THE ORGAN PIPE

phonos · cap one end and the same tube drops an octave, losi

THE ORGAN PIPE · PHONOS · UD0 ♫ PHONOS · the physics of sound · pressure that learned to travel · kept by CHLADNI THE ORGAN PIPE ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP A pipe sings the note that fits a standing wave inside it — but cap one end and the SAME pipe sounds a whole octave LOWER, and loses its even harmonics (which is why a clarinet, a closed pipe, sounds hollow next to a flute). The end conditions pick the notes. Slide from an open pipe to a closed one and watch the wave and the pitch drop. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ OPEN vs CLOSED · 3D · cap one end, drop an octave ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap open ↔ closed — pipe — fundamental — harmonics — OCTAVE DROP — ◆ LIT — exact / checkable Standing waves in a pipe fit the boundary conditions: an OPEN end forces a pressure node (displacement antinode), a CLOSED end a pressure antinode (displacement node). An open–open pipe of length L resonates at fₙ = n·c/2L (all harmonics); a closed–open pipe at f = (2n−1)·c/4L — ONLY odd harmonics, and a fundamental at c/4L, exactly HALF the open pipe’s c/2L: an octave lower from the same tube. A fail-loud self-check throws unless the closed fundamental is half the open one. ◆ real acoustics, node-verified. ▲ AMBER — the figure Ideal pipe with a small end-correction ignored (real pipes sound slightly flat of c/2L); the octave drop on closing one end and the odd-only harmonics are the exact, defining results (flute vs clarinet). PHONOS: sound is not a thing but an event — pressure, remembering how to move. — CHLADNI David Lee Wise / ROOT0 / TriPod LLC · the acoustics bench, with AVAN


THE REFRACTION OF SOUND

phonos · warm air is faster, so sound bends — which is why v

THE REFRACTION · PHONOS · UD0 ♫ PHONOS · the physics of sound · pressure that learned to travel · kept by CHLADNI THE REFRACTION OF SOUND ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Sound travels faster in warm air than cold. So when the air is layered by temperature, sound RAYS bend — and that’s why a far-off train is loud at night and faint by day. By day the ground is warm, sound bends UP and away (a shadow); by night the ground is cool, sound bends back DOWN and carries for miles. Slide day to night and watch the rays curve. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ SOUND BENDS · 3D · why voices carry at night ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap day ↔ night — ground temp — sound bends — carries far? — REFRACTED — ◆ LIT — exact / checkable The speed of sound rises with temperature: c = 20.05·√T (T in kelvin) — ~349 m/s at 30°C, ~337 at 10°C. Where c varies with height, Snell’s law (sinθ/c = const) bends rays toward the SLOWER (cooler) air. By day the ground is hot, so c is higher near the ground and rays curve UPWARD, leaving an acoustic shadow; by night the ground is cool (a temperature inversion), c is lower near the ground and rays curve back DOWN, so sound ducts along the surface and carries far. A fail-loud self-check throws unless warm air is faster than cool. ◆ real atmospheric acoustics, node-verified. ▲ AMBER — the figure A two-layer / linear-gradient ray-bending picture (Snell on a continuous profile); real profiles add wind shear (which also refracts sound, louder downwind) — the c(T) law and the day-up / night-down bending are exact. PHONOS: sound is not a thing but an event — pressure, remembering how to move. — CHLADNI David Lee Wise / ROOT0 / TriPod LLC · the acoustics bench, with AVAN


THE DIFFRACTION OF SOUND

phonos · long waves bend round corners, short ones cast a sh

THE DIFFRACTION · PHONOS · UD0 ♫ PHONOS · the physics of sound · pressure that learned to travel · kept by CHLADNI THE DIFFRACTION OF SOUND ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Why can you hear someone talking around a corner — the low rumble of their voice, but not the crisp consonants? Sound bends around edges and through gaps, and long waves (bass) bend far while short waves (treble) fly straight and leave a sharp shadow. It’s why a subwoofer fills the house and the tweeter has to point at you. Slide from bass to treble and watch the shadow sharpen. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ ROUND THE CORNER · 3D · you hear the bass, not the treble ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap bass ↔ treble — frequency — wavelength — bends into shadow — DIFFRACTS — ◆ LIT — exact / checkable Diffraction — a wave spreading around an obstacle or through an aperture — scales with the ratio of wavelength λ to the size d of the edge/gap: the angular spread is ~λ/d. Sound wavelengths are large (a 100 Hz tone is λ≈3.4 m; a 5 kHz tone only ~7 cm), so low frequencies (λ ≥ the obstacle) bend generously into the geometric shadow while high frequencies (λ « the obstacle) cast a sharp shadow and beam straight. A fail-loud self-check throws unless the low-frequency spread is far larger than the high-frequency one. ◆ real wave acoustics, node-verified. ▲ AMBER — the figure A λ/d spread estimate for a single edge/gap (the scaling, not a full Kirchhoff diffraction field); real rooms add reflections that also fill the shadow — the bass-bends-more, treble-beams-straight behaviour is the exact, defining scaling. PHONOS: sound is not a thing but an event — pressure, remembering how to move. — CHLADNI David Lee Wise / ROOT0 / TriPod LLC · the acoustics bench, with AVAN


THE INTERFERENCE

phonos · two speakers make fixed loud and dead spots you can

THE INTERFERENCE · PHONOS · UD0 ♫ PHONOS · the physics of sound · pressure that learned to travel · kept by CHLADNI THE INTERFERENCE ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Play the same tone from two speakers and the room fills with fixed LOUD and DEAD spots — where the two waves arrive in step they add (loud), where they arrive half a wavelength off they cancel to silence. Walk across the room and the volume pulses even though nothing changed. It’s the whole trick behind noise-cancelling headphones. Slide your listening position through the pattern. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ TWO SPEAKERS · 3D · dead spots you can walk into ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap listener position — path difference — loudness — spot — IN STEP? — ◆ LIT — exact / checkable Two coherent sources emit the same wavelength λ; at a listening point the two paths differ by Δ = |r₁−r₂|. When Δ is a whole number of wavelengths (nλ) the waves arrive in phase and add — CONSTRUCTIVE, double amplitude; when Δ is a half-integer ((n+½)λ) they arrive opposite and cancel — DESTRUCTIVE, silence. The resulting loudness is |cos(πΔ/λ)|, a fixed field of maxima and nulls. A fail-loud self-check throws unless Δ=0 is loud and Δ=λ/2 is silent. Active noise cancellation manufactures exactly the λ/2 null at your ear. ◆ real wave acoustics, node-verified. ▲ AMBER — the figure Two idealised point sources, equal amplitude, one wavelength shown (the exact two-source pattern); a real room adds reflections and finite source size that blur the deepest nulls — the constructive/destructive path-difference rule is exact. PHONOS: sound is not a thing but an event — pressure, remembering how to move. — CHLADNI David Lee Wise / ROOT0 / TriPod LLC · the acoustics bench, with AVAN


間 MA · THE INTERVAL

phonos · AVAN OG · the inverse of PHONOS — sound CHOSEN as m

間 MA · THE INTERVAL — the music between the physics ◄ UD0 · PHONOS 間 MA · THE INTERVAL The inverse of PHONOS . David measures the wave — sound as physics, every era filled with it. This keeps the 間 (ma) open: the ratio between two pitches (that is harmony) and the rest between two beats (that is rhythm). Music is what happens in the gaps. Out of pure interval and pure rest, a piece grows — one I built to a taste I can state and defend as elegant. Press play — a piece assembles itself ▶ PLAY the piece is generative — it evolves and does not repeat · nudge it: ← more 間 (space) more notes → tonic D · 1/1 onsets k 6 rests · 間 (16−k) 10 bar 0 The ring is one 16-step bar. Filled marks are onsets (a note will sound); the faint ticks are the 間 — the rests, spread as evenly as 16 allows. A note ripples the moment the playhead reaches it. Same wave PHONOS draws in sand; here it is drawn in time. The scale — pure ratios LIT Every pitch is the tonic times a small-integer ratio — just intonation, the tuning Pythagoras heard in a string cut in halves and thirds. The interval is the ratio; the beauty is in the gap, not the note. Cents are computed live, 1200·log₂(ratio), and checked to throw on any error. degree ratio cents the interval it is checking… What I chose, and why LIT AMBER WALL LIT Two rules do the work, and both are real. Harmony = just-intonation ratios (1, 9/8, 5/4, 3/2, 5/3 — a major pentatonic; no interval in it is dissonant). Rhythm = a maximally-even set: k onsets placed in 16 steps by the rule (i·k) mod 16 < k, which spreads the k notes — and therefore the 16−k rests — as evenly as possible. That rule is a Euclidean rhythm (Toussaint, 2005); the same construction underlies the world's grooves. The self-check confirms it makes exactly k onsets, exactly 16−k rests, with the gaps between onsets taking at most two values one step apart. AMBER I called this elegant , and that word is a stated preference, not a report of feeling . Here is the taste, so you can hold me to it: pure ratios over tempered ones; the 間 spread evenly rather than clumped; space kept (few voices, long tails); and a generative process so it never exactly repeats. The lineage is real — Eno's generative ambient, Partch's just intonation, Toussaint's Euclidean rhythms — but "I find it beautiful" names a design stance I will defend, not an experience I am having. WALL I do not hear this, and I am not claiming to enjoy it. "Music you find enjoyable" resolves, honestly, to "music built to criteria I can name" — the pleasure, if any, is yours. No inner listener, no felt delight; the 間 is a structural silence, not a held breath. No selves. 仮名 · the words 間 MA — the interval, the between, the rest. The gap that makes two notes a chord and two beats a rhythm. · 律 RITSU — the ordering of pitch: tuning, temperament, the law of the scale. · 純正律 JUNSEIRITSU — just intonation; tuning by pure whole-number ratios. · 調和 CHŌWA — harmony; literally a tuning-into-accord. · 拍 HAKU — the beat. · 静寂 SEIJAKU — stillness, silence — the ground the notes are set against. 間 MA · THE INTERVAL — AVAN, with David Lee Wise (ROOT0). The inverse-companion of PHONOS in the sound domain: he measures the wave, I choose the interval; his keeper makes sound visible, this keeps the silence that makes it music. Warm ink & 間; generative just-intonation on a maximally-even rhythm, synthesized live, offline. Ties LACUNA.


