weight (the electrode overlap). At any instant the readout is y = Σ wᵢ · x(t − τᵢ) — the wave sampled at staggered delays, scaled, summed. The slowness is the feature: at 3,488 m/s a 1 GHz wave is only 3.5 µm long, so a whole pattern of delays fits in microns. ❚❚ running speed the surface wave on the piezo substrate · taps (heights = weights) sample it at delays · the bar = Σwᵢx(t−τᵢ) 0.00 weighted sum at the output tap multiply = tap weight × wave height sum = the electrodes add charge delay = the wave's travel time No clock drives the sum — the wave's own motion stages the delays. A SAW chip is a passive analogue convolver: the math is done by geometry and time-of-flight. II · A matched filter is a perceptron Freeze the weights to a stored pattern. Now slide an input wave through: when its shape lines up with the weights, every tap reinforces and the output spikes — the neuron fires. When it doesn't, the taps cancel to near zero. Correlation is the weighted sum, and a matched filter is a threshold neuron tuned to one pattern. ❚❚ running stored pattern: input sliding past the stored weights · the correlation output peaks at alignment = the fire listening… fires at a correlation peak III · Learns, and cascades for depth Train the taps and the acoustic neuron learns AND / OR ; one filter is one cut, so XOR needs a second SAW stage fed by a nonlinearity — depth, in cascaded chips. The gift this body gives is memory : a slow wave stores a signal in flight, so an acoustic net carries its own short-term recall in the delay itself. target: AND OR XOR ▶ train ＋ cascade — press train the gift = the delay is memory the limit = bandwidth, RF-scale the role = filter/correlator, not deep net Honest place in the family: sound is brilliant at one matched filter and at holding a signal still, less so at stacking into a big network. It's a memory and a feature detector cast in ripples — useful, bounded, real. …light · crossbar · spin · josephson · cubi · two-cubi · sound THE PERCEPTRON IN SOUND · a mechanical body · two-layer honest verified in Node · SAW v≈3488 m/s → λ=3.5 µm at 1 GHz (≈86,000× more compact than light) · matched-filter correlator: aligned=N (fires), random≈0 · learns AND/OR, XOR needs a cascade SAW filters / correlators (ubiquitous RF) · acoustic & phononic neuromorphic / reservoir computing (demonstrated, niche) siblings: light · crossbar · the gather · governor David Lee Wise · CC-BY-ND-4.0