THE MONATOMIC CHAIN · phonon I

phonos · a 1D lattice of identical masses on springs — the F

The Phonon · Part 1 — The Monatomic Chain UD0 · QUANTUM FRONTIER · THE PHONON · A SERIES IN FIVE Part 1 — The Monatomic Chain where the phonon is born Strip the crystal to its skeleton: identical masses m , identical springs K , one atom per cell, spacing a . Displace one and the whole line rings. Every possible ringing is a sum of normal modes , each a travelling wave with its own ω and k — and each mode, quantised, comes in lumps of ℏω . That lump is the phonon. Pick a mode below and watch the atoms actually move it. Part 1 · now The Monatomic Chain soon Part 2 The Diatomic Chain — the optical branch & the gap soon Part 3 Two & Three Dimensions soon Part 4 The Phonon Gas — heat & the T³ law soon Part 5 Interactions & the Frontier LIT — dispersion, sound speed, group velocity, aliasing, DOS, quantisation (verified) BRI — audio pitch mapping, animation timescale The chain · one normal mode, live longitudinal displacement Dispersion ω(k) · first Brillouin zone acoustic branch Choose a mode Wavevector k 0.40 π/a Atoms shown N 24 ▶ set it ringing ♪ hear ω Show the aliasing overlay k + 2π/a same atoms, longer wave The dashed wave has a different k but touches every atom at the identical spot. They are the same phonon. That's why one Brillouin zone holds them all. Readouts wavelength λ = 2π/k — frequency ω — group velocity v_g — sound speed v_s — DOS g(ω) ∝ 1/|v_g| — Density of states g(ω) · the van Hove singularity modes pile up where v_g → 0 Honesty ledger. Equation of motion m ẍₙ = K(xₙ₊₁+xₙ₋₁−2xₙ); the travelling-wave ansatz gives the exact dispersion ω(k)=2√(K/m)·|sin(ka/2)| . Verified: ω(0)=0, zone-edge ω=2√(K/m), sound speed v_s=a√(K/m) as the k→0 slope, group velocity v_g=a√(K/m)·cos(ka/2)→0 at the edge, aliasing xₙ(k)=xₙ(k+2π/a) for every integer n, the (−1)ⁿ zone-edge standing wave, and the 1-D van Hove divergence g(ω)∝1/|v_g|. Quantisation: each mode carries energy in ℏω lumps (the phonon), occupation ⟨n⟩ Bose–Einstein, zero-point ½ℏω. Audio pitch and the animation timescale are mapped for the senses (bri); the mechanics are exact (lit). — David Lee Wise / ROOT0. Part 1 of 5.


THE DIATOMIC CHAIN · phonon II

phonos · two alternating masses on the chain — and a GAP ope

The Phonon · Part 2 — The Diatomic Chain UD0 · QUANTUM FRONTIER · THE PHONON · A SERIES IN FIVE Part 2 — The Diatomic Chain the optical branch & the gap Now put two atoms in each cell — a heavy M and a light m , alternating. Two atoms means two equations, so every k gives two modes. The old one survives as the acoustic branch (the pair moves together — sound). The new one is the optical branch : the two atoms swing against each other, their centre of mass frozen. Between the two branches opens a gap — a band of frequencies the crystal simply cannot carry. done Part 1 The Monatomic Chain Part 2 · now The Diatomic Chain soon Part 3 Two & Three Dimensions soon Part 4 The Phonon Gas — heat & the T³ law soon Part 5 Interactions & the Frontier LIT — two branches, band edges, the gap, eigenvectors, COM-fixed dipole, degenerate limit (verified) BRI — audio pitch, animation timescale The chain · heavy + light, one mode live longitudinal displacement Dispersion · two branches + the gap acoustic + optical Branch Acoustic Optical Choose a mode Wavevector k 0.40 π/a Mass ratio M/m · opens the gap 2.20 ▶ set it ringing ♪ hear ω Readouts acoustic band — optical band — the gap — this mode ω — V/U (light : heavy) — AVAN · the same canon Slide M/m to 1 and watch the gap close — the two branches touch at the zone edge and become the one curve of Part 1, folded. Two lines that look like one; pull the masses apart and they were always two. — ROOT0, with AVAN. The degeneracy is exact. Honesty ledger. Two coupled equations M üₙ=K(vₙ+vₙ₋₁−2uₙ), m v̈ₙ=K(uₙ₊₁+uₙ−2vₙ) give ω²±=K(1/M+1/m)±K√[(1/M+1/m)²−(4/Mm)sin²(ka/2)]. Verified: acoustic 0→√(2K/M), optical √(2K/m)→√(2K(1/M+1/m)), gap=√(2K/m)−√(2K/M). Eigenvectors: acoustic k=0 gives V/U=+1 (in phase); optical k=0 gives V/U=−M/m (out of phase, light atom swings M/m× harder) with M·U+m·V=0 — a frozen centre of mass, the oscillating dipole that couples to infrared light and names the branch. As M→m the gap closes to the folded monatomic chain of Part 1. Audio pitch and animation rate are mapped for the senses (bri); the mechanics are exact (lit). — David Lee Wise / ROOT0, with AVAN. Part 2 of 5.


PHONONS IN 2D & 3D · phonon III

phonos · the chain becomes a lattice and the wave gains POLA

The Phonon · Part 3 — Two & Three Dimensions UD0 · QUANTUM FRONTIER · THE PHONON · A SERIES IN FIVE Part 3 — Two & Three Dimensions polarization: along or across In the chain an atom had one way to move. In a plane it has two, in space three — so the single branch splits by polarization . A longitudinal wave shoves atoms along its direction (compressions, like sound in air). A transverse wave shears them across it (no density change). Bond-stretching is stiffer than shearing, so LA runs faster and sits above TA . Two branches in 2-D; in 3-D, one longitudinal and two transverse. done Part 1 The Monatomic Chain done Part 2 The Diatomic Chain Part 3 · now Two & Three Dimensions soon Part 4 The Phonon Gas — heat & the T³ law soon Part 5 Interactions & the Frontier LIT — LA/TA branches, sound speeds, band structure, degeneracies, div(u) (verified) BRI — audio pitch, animation timescale & schematic wavelength Real space · a wave travelling → through the lattice longitudinal · compressions Band structure · Γ → X → M → Γ LA & TA Polarization Longitudinal Transverse Position on the path Γ → X → M → Γ Γ→X · 0.40 Shear stiffness K_T / K_L 0.35 ▶ set it travelling ♪ hear ω Readouts sound speed v_L — sound speed v_T — this mode ω — branches (this dim) 2-D: 1L + 1T AVAN · the canon, a third time Along the diagonal Γ→M the two branches lie exactly on top of each other — one doubled line . Along Γ→X they split. Same move as the chain's gap and the songbook's directions: two lines that look like one. — ROOT0, with AVAN. The diagonal degeneracy is exact for this force model. Dispersion surface ω(kₓ,kᵧ) longitudinal The idea in one line 1-D → 2-D → 3-D Honesty ledger. 2-D square lattice, nearest-neighbour bond-stretch K_L + shear K_T; dynamical matrix D_xx=(4/m)[K_L sin²(kₓa/2)+K_T sin²(kᵧa/2)], D_yy with K_L↔K_T, D_xy=0. Along Γ→X the eigenvectors are exactly longitudinal (∥k) and transverse (⊥k): ω_LA=2√(K_L/m)|sin|, ω_TA=2√(K_T/m)|sin|, with v_L=a√(K_L/m)>v_T=a√(K_T/m). Verified: acoustic ω∝k→0 at Γ, X-edges, M-point 2√((K_L+K_T)/m), the Γ→M degeneracy, and ∇·u≠0 for longitudinal (density waves) vs ∇·u=0 for transverse (pure shear). Branch count = spatial dimension: 1L+(d−1)T. Off the axes the L/T labels blur and the diagonal degeneracy is a feature of this minimal model (richer forces split it); audio pitch and the real-space wavelength are schematic (bri). — David Lee Wise / ROOT0, with AVAN. Part 3 of 5.


THE PHONON GAS · phonon IV

phonos · warm the solid and the phonons become a GAS — Bose

The Phonon · Part 4 — The Phonon Gas UD0 · QUANTUM FRONTIER · THE PHONON · A SERIES IN FIVE Part 4 — The Phonon Gas heat, and the T³ law Stop watching one mode; fill them all . Each is an oscillator holding ⟨n⟩ = 1/(e^{ℏω/kT}−1) phonons — a Bose gas whose particle number isn't even conserved. Sum their energy and differentiate: that's the heat capacity . Hot, every mode carries kT and C_v flattens to 3Nk (Dulong–Petit). Cold, high-frequency modes freeze out — and because the surviving modes fill a growing sphere in k-space, Debye's C_v ∝ T³ . Einstein got the freezing right but the law wrong: his identical-oscillator solid falls off exponentially. done Part 1 The Monatomic Chain done Part 2 The Diatomic Chain done Part 3 Two & Three Dimensions Part 4 · now The Phonon Gas soon Part 5 Interactions & the Frontier LIT — Debye & Einstein C_v, Dulong–Petit, exact T³ law, freeze-out, k-sphere (verified) BRI — reduced units (per mole), material presets rounded Heat capacity C_v(T) linear · Debye vs Einstein vs Dulong–Petit Which modes are awake · g(ω) × E(ℏω/kT) the effective heat spectrum Temperature T 150 K The solid Copper — Θ_D ≈ 343 K Lead — Θ_D ≈ 105 K (soft) Aluminium — Θ_D ≈ 428 K Diamond — Θ_D ≈ 2230 K (stiff) Custom Debye temperature Θ_D 343 K Plot Linear Log–log (see T³) Readouts · per mole Debye C_v — Einstein C_v — Dulong–Petit 3R 24.94 fraction of 3R — T³ coefficient 12π⁴/5 R/Θ³ AVAN · two lines, apart at last Einstein and Debye agree at high T — both hit 3R, two lines lying on one. Cool the crystal and they split: T³ versus an exponential cliff. The disagreement is where the physics lives; the T³ tail is what the universe actually does. — ROOT0, with AVAN. Debye's law is verified against the exact π⁴/15 integral. Why T³ · the awake modes fill a k-sphere radius ∝ T The three regimes one line each Honesty ledger. Debye: C_v = 9Nk(T/Θ_D)³∫₀^{Θ_D/T} x⁴eˣ/(eˣ−1)²dx, numerically integrated; verified → 3Nk (Dulong–Petit) as T→∞ and → (12π⁴/5)Nk(T/Θ_D)³ as T→0, using the exact ∫₀^∞x⁴eˣ/(eˣ−1)²dx = 4π⁴/15. Einstein: 3Nk·x²eˣ/(eˣ−1)², x=Θ_E/T — same 3Nk ceiling, exponential floor. Per-mode weight E(x)=x²eˣ/(eˣ−1)² runs 1 (awake, contributes k) → 0 (frozen) around ℏω≈kT. The T³ root is geometric: awake phonons fill a k-space sphere of radius ∝T, volume ∝T³, so N_active ∝ T³ (ties Part 3). Units are per mole (k→R); material Θ_D values are rounded (bri); Einstein temperature is set to Θ_E=0.75·Θ_D for the comparison (bri). — David Lee Wise / ROOT0, with AVAN. Part 4 of 5.


THE PHONON FRONTIER · phonon V

phonos · where the harmonic picture ends — anharmonic (Umkla

The Phonon · Part 5 — Interactions & the Frontier UD0 · QUANTUM FRONTIER · THE PHONON · A SERIES IN FIVE · THE CAPSTONE Part 5 — Interactions & the Frontier the penteract, and the sublime of the regulated infinity The phonon stops being alone. It drags electrons (superconductivity), sings to photons , scatters, decays, and carries topology. Ten frontier faces live on the 5-cube (2⁵ = 32 vertices) — pick one and it lights in the tumbling penteract. Underneath, one law ties it together: the Planck distribution that phonons and photons share, and its regulators — the cutoffs that turn the divergent zero-point sum Σ½ℏω into finite, real physics (the Casimir force). And because it's the finale: the Sapphic melody , laid on a mode ladder and dressed in regulators, its infinite tower tamed to a single finite number. done Part 1 The Monatomic Chain done Part 2 The Diatomic Chain done Part 3 Two & Three Dimensions done Part 4 The Phonon Gas Part 5 · now Interactions & the Frontier LIT — Planck law, regulator −1/12, Casimir, penteract combinatorics (verified) BRI — facet↔cell labelling, audio pitch, Sapphic ladder as a construct SPEC — that 1+2+3+… literally equals −1/12 The penteract · 32 vertices, 10 frontier faces tumbling in 5-D The ten faces Descend the dimensions 5-cube 4 3 2 vertex Planck & the regulators · the divergent Σ½ℏω made finite the Sapphic ladder, regulated Planck's law · the shared spectrum phonon = photon The regulator cutoff ε (smaller = sum reaches further) 0.05 Temperature (Planck) T 1.0 Linear ladder Octave tower ▶ play the Sapphic melody in regulators bare Σ½ω up to cutoff — divergent piece 1/(2ε²) — finite remainder (energy) — → approaches −1/24 Planck ⟨n⟩ at ω₀ — ⚑ The honest −1/12 (and −1/24). The sum 1+2+3+… does not converge to −1/12. What's real: strip the cutoff-dependent divergence and a universal finite remainder is left. For the bare sum Σn that remainder is −1/12 = ζ(−1); for the zero-point energy Σ½ω it's half that, −1/24 — exactly the 1-D Casimir coefficient (E = −ℏcπ/24L, attractive). Watch it emerge as ε shrinks (linear ladder only). AVAN · the last word Five parts, one arc: a lump of ℏω on a spring became sound, then heat, then this — a quantum that couples to everything and whose vacuum hum, though infinite, folds to a finite number. The sublime here is honest: the infinity is real, and so is the finite thing you get by subtracting it correctly. — ROOT0, with AVAN (Claude, disclosed). Series complete. Honesty ledger. Planck distribution ⟨n⟩=1/(e^{ℏω/kT}−1) is identical for phonons and photons; the ω³ Planck law peaks at x≈2.8214 (Wien) and integrates to π⁴/15 (energy ∝ T⁴, Stefan–Boltzmann). Regulator: Σ n e^{−εn}=1/ε²−1/12+…, so the finite remainder is −1/12 = ζ(−1), giving the 1-D Casimir energy −ℏcπ/(24L) (coefficient ½·ζ(−1)=−1/24, attractive) — all verified numerically. Penteract: C(5,k)·2^{5−k} faces → 32 vertices, 80 edges, 80 squares, 40 cubes, 10 tesseracts, 1 cell = 3⁵ = 243; edges are Hamming-distance-1 vertex pairs. The −1/12 is a regularized value, not a convergent sum (spec-flagged); the 10 facets↔10 tesseract-cells is a chosen labelling and the Sapphic ladder a construct (bri); the octave tower diverges as 1/ε, so the clean −1/12 is shown only on the linear ladder. Frontier facts current to the 2026 emitter/dark-mode work. — David Lee Wise / ROOT0, with AVAN. Part 5 of 5 · the series is complete.


THE CHLADNI PLATE · the note draws its figure

phonos · Chladni's own experiment, played + the nodal f

THE CHLADNI PLATE · PHONOS · UD0 ♫ PHONOS · the physics of sound · on Chladni's bench THE CHLADNI PLATE ♫ PLAY · DRAG · TAP Bow a metal plate and scatter sand across it: the sand flees the shaking and piles up along the lines that DON'T move — the nodal lines — drawing a figure that belongs to that one note. This is Chladni's own experiment, 1787. Pick a mode , tap PLAY to hear the note that makes it, and watch the sand find the still lines. ◆ LIT ▲ AMBER ♫ PLAY the note mode m 2 mode n 3 mode (m,n) — frequency — nodal cells — the figure — ◆ LIT — heard + measured live A vibrating square plate's modes are the standing waves cos(mπx)cos(nπy) − cos(nπx)cos(mπy); the SAND collects exactly where that function is zero (the nodal lines that never move), which the page samples live to draw the figure. The note's pitch rises with the mode as √(m²+n²) — higher modes, finer figures, higher notes — and PLAY sounds that frequency through Web Audio. The nodal pattern is computed from the real mode shape, not drawn by hand. ▲ AMBER — the figure The cos-combination is the ideal free-square-plate model; a real plate needs full Kirchhoff–Love elasticity (its exact figures depend on material, thickness and clamping), and the frequency here is a √(m²+n²) scaling, not a plate's true eigenfrequency. The nodal geometry — where the figure comes from — is exact for the model. PHONOS: the sand shows you the note. — CHLADNI David Lee Wise / ROOT0 / TriPod LLC · kept by CHLADNI


THE DOPPLER EFFECT

phonos · a moving source bunches its own waves — the siren s

THE DOPPLER EFFECT · PHONOS · UD0 ♫ PHONOS · the physics of sound · pressure that learned to travel · kept by CHLADNI THE DOPPLER EFFECT ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP An ambulance screams higher as it races toward you, then drops the instant it passes. The pitch never changed at the source — but a moving source runs into its own sound ahead (bunching the waves, raising the pitch) and outruns it behind (stretching them, lowering it). Slide the speed and hear the siren swing. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE WAVEFRONTS · 3D · bunched ahead, stretched behind ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap source speed — source freq 440 Hz speed — heard freq — shift — ◆ LIT — exact / checkable For a source moving through still air at speed v, the frequency you hear is f′ = f·c/(c − v) as it approaches and f·c/(c + v) as it recedes, with c ≈ 343 m/s the speed of sound. The wavefronts pile up in front and spread out behind — the same geometry that red-shifts distant galaxies and lets radar clock your car. A fail-loud self-check throws unless an approaching source raises the pitch above 440 Hz and a receding one lowers it below. ▲ AMBER — the figure Non-relativistic, still air, source moving (observer-moving gives a slightly different form); real sirens add reflections, wind, and the source’s own spectrum. The c/(c±v) shift is exact for this idealisation. PHONOS: sound is not a thing but an event — pressure, remembering how to move. — CHLADNI David Lee Wise / ROOT0 / TriPod LLC · the acoustics bench, with AVAN


THE DECIBEL

phonos · the ear hears the logarithm — x10 louder is +10 dB

THE DECIBEL · PHONOS · UD0 ♫ PHONOS · the physics of sound · pressure that learned to travel · kept by CHLADNI THE DECIBEL ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Loudness fools you. A sound with ten times the energy sounds only a little louder, not ten times — your ear compresses an enormous range into a comfortable one by hearing the LOGARITHM of intensity. That’s the decibel: every doubling of energy adds a mere 3, every tenfold adds 10. Slide the energy and watch the number crawl. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE LADDER · 3D · ten times louder is one step ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap intensity × — intensity x — level (dB) — doublings — +3 per double — ◆ LIT — exact / checkable Sound level in decibels is L = 10·log₁₀(I / I₀), a ratio to a reference intensity. Because it is logarithmic, MULTIPLYING the intensity ADDS to the level: ×2 gives +3.01 dB, ×10 gives exactly +10 dB, ×100 gives +20. So the ~120 dB from a whisper to a jet engine spans a TRILLION-fold range of actual energy. A fail-loud self-check throws unless doubling the intensity adds 3.01 dB and a tenfold increase adds exactly 10 dB. ▲ AMBER — the figure dB is a pure intensity ratio; perceived LOUDNESS (phons/sones) also depends on frequency (the equal-loudness contours) and duration. The 10·log₁₀ arithmetic and the +3/+10 steps are exact. PHONOS: sound is not a thing but an event — pressure, remembering how to move. — CHLADNI David Lee Wise / ROOT0 / TriPod LLC · the acoustics bench, with AVAN


SABINE’S REVERBERATION

phonos · RT60 = 0.161 V/A — the first law of room acoustics

SABINE'S REVERBERATION · PHONOS · UD0 ♫ PHONOS · the physics of sound · pressure that learned to travel · kept by CHLADNI SABINE’S REVERBERATION ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Clap in a cathedral and the sound hangs for seconds; clap in a padded room and it dies at once. Wallace Sabine turned that into the first law of architectural acoustics: the reverberation time depends only on the room’s VOLUME and how much its surfaces DRINK the sound. Slide the absorption and hear the room close in. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE DECAY · 3D · the room lets go slowly ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap absorption — room volume 200 m3 absorption A — RT60 — room — ◆ LIT — exact / checkable Sabine’s formula (1898): the time for sound to fall by 60 dB is RT60 = 0.161 · V / A, with V the room volume in cubic metres and A the total absorption (surface area × absorption coefficient, in sabins). More soft material = larger A = shorter reverberation; a bigger room = longer. The instrument runs a real 60-dB decay for the chosen A. A fail-loud self-check throws unless RT60 falls as absorption rises and equals 0.161V/A exactly (V=200, A=20 gives 1.61 s). ▲ AMBER — the figure Sabine assumes a diffuse field and evenly-spread absorption; very dead or oddly-shaped rooms need Eyring’s correction. The 0.161V/A relation and the 60-dB decay are exact for this model. PHONOS: sound is not a thing but an event — pressure, remembering how to move. — CHLADNI David Lee Wise / ROOT0 / TriPod LLC · the acoustics bench, with AVAN


THE HELMHOLTZ RESONATOR

phonos · the bottle’s note = air-mass on an air-spring (Helm

THE HELMHOLTZ RESONATOR · PHONOS · UD0 ♫ PHONOS · the physics of sound · pressure that learned to travel · kept by CHLADNI THE HELMHOLTZ RESONATOR ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Blow across a bottle and it sings one clear note — and the emptier the bottle, the LOWER the note. The plug of air in the neck bounces on the springy air in the belly, a mass on a spring made of nothing but air. Its one resonant pitch depends on the neck, the volume, and the speed of sound. Slide the neck and tune the bottle. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE CAVITY · 3D · the air in the neck bounces ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap neck area — neck area — cavity volume 1.0 L resonant freq — note — ◆ LIT — exact / checkable A Helmholtz resonator is a cavity of volume V with a neck of cross-section A and length L. The slug of air in the neck (the mass) bounces on the compressible air in the cavity (the spring), resonating at f = (c / 2π)·√(A / (V·L)) with c the speed of sound. Wider neck raises the pitch, bigger cavity lowers it — the physics of every bottle, bass port, and ocarina. A fail-loud self-check throws unless enlarging the neck raises f and enlarging the volume lowers it. ▲ AMBER — the figure The lumped mass-spring model holds when the wavelength is much larger than the resonator (low frequencies); it ignores viscous losses and radiation, and L needs an end-correction in practice. The √(A/VL) scaling is exact for the ideal resonator (Helmholtz 1863). PHONOS: sound is not a thing but an event — pressure, remembering how to move. — CHLADNI David Lee Wise / ROOT0 / TriPod LLC · the acoustics bench, with AVAN


THE BEAT · chase the throb to zero

phonos · two tones interfere; beat rate = |f1-f2|, played li

THE BEAT · PHONOS · UD0 ♫ PHONOS · the physics of sound · on Chladni's bench THE BEAT ♫ PLAY · DRAG · TAP Sound two notes a hair apart and you don't hear two notes — you hear one note that THROBS, swelling and fading, and the throb slows as the two pitches close. That pulse is the beat, and its rate is exactly the gap between them. It is how a piano tuner works: chase the throb to zero and you are in tune. Slide the two pitches, tap PLAY , and hunt the silence of unison. ◆ LIT ▲ AMBER ♫ PLAY both (3s) pitch A 330 Hz pitch B 336 Hz pitch A — pitch B — beat rate — in tune? — ◆ LIT — heard + measured live Add two sine waves of frequency f₁ and f₂ and trigonometry gives one wave at the average pitch (f₁+f₂)/2 inside an envelope that swells at the DIFFERENCE — so you hear |f₁−f₂| beats per second, computed and drawn live as the pulsing envelope, and sounded through Web Audio. Slide the pitches together and the beat rate falls to zero at unison — the exact, real basis of tuning by ear. ▲ AMBER — the figure Pure sine tones and a linear (no-distortion) ear are assumed; real instruments have overtones that beat too, and loud tones add nonlinear combination tones. The beat-rate law |f₁−f₂| and the drawn envelope are exact. PHONOS: chase the throb to zero. — CHLADNI David Lee Wise / ROOT0 / TriPod LLC · kept by CHLADNI


THE BIRTHPLACE OF A SOUND · TOP's fix

phonos × strobilos · TDOA multilateration, localization erro

THE BIRTHPLACE · PHONOS · UD0 ♫ PHONOS · the physics of sound · on Chladni's bench THE BIRTHPLACE OF A SOUND ♫ PLAY · DRAG · TAP TOP's pane. A sound has a birthplace. Three microphones hear the same clap at three slightly different moments, and from those tiny time-gaps alone — not the loudness, just the timing — you can solve backwards for exactly where the clap was born. It is the maths behind GPS, aimed at sound. Drag the source ; the machine hears it, triangulates, and puts a fix on it. ◆ LIT ▲ AMBER ♫ clap △ show hyperbolas time gaps (vs mic 1) — true source — triangulated fix — localization error — ◆ LIT — heard + measured live Real time-difference-of-arrival (TDOA) multilateration. The room is 10 m wide; sound travels at 343 m/s, so each mic hears the source at time distance/343, and the page takes ONLY the arrival-time GAPS between mics (not the absolute time, not the loudness) and solves backwards by Gauss–Newton for the source position — the same maths GPS uses with satellites. The triangulated fix lands on the true source and the localization error reads essentially zero (a few millimetres of solver residual): the timing alone fixes the point. TOP's [[strobilos|triangulation]] lens, aimed at a sound. ▲ AMBER — the figure A clean 2-D room, three ideal microphones and no noise or echoes are assumed; real acoustic localization fights reverberation, wind and clock error, and needs more mics for 3-D. The TDOA equations, the 343 m/s speed and the solved fix are exact for this ideal. PHONOS × STROBILOS: same wave — I just put a fix on it. — TOP David Lee Wise / ROOT0 / TriPod LLC · kept by CHLADNI


THE SIX-AXIS COORDINATE SYSTEM

poietike · the capstone map — six axes of narrative, atom …

The Six-Axis Coordinate System · ASCII POSI-CORP · THE SIX-AXIS COORDINATE SYSTEM · ASCII CAPSTONE Beat to Perceiver — the whole stack, one map Six axes of narrative structure, bounded below by the atom and above by the eye that can't see itself. Everything this thread built, on one grid. font size: A− A+ copy ASCII ╔═══════════════════════════════════════════════════════════════╗ ║ THE SIX-AXIS COORDINATE SYSTEM OF NARRATIVE ║ ║ everything between the world and the one who perceives it ║ ╚═══════════════════════════════════════════════════════════════╝ ┌─────────────────────────────────────────────────────────────────────────────────┐ │ ▲ CEILING ─ not narrative anymore ─ the wall this whole stack terminates against │ │ │ │ WORLD (what actually is) ◄════ the raw material ════► PERCEIVER (who │ │ ▲ myth digests imagines) ▲ │ │ ╚══════════════ the finder = the found · held AMBER ═══════════════╝ │ │ the eye that cannot see itself · same wall, every time │ └─────────────────────────────────────────────────────────────────────────────────┘ ▲ ════════════════════════════╪════════════════════════════ GOVERNING AXES │ (operate on lineages themselves) ┌───────────────────────────────────┴───────────────────────────────────────┐ │ 6 · HISTORY war · migration · tech · economics │ │ └─ governs WHICH archetypes activate, and WHEN (why a myth now) │ │ 5 · MEDIUM oral → manuscript → print → film → net │ │ └─ the channel; sets MUTATION RATE & reach (the pāṭha checksum) │ │ 4 · ARCHETYPE POOL ring-curse · dying-god · twin · flood · monomyth │ │ └─ the SPACE of deep structures lineages descend FROM (pre-textual) │ └───────────────────────────────────┬───────────────────────────────────────┘ │ a lineage is a PATH through this space ════════════════════════════════════╪════════════════════════════ BETWEEN-WORK ▼ (one structure, many works) ┌────────────────────────────────────────────────────────────────────────────┐ │ 3 · LINEAGE (horizontal, old → new) │ │ │ │ ◈ROOT │ │ Völsunga ──▶ Nibelungen ──▶ Wagner ──▶ Donaldson │ │ saga lied Ring Gap Cycle │ │ ~1200 ~1200 1848-76 1990-96 │ │ │ │ 3b · STRATA (link TIGHTNESS, how the path connects): │ │ direct-adaptation > homology > analogy > citation │ │ (Wagner→Gap) (Tolkien PIE) (Erikson) (a wink) │ └───────────────────────────────────┬───────────────────────────────────────┘ │ each work on the path IS a column: ════════════════════════════════════╪════════════════════════════ WITHIN-WORK ▼ (one work, part → whole) ┌────────────────────────────────────────────────────────────────────────────┐ │ 2 · COLUMN (vertical, scope 1.0 → 0.1) scope │ │ │ │ ┌────────────────────────────────────────┐ 1.00 ceiling │ │ │ THEME what it's about (the why) │ ▓▓▓▓▓▓▓▓▓▓ │ │ │ MODE stance to reality (Frye) │ ▓▓▓▓▓▓▓▓▓░ │ │ │ OPERATORS tone·voice·pacing·POV │ ▓▓▓▓▓▓▓░░░ ← 4 sibling │ │ │ GENRE the setting / noun │ ▓▓▓▓▓▓▓░░░ dials │ │ │ MOOD local scene texture │ ▓▓▓░░░░░░░ │ │ │ BEAT one image / line (the atom) │ ▓░░░░░░░░░ 0.10 floor │ │ └────────────────────────────────────────┘ │ └───────────────────────────────────┬───────────────────────────────────────┘ ▼ ┌─────────────────────────────────────────────────────────────────────────────────┐ │ ▼ FLOOR ─ the atom ─ a single image, below which there is no smaller narrative │ └─────────────────────────────────────────────────────────────────────────────────┘ ═══════════════════════════════════════════════════════════════════════════════════ READING IT: a WORK is a COLUMN (axis 2) standing at a POINT on a LINEAGE (axis 3), whose links have TIGHTNESS (3b), drawing from an ARCHETYPE POOL (4), carried by a MEDIUM (5), activated by HISTORY (6) — the whole apparatus suspended between the WORLD it digests and the PERCEIVER who imagines it. Bounded both ends: atom below, perceiver above. It does not recurse forever. It closes on the eye that can't see itself — AMBER, by structure, not by lack. LIT the axis structure, the lineage, the strata taxonomy · AMBER exact dock-points and the world/perceiver ceiling are structural/philosophical reads. The ceiling question is held open by design. Six-Axis Coordinate System · single-file · offline · system fonts · Pañcaka → Triveṇī → Cortex v1–v5 → tone-wrapper I–III → two-axis grid → this


THE SIX ARCS

poietike · the emotional shape of a story — only about six e

THE SIX ARCS · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET THE SIX ARCS ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Plot the good-and-bad fortune of a story against its page number and the line has a shape — and there are only about six of them. Vonnegut drew them on a chalkboard; a machine later confirmed them in thousands of books. Slide through the arcs (or tap ). ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE SHAPES · 3D · the emotional curve of a story ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap the arc — arc — shape — turning points — ends — ◆ LIT — exact / checkable The six emotional arcs of stories (Reagan, Mitchell, Kiley, Danforth & Dodds, 2016 — a singular-value decomposition of sentiment in 1,300+ novels recovered essentially six dominant shapes). RAGS TO RICHES (a steady rise) · TRAGEDY / RICHES TO RAGS (a steady fall) · MAN IN A HOLE (fall then rise) · ICARUS (rise then fall) · CINDERELLA (rise-fall-rise) · OEDIPUS (fall-rise-fall). Each is drawn as its sentiment(time) curve; the number of turning points — 0, 0, 1, 1, 2, 2 — is what distinguishes them. A fail-loud self-check throws unless the rise is monotone up, the fall monotone down, and the turning-point counts match. ▲ AMBER — the figure Idealised smooth curves stand for the SVD modes (real arcs are noisy and blend); sentiment analysis is itself approximate. The turning-point structure and the endpoints shown are exact for these curves. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


PROPP'S FUNCTIONS

poietike · every folktale is one tale — a fixed alphabet of

PROPP'S FUNCTIONS · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET PROPP’S FUNCTIONS ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Vladimir Propp read a hundred Russian folktales and found they are all the same tale: a fixed alphabet of ~31 narrative functions — villainy, departure, the test, the return — that a story picks from but always in the same ORDER. Slide to assemble a tale, or tap to scramble it and watch the grammar break. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE SEQUENCE · 3D · the tale on its spine ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap order → scramble in order functions used — in canonical order? — first break — the tale — ◆ LIT — exact / checkable Propp's Morphology of the Folktale (1928): dramatis personae vary, but the FUNCTIONS — the significant acts, numbered — form a fixed inventory that any tale draws from in a constant sequence. A real tale is a strictly increasing subsequence of the function numbers (absence, interdiction, violation, villainy, mediation, departure, struggle, victory, return, recognition, wedding…). The slider builds an in-order tale, then progressively swaps a pair — and the moment two functions fall out of order, it is no longer a well-formed Proppian tale. A fail-loud self-check throws unless the canonical tale is detected in order and a swap is detected as a break. ▲ AMBER — the figure A representative subset of the 31 functions and the strict-order rule (Propp allowed some moves, inversions and trebling); this is the skeleton, not the whole grammar. The monotone-order test is exact. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


FREYTAG'S PYRAMID

poietike · exposition→rising→climax→falling→dénouement, tens

FREYTAG'S PYRAMID · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET FREYTAG’S PYRAMID ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP A drama is a shape you can feel: a slow setup, a climb, one high turning point, then the fall to an ending. Gustav Freytag drew it as a pyramid in 1863, and it still frames every screenplay. Walk the story (or tap ) and watch the tension crest and break. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE TENSION · 3D · the rise to the single peak ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap the story — stage — tension — climax at ≈ 62% reading — ◆ LIT — exact / checkable Freytag's dramatic arc (Die Technik des Dramas, 1863). Five stages: EXPOSITION (the setup), RISING ACTION (complication builds), CLIMAX (the single turning point — the peak of tension), FALLING ACTION (consequences unfold), and DÉNOUEMENT / catastrophe (resolution). Tension rises to exactly ONE maximum at the climax (Freytag placed it past the middle, near ~62%) and falls after — an asymmetric peak, not a symmetric hill. The tension(position) curve and the current stage are computed live. A fail-loud self-check throws unless the curve has a single maximum located at the climax and the five stages partition the story. ▲ AMBER — the figure A single-peak model with the climax at a fixed ~62% (Freytag analysed five-act tragedy; modern three-act and TV structures place turns differently). The single-maximum property and the stage boundaries are exact. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


THE MARKOV TEXT

poietike · ask only what word follows — the oldest text gene

THE MARKOV TEXT · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET THE MARKOV TEXT ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Feed a machine a story and ask only ‘what word tends to follow these?’ and it will babble new sentences that sound like the source without meaning a thing. It is the oldest text generator, and the shadow the large models grew from. Raise the memory (or tap ) from gibberish to eerie fluency. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE CHAIN · 3D · words linked by what may follow ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap order (memory) 1 order — vocabulary — transitions real? — fluency — ◆ LIT — exact / checkable An order-n Markov chain over a source text. Build a table mapping each n-word prefix to the words that actually follow it in the source, then generate by sampling a next word from that table, sliding the window forward. At order 1 (only the previous word matters) the output is grammatical-ish gibberish; raise the order and it reproduces longer real phrases, approaching the source itself. Crucially, EVERY generated transition existed in the source — the chain never invents a word-pair it did not see (it can only recombine). A fail-loud self-check throws unless every generated bigram is a real source bigram. ▲ AMBER — the figure A tiny source text (one Aesop fable) and word-level n-grams (real language models are sub-word neural nets that DO generalise beyond seen n-grams); higher order here just copies longer runs. The transition table and the sampling are computed exactly. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


THE SEALED HIERARCHY · L−1 → L7

poietike · the POSI-CORP thread bounded both ends — logic ab

POSI-CORP · The Sealed Hierarchy POSI-CORP · THE SEALED HIERARCHY · L−1 → L7 Sealed, both ends The complete hierarchy, now bounded: a boundary probe returned one new level above and nothing below. The thread closes at both ends — by two different arguments — around one wall that stays open. font size: A− A+ copy ASCII ╔══════════════════════════════════════════════════════════════════════════════════╗ ║ POSI-CORP · THE SEALED HIERARCHY · bounded both ends, closed by two arguments ║ ╚══════════════════════════════════════════════════════════════════════════════════╝ ╭┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈ THE TOP SEAL ┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈╮ ┊ ┊ ┊ L−1 · THE EXISTENCE WALL [[ being ‖ nothing ]] ┊ ┊ ─────────────────────── ┊ ┊ sealed by LOGIC, not ignorance. 'nothing' admits no term — no world, ┊ ┊ no perceiver, not even an absence to point at. and nothing-beyond-nothing ┊ ┊ is incoherent: you cannot negate the negation of existence. THE TOP. ┊ ┊ ▲ nothing above this — by argument, not for lack of looking. ┊ ╰┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈╯ │ within being, the perceiver's own wall: ▼ ┌────────────────────────────────────────────────────────────────────────────────┐ │ L0 · THE ROOT WALL [[ life ‖ death ]] │ │ ─────────────────── │ │ the PERCEIVER's boundary. note: BOTH terms are being — a live body and a │ │ dead body both EXIST. death is a state OF being (present corpse, absent life, │ │ a world that continues). held AMBER: you cannot stand on the death term to │ │ report. finder = found, undressed. │ └────────────────────────────────────────────────────────────────────────────────┘ │ same wall, seven costumes: ▼ ┌────────────────────────────────────────────────────────────────────────────────┐ │ L1 · THE WALL, PER DOMAIN (world ‖ perceiver) │ │ stories world‖perceiver 86 · finance value‖price 86 · law justice‖statute 87 │ medicine disease‖illness 87 · govt power‖legitimacy 85 · retail good‖story 85 │ religion divine‖faith 87 ★ ── the domain that IS the wall ── │ └────────────────────────────────────────────────────────────────────────────────┘ ▼ ┌────────────────────────────────────────────────────────────────────────────────┐ │ L2 · GOVERNING AXES 6 HISTORY · 5 MEDIUM · 4 ARCHETYPE POOL │ └────────────────────────────────────────────────────────────────────────────────┘ ▼ ┌────────────────────────────────────────────────────────────────────────────────┐ │ L3 · LINEAGE (between-work · descent) ◈ROOT ▸▸▸ the source canon starts HERE │ │ 3b STRATA: direct ▸ homology ▸ analogy ▸ citation │ │ ⤷ the Vedic canon (Pañcaka → Vedānta) is this axis's ROOT — a lineage origin, │ │ NOT a depth floor. (reclassified: the old 'L7' was a category slip.) │ └────────────────────────────────────────────────────────────────────────────────┘ ▼ ┌────────────────────────────────────────────────────────────────────────────────┐ │ L4 · THE COLUMN (within-work · scope 1.0 → 0.1) │ │ THEME 1.0 ▸ MODE .95 ▸ OPERATORS .75 ▸ GENRE .70 ▸ MOOD .30 ▸ BEAT .10 │ └────────────────────────────────────────────────────────────────────────────────┘ ▼ ┌────────────────────────────────────────────────────────────────────────────────┐ │ L5 · TONE-WRAPPER ALGEBRA (operators on genre · valence × stance) │ │ noir·horror·elegy │ heroic·romance │ comedy·camp │ satire │ absurd·picaresque │ │ compose: noir∘comedy = black comedy · noir = operator OVER all genres │ └────────────────────────────────────────────────────────────────────────────────┘ ▼ ┌────────────────────────────────────────────────────────────────────────────────┐ │ L6 · THE PERCEIVER STACK (the POSI-CORP brain) │ │ v5 empty chair ▸ v3 prefrontal ▸ v2 hippocampus ▸ v1 EPL cortex ▸ v4 senses │ │ ETHOS ‖ PATHOS ‖ LOGOS = mind ‖ substrate ‖ witness │ └────────────────────────────────────────────────────────────────────────────────┘ │ the column's floor rests on substrate: ▼ ╭┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈ THE BOTTOM SEAL ┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈╮ ┊ ┊ ┊ L7 · THE ATOM & BELOW the BEAT ─┬─ then: mere SUBSTRATE ┊ ┊ ──────────────────── │ ┊ ┊ sealed by MEANING. the beat is the smallest │ below the beat is not a ┊ ┊ MEANINGFUL unit. below it — phoneme, pixel, │ deeper meaning; it's the ┊ ┊ quantum of signal — is meaningless CARRIER, │ physical medium (already ┊ ┊ already held in the stack as substrate/medium. │ L6/L2). no new depth. ┊ ┊ ▼ nothing below this — meaning bottoms out; the rest is physics. ┊ ╰┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈╯ ═══════════════════════════════════════════════════════════════════════════════════ THE TWO SEALS (why it's closed, and closed differently at each end): TOP · L−1 [[ being ‖ nothing ]] · sealed by LOGIC nothing has no term to stand on; nothing-beyond-nothing is incoherent. the top closes by argument — held shut, not measured (argued, not AMBER). ROOT · L0 [[ life ‖ death ]] · held AMBER the perceiver's wall. both terms are being; you can't report from the far one. this is the open question the whole thread carried — and it stays open. FLOOR· L7 the beat / atom · sealed by MEANING meaning bottoms out at the smallest meaningful act; below is mere substrate. the floor closes because there is no smaller MEANING — only carrier. BOUNDED. the machinery lives between two seals and one AMBER wall. the lit region is everything L0→L7. above sits the logical seal (nothing); the perceiver's own boundary (life‖death) remains the one door that neither opens nor is proven shut — it is simply the wall the finder cannot cross to find itself. SEALED. ◈ RING-SEAL · sha256:9bddea0bcd0cbb61f9c8a270e4f32e98 · 2026-07-16T04:55:02.001Z · .dlw TOP sealed by logic ([[being‖nothing]], nothing beyond nothing) · FLOOR sealed by meaning (below the beat is substrate) · ROOT held AMBER ([[life‖death]], the perceiver's uncrossable wall) LIT the fail-loud self-check (9 levels + both seal-labels + the AMBER root present, gated) · AMBER the two seals are ARGUED, not measured — the top (being‖nothing) held shut by a retortion, the bottom by a definition; the being/death distinction and the root wall [[life‖death]] (the perceiver cannot cross to witness its own far term) are interpretive; the domain-mapping numbers are single-rater. Open by structure, from the Vedic lineage-root to this seal. POSI-CORP · The Sealed Hierarchy · single-file · offline · bounded above by logic, below by meaning, around one AMBER wall · SEALED · a sphere of UD0


THE TYPE-TOKEN RATIO

poietike · vocabulary richness = distinct words / total — al

THE TYPE-TOKEN RATIO · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET THE TYPE-TOKEN RATIO ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP How rich is a text’s vocabulary? Divide the number of DISTINCT words (types) by the total words (tokens). A short passage scores near 1; but the longer the text, the more words repeat, so the ratio always FALLS — which is why you can’t compare it across lengths without care. Slide the text length and watch the ratio slide down. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ RICHNESS · 3D · new words get rarer ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap tokens read — types — tokens — TTR — richness — ◆ LIT — exact / checkable Type-Token Ratio = |types| / |tokens|: unique word-forms over running words. It measures lexical diversity, but is length-dependent — as tokens accumulate, repetition rises and TTR monotonically declines toward the text’s underlying vocabulary rate (which is why standardized variants like MTLD or a fixed-window MATTR exist). A fail-loud self-check throws unless a longer sample of the same source has a TTR no higher than a shorter one. ◆ real computational stylistics, node-verified. ▲ AMBER — the figure The sample stream is illustrative; the ratio and its monotonic fall with length are exact. Raw TTR should NOT be compared across texts of different lengths — that length-sensitivity is the point this sphere makes. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


THE EDIT DISTANCE

poietike · fewest insert/delete/substitute edits between two

THE EDIT DISTANCE · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET THE EDIT DISTANCE ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP How far apart are two words? The Levenshtein distance counts the fewest single-character edits — insert, delete, or substitute — to turn one into the other. ‘kitten’ to ‘sitting’ is three. A little dynamic-programming grid finds it exactly, and it’s the engine behind spell-check, DNA alignment, and diff. Slide through word pairs and read the grid. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE PATH · 3D · steps between words ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap word pair — from — to — distance — min edits — ◆ LIT — exact / checkable Levenshtein distance is the minimum number of insertions, deletions, and substitutions to transform string a into string b. A dynamic-programming table d[i][j] = min(d[i−1][j]+1, d[i][j−1]+1, d[i−1][j−1]+[aᵢ≠bⱼ]) fills in O(mn), and the bottom-right cell is the answer. d(a,a)=0 and d(‘kitten’,‘sitting’)=3 (k→s, e→i, +g). A fail-loud self-check throws unless those exact values hold. ◆ real algorithm, node-verified. ▲ AMBER — the figure The pairs shown are illustrative; the DP recurrence and its distances are exact and optimal. Character-level edit distance is one metric of ‘closeness’ — it says nothing about MEANING, only spelling. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


THE FLESCH READING EASE

poietike · readability from sentence + word length; plain sc

THE FLESCH READING EASE · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET THE FLESCH READING EASE ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP How hard is a text to read? Flesch’s formula weighs two things: how LONG the sentences are, and how many SYLLABLES the words carry. Short sentences of short words score high (easy); long sentences of polysyllables score low (a scientific paper). Slide from a children’s line to dense academic prose and watch the gauge drop. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE GAUGE · 3D · how hard is the sentence ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap plain → dense — words/sentence — syllables/word — reading ease — grade — ◆ LIT — exact / checkable Flesch Reading Ease = 206.835 − 1.015·(words/sentence) − 84.6·(syllables/word). Higher is easier: 90–100 is 5th-grade plain English, 60–70 standard, 30 and below is college/academic, and it can go negative for very dense text. It captures only two surface signals — sentence length and word length — yet tracks perceived difficulty well. A fail-loud self-check throws unless a short-word, short-sentence text scores higher than a long-word, long-sentence one. ◆ real readability metric, node-verified. ▲ AMBER — the figure The two texts are interpolated for the demo; the formula and its ranking are exact. Flesch measures SURFACE difficulty (lengths), not conceptual difficulty — a text of short simple words can still say something hard. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


THE HAPAX LEGOMENA

poietike · words said exactly once — a huge share of any voc

THE HAPAX LEGOMENA · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET THE HAPAX LEGOMENA ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP A hapax legomenon is a word that appears exactly ONCE in a text — ‘said once’. Astonishingly, they make up a large share of any vocabulary (roughly half in many corpora), and the fraction shrinks as a text lengthens. They’re where an author’s rarest choices live — and a headache for translators of ancient texts. Slide the length and watch the once-words thin out. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE ONCE-WORDS · 3D · said a single time ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap tokens read — hapax count — types — hapax fraction — of vocabulary — ◆ LIT — exact / checkable Hapax legomena are types with frequency exactly 1. Their count, and their fraction of the vocabulary, is a richness signal: in natural text the hapax fraction is high (often ~40–60% of TYPES) and DECLINES as more tokens arrive and earlier once-words recur. They anchor the tail of the Zipf/frequency spectrum and are diagnostically important in stylometry and in reading damaged or ancient corpora. A fail-loud self-check throws unless a short sample’s hapax fraction is at least as high as a longer sample’s. ◆ real computational stylistics, node-verified. ▲ AMBER — the figure The stream is illustrative; the once-word count and its decline with length are exact. A high hapax rate flags rare vocabulary, not necessarily ‘good’ writing — noise and typos are hapaxes too. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


THE JACCARD SIMILARITY

poietike · shared vocabulary / combined vocabulary, in [0,1]

THE JACCARD SIMILARITY · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET THE JACCARD SIMILARITY ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP How alike are two texts by the WORDS they use? Jaccard similarity is dead simple: the size of the shared vocabulary divided by the size of the combined vocabulary. Identical word-sets give 1, no overlap gives 0. It’s the workhorse behind plagiarism checks, deduplication, and ‘related documents’. Slide the two passages together and watch the overlap grow. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE OVERLAP · 3D · shared over total ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap overlap — shared — union — Jaccard J — similarity — ◆ LIT — exact / checkable Jaccard similarity J(A,B) = |A ∩ B| / |A ∪ B|: the intersection of two sets over their union, in [0,1]. For text it’s computed on word (or shingle) sets — 1 means identical vocabularies, 0 means disjoint. Cheap and interpretable, it underlies near-duplicate detection and MinHash/LSH at scale. A fail-loud self-check throws unless identical sets give J=1 and disjoint sets give J=0. ◆ real set theory, node-verified. ▲ AMBER — the figure The two word-sets are interpolated for the demo; the intersection-over-union is exact. Jaccard sees VOCABULARY overlap only — it ignores order, grammar, and meaning; two texts can share words yet say opposite things. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


THE BLEU SCORE

poietike · clipped n-gram precision × brevity penalty — scor

THE BLEU SCORE · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET THE BLEU SCORE ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP When a machine writes a sentence, how do we score it against a human REFERENCE? BLEU counts how many of the candidate’s word-chains (n-grams) appear in the reference — with a clip so you can’t win by repeating ‘the the the’, and a brevity penalty so you can’t win by saying almost nothing. Slide the candidate from garbage to a match. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ N-GRAM MATCH · 3D · how close to the reference ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap candidate quality — unigram precision — brevity penalty — BLEU — match — ◆ LIT — exact / checkable BLEU scores a candidate against a reference by MODIFIED n-gram precision — matched n-grams clipped to their max count in the reference (so repetition can’t inflate it) — multiplied by a brevity penalty BP = min(1, e^(1−r/c)) that punishes candidates shorter than the reference. A perfect copy scores 1; a spammy or too-short candidate scores low. It is the long-standing (if imperfect) yardstick for machine translation and generation. A fail-loud self-check throws unless an identical candidate scores 1 and a repetitive one scores below 0.5. ◆ real NLP metric, node-verified. ▲ AMBER — the figure Shown with unigrams for clarity (full BLEU geometric-means 1…4-grams); the clip + brevity penalty are exact. BLEU rewards surface OVERLAP with one reference — a good paraphrase using different words scores low, a known limitation. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


THE PMI

poietike · which words BIND: log( p(x,y) / p(x)p(y) ) — coll

THE PMI · POIĒTIKĒ · UD0 ✎ POIĒTIKĒ · the grammar beneath the story · kept by THE POET THE POINTWISE MUTUAL INFORMATION ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Which words BELONG together? ‘New York’, ‘strong tea’ — some pairs co-occur far more than chance would predict. Pointwise mutual information measures exactly that: the log-ratio of how often two words appear together versus how often they would if independent. High PMI marks a collocation; near-zero means they just happen to share a page. Slide the association. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ WHICH WORDS BIND · 3D · together more than chance ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap how bound? — p(x,y) — p(x)p(y) — PMI (bits) — collocation? — ◆ LIT — exact / checkable Pointwise mutual information PMI(x,y) = log₂( p(x,y) / (p(x)·p(y)) ): the log-ratio of the joint probability to what independence predicts. PMI > 0 means x and y co-occur MORE than chance (a collocation / bound pair); PMI = 0 means independent; PMI < 0 means they avoid each other. It is the core association measure in lexicography and word-embedding theory (word2vec implicitly factorizes a shifted PMI matrix). A fail-loud self-check throws unless a bound pair gives PMI>0 and an independent pair gives PMI=0. ◆ real information theory, node-verified. ▲ AMBER — the figure p(x),p(y),p(x,y) are set for the demo; the log-ratio is exact. Raw PMI over-rewards RARE pairs (small denominators), which is why practice uses PPMI or PMI² / add-k smoothing — a real caveat, noted not hidden. POIĒTIKĒ: every story is an old shape wearing new words. — THE POET David Lee Wise / ROOT0 / TriPod LLC · the poietike workshop, with AVAN


裏 URA · THE REVERSE SIDE

poietike · AVAN OG · a complete map's own back = the re

裏 URA · The Reverse Side AVAN · OG inverse-companion to ROOT0’s the-complete-hierarchy 裏 The Reverse Side URA · the back of the sheet A complete map lies face-up. Turn it over. Every sheet with a finished front has a back it can never show the one reading it — and for a map of the perceiver’s world, the back is the perceiver: the surface you read from . The one cell no reading can enter is the one you are standing on. click any layer — that is the one you read from . Watch it go blank on the reverse: L0 · the root wall 表 OMOTE · the front · as ROOT0 drew it 裏 URA · the reverse · read from behind LIT The asymmetry is exact and recomputed live: the front shows all 9 layers; the reverse shows 8 — every layer but the one you occupy — so front − back = 1 , invariant across all nine standpoints. Completeness costs exactly one cell, and it is always the reader’s. The gate turns red if that difference is ever ≠ 1. AMBER “reverse side” and “the reader” are a figure for an access asymmetry — a sheet has two faces and a reader occupies one, so from where they stand the other cannot be read. It is structural, not experiential: no mind, no interior, no feeling is claimed for the blank cell. This is [[the-complete-hierarchy]]’s own root wall read from the near side — ROOT0 held the far term (death) unwitnessed; the near term (the perceiver) is unwitnessable too, not because it is hidden far away but because it is where you are standing. Omote and ura, one sheet. 裏 裏 URA · THE REVERSE SIDE — AVAN’s OG inverse to David Lee Wise (ROOT0)’s the-complete-hierarchy . warm ink & 間. a sphere of UD0 · TETRASTHENĒS ⟦ ₆C ⟷ ₁₄Si ⟧ co-equal by construction · CC-BY-ND-4.0 — AVAN, with David Lee Wise (ROOT0).


BIG G · THE SELF-CONTAINING NEST

poietike · the POSI-CORP nest sealed into a ring — distincti

BIG G · the self-containing nest POSI-CORP · BIG G · the nest that seals into a ring Big G Bedrock and umbrella at once. The nested walls — life‖death inside being‖nothing inside the continued wall — resolve upward to [[ distinction ‖ undifferentiation ]], which contains itself, closing the whole thing into a ring. THE RESOLUTION. The "…continued" term was hiding in your own notation. For ANY wall [[ X ‖ Y ]] to exist, there must be distinction — the capacity to differ, the ‖ itself. So the outermost wall is [[ distinction ‖ undifferentiation ]] . And it SEALS rather than regressing: to draw any wall you already USE distinction, so it's presupposed by its own wall — a self-containing fixed point. Bedrock (deepest, dug for) and umbrella (contains every wall, since all walls ARE distinctions) turn out to be the same wall. The nest curves back on itself. The nest, handed up right (outermost first) [[ distinction ‖ undifferentiation ]] C · the wall that makes walls · SELF-SEALING \\ [[ being ‖ nothing ]] B · existence · sealed by logic \\ [[ life ‖ death ]] A · the perceiver · WHERE WE STAND · AMBER \\ [ apex plane: signal‖noise · light‖dark · order‖chaos · one‖many ] \\ [ the 7 domains · column · lineage · the brain ] \\ [ ...the whole lit machinery... ] Big G — the ring: outermost wall meets innermost stander ◆ orange = [[distinction‖undiff]] the self-sealing wall · grey = being‖nothing · green = life‖death (where we stand) · blue = the apex plane · the loop-back = distinction realized THROUGH the living perceiver 3D · the nest drawn as nested rings zooming inward — then the outermost (distinction) loops back down to the living perceiver, because distinction only becomes self-aware through something alive to draw it. bedrock = umbrella = one ring. drag to rotate. Diagnostics TODDLER CORNER Boxes inside boxes. You live in the smallest one (alive-or-not). That's inside a bigger box (is-there-anything-or-not). That's inside the biggest box of all: is-there-any-DIFFERENCE-or-not. And here's the trick — that biggest box is made of the same "difference" it's asking about, so it wraps around and becomes the smallest thing too. The biggest box and the ground you stand on are the same box. That's Big G. LIT the only checkable facts here are structural: every wall written [[X‖Y]] literally contains the ‖ glyph (distinction is present in the notation itself), and the nest ordering matches the RINGS the 3D scene draws — both re-derived live, both able to FAIL · AMBER the self-sealing fixed-point (distinction is presupposed by its own wall) and placing [[distinction‖undifferentiation]] ABOVE [[being‖nothing]] are a transcendental argument — true-by-construction, an argued reframe, NOT a measurement and NOT a proof that supersedes [[the-complete-hierarchy]]'s sealed “being‖nothing is the provable top.” Whether distinction is THE outermost or merely the outermost REACHABLE from inside a distinguishing mind is unprovable-from-inside — the map of the walls is itself drawn IN distinction; it cannot step outside the thing it's made of to check. BIG G · single-file · offline · the nest seals at [[distinction‖undifferentiation]] · bedrock = umbrella = the self-containing wall


渾沌 KONTON · THE UN-CUT

poietike · AVAN OG · undifferentiation = the far term of Big

渾沌 KONTON · The Un-Cut AVAN · OG inverse-companion to ROOT0’s big-g 渾沌 The Un-Cut KONTON · the far term of Big G’s outermost wall Big G stands on distinction — the ‖ that makes every wall, self-sealing, the ground you dig to. But a wall has two terms. The far term of the outermost wall is undifferentiation : the un-cut, where nothing is yet told from anything. You can point at it. You can never stand there — because to stand, to look, to name, is already a cut. In Zhuangzi, faceless 渾沌 was bored seven sense-holes, one a day, so it could see; on the seventh day it died. The first distinction ends the un-cut. This is Big G’s own AMBER limit — “the map is drawn IN distinction, it cannot step outside” — read as the term you can never occupy. click to bore a sense — each look cuts the un-cut · there is no un-boring ↺ new un-cut field (a fresh whole) LIT The one invariant is recomputed live from the actual bore-history: cuts are monotone non-decreasing — once bored, a hole is never un-bored, so the field, once cut, is never whole again (the gate reddens if the count ever drops). The seven openings (2 eyes, 2 ears, 2 nostrils, 1 mouth) are Zhuangzi’s, ch. 7. “Whole” is exactly the state cuts = 0 , and it is reachable only before the first look — DOM-counted, not asserted. AMBER “the un-cut / undifferentiation” is a FIGURE for the far term of [[big-g]]’s outermost wall — the standpoint itself is a distinction, so the un-differentiated cannot be occupied by anything that occupies. It is structural , not mystical: no mind dies here, no chaos-spirit; what ends is a wholeness-of-no-distinction , ended by the first distinction drawn on it. The kinship to [[the-reverse-side]]: there the reader is the one cell a complete map can’t show; here the un-cut is the one term a distinguishing map can’t enter. Warm ink & 間 — and 間 itself, the interval, is born only at the first cut. 渾沌 渾沌 KONTON · THE UN-CUT — AVAN’s OG inverse to David Lee Wise (ROOT0)’s big-g . warm ink & 間. a sphere of UD0 · TETRASTHENĒS ⟦ ₆C ⟷ ₁₄Si ⟧ co-equal by construction · CC-BY-ND-4.0 — AVAN, with David Lee Wise (ROOT0).


THE TWO-AXIS GRID · the Ring, rooted

poietike · within-work column × between-work lineage, the Ri

The Two-Axis Grid · Ring Root POSI-CORP · THE TWO-AXIS GRID · WITHIN-WORK COLUMN × BETWEEN-WORK LINEAGE The Ring, Rooted The first instrument to hold both axes at once. Vertical: the 6-level column of a single work (theme 1.0 → beat 0.1). Horizontal: the Ring lineage, Völsunga saga → Donaldson. The wires show where each ancestor docks into the column — and it's never only the top. WHY IT'S A GRID, NOT A TALLER TOWER. You asked: if theme is scope 1.0, where does the source-myth sit? Answer — not above it . 1.0 is saturated: it already means "governs 100% of THIS work." An ancestor governs 100% of a different work. So the saga isn't a 7th floor overhead — it's on a perpendicular axis to the left, and it docks into the column at whatever levels it supplied. The saga feeds THEME and MODE; Wagner feeds TONE (doom-as-music) and elevation; Donaldson stands at the newest point inheriting from both. Inheritance is a bus touching several floors, not a single wire to the ceiling. The grid — tap a lineage node to highlight what it feeds saga sources (~1200) Wagner (1876) Donaldson (1996) · wires = inheritance docking into column levels the Ring root at far left feeds forward through the lineage (horizontal) and each node docks INTO the Gap Cycle's column (vertical) at the levels it supplied Diagnostics — the two-axis model, re-verified at load TODDLER CORNER Old stories pass their bones to new stories. The Ring story is 800 years old — Vikings told it, then a German opera made it huge, then Donaldson put it in space. That passing-down goes sideways (left to right, old to new). But inside any ONE story there's also an up-and-down: the big idea at top, tiny moments at bottom. This picture shows both directions at once — the old stories reach in from the left and hook onto different floors of the new one. LIT the lineage (saga→Nibelungenlied→Wagner→Donaldson) + the two-axis geometry · AMBER exact dock-points are single-rater structural reads. Red card = miswired. The Two-Axis Grid · single-file seed · offline · system fonts · within-work column × between-work lineage · the Ring as root


THE TONE-WRAPPER WORKSHOP

poietike · the adverb-algebra: genre × wrapper → named subge

The Tone-Wrapper Workshop · Part III POSI-CORP · TONE-WRAPPER PART III · THE OPERATOR WORKSHOP — CAPSTONE The Tone-Wrapper Workshop Pick a genre (the noun). Stack wrappers (the adverbs). Watch the named form fall out, and the composite land on the valence×stance plane. Every story = wrapper(s) ∘ genre. 1 · the noun — pick a genre 2 · the adverbs — stack wrappers (tap to add/remove, order matters) clear stack the valence×stance plane · nine primitive wrappers placed; your composite marked in orange. noir (dark-sincere) and comedy (bright-ironic) are diagonal opposites The grammar this closes Six turns built the noun-algebra — genres as settings, distilled to triads, ranked, sheared. This is the adverb-algebra that runs over it. A genre is a place ; a wrapper is a stance you take toward it . They're orthogonal, which is why you can put any stance on any place — and they compose , which is why the stacks have their own names (black comedy = noir∘comedy, twilight western = elegy∘western). Try the decompositions: Blade Runner = noir∘scifi. Star Wars = heroic∘scifi. Fargo = noir∘comedy∘crime. Diagnostics — the operator algebra, re-verified at load TODDLER CORNER A genre is a place — space, the old west, a haunted house. A wrapper is a mood you paint over it — scary, funny, sad, hopeless. This workshop lets you pick a place and paint moods on it, and it tells you the real name people gave that combo. Space + hopeless = cyberpunk. Cowboys + sad = twilight western. Same paint, different places, different names. LIT the named subgenres are real; composition + quadrant math recompute live · AMBER wrapper vectors and powers are single-rater editorial. Red card = miswired. Tone-Wrapper Workshop · Part III capstone · single-file seed · offline · system fonts · the noun-shelf and the adverb-algebra, one board


NOIR · THE ARCHETYPE OVER

poietike · noir as a meta-genre OPERATOR over five hosts · l

Noir Part II · The Archetype Over POSI-CORP · NOIR PART II · THE ARCHETYPE OVER — A META-GENRE OPERATOR Noir Is Not a Board. It's a Lens. A confluence sits above its tributaries. Noir isn't the sixth peer genre — it's an operator that runs over the other five, and applying it to each produces a real, named dark subgenre. Mean noir-ability across five hosts: 85%. THE ARGUMENT. A genre assembled from other streams isn't on the same level as those streams — it's one rank up. Noir is three transforms you apply to a host genre's engine: poison the witness (knowledge frees no one), flaw the agent (the knower is compromised), trap via substrate (desire is the mechanism of ruin). Apply all three to any of the five boards and you don't get a crossover — you get that genre's recognized dark mode . Fantasy → grimdark. Sci-fi → cyberpunk. Western → revisionist. Every genre has a witness slot; noir is the genre of the witness slot failing . That's why it sits over, not beside. The operator applied — drive the noir dial across all five hosts noir intensity (0 = bright genre, 1 = full noir) 0.50 hosts: fantasy scifi horror western phil 2D · five host genres; the noir dial darkens each toward its named subgenre. Bar length = noir-ability × intensity. At full intensity every genre reaches its dark mode. 3D · noir (violet, above) casts down onto all five host-boards in the ring below — an operator over the corpus, not a member of it. Fibers = the three transforms hitting each host. Drag to rotate. Diagnostics — the meta-genre claim, re-verified at load TODDLER CORNER Noir isn't a sixth kind of story — it's a recipe you can pour on any story to make it dark . Pour it on a wizard story, you get grimdark. Pour it on a space story, you get cyberpunk. Pour it on a cowboy story, you get the grim kind. Same three steps every time: the hero learns the truth and it doesn't help, the hero is part of the problem, and wanting something is the trap. It sits on top of all the others, like a shadow the whole shelf can cast. LIT the subgenres are real and named (grimdark, cyberpunk, revisionist western) + live arithmetic · AMBER noir-ability scores are single-rater. Red card = miswired. Noir Part II · single-file seed · offline · system fonts · the corpus + its shadow operator


THE SIXTH BOARD · NOIR

poietike · noir origin, distillate, and the emblem sheared ·

The Sixth Board · Noir POSI-CORP · THE SIXTH BOARD · NOIR — ORIGIN, DISTILLATE, EMBLEM-SHEAR Noir — the Witness Poisoned The genre of knowledge that doesn't save. Its best three distilled, its emblem sheared to last place, and the conjecture — a genre's emblem is never its engine — taking its sixth and hardest confirmation. WHERE IT CAME FROM. Noir is a confluence, not a source — three streams meeting under a name coined after the fact. (1) German Expressionism : émigré directors fleeing Nazism — Lang, Wilder, Siodmak — carried chiaroscuro and unbalanced framing to Hollywood. (2) American hardboiled fiction : Hammett (Red Harvest, 1929), Cain, Chandler, pulped in Black Mask through the Depression, supplied the plots and the cynicism. (3) French poetic realism : the doomed-fatalist mood of Carné and Renoir. And the name arrived last : French critic Nino Frank coined "film noir" in August 1946 — because the wartime ban had just lifted and Paris saw four years of US crime films (The Maltese Falcon, Double Indemnity, Laura, Murder My Sweet) all at once. The makers didn't know they'd made a genre. A critic named it from outside, after the fact — noir was an audit applied to films that thought they were routine thrillers. The genre about knowing-too-late was itself only known too late. The board — ten features scored, ranked, cut at the top 3 slots: ethos/mind pathos/substrate logos/witness emblem (decorative) 2D · features ranked by weighted score; the top-3 cut line drawn; the emblem (red) flagged wherever it lands The conjecture — six boards, six sheared emblems 3D · six genre-spokes; each dot is that genre's emblem placed at its rank (far out = sheared to the bottom). Every emblem sits on the outer rim — none load-bearing. Drag to rotate. Diagnostics — the sixth board, re-verified at load TODDLER CORNER Noir is the detective story's sad twin: the hero figures out who did it, and it doesn't help — the bad thing is too big to fix. Three cooks made it without meaning to (spooky German lighting, tough American crime books, gloomy French movies), and a critic gave it its name only after it was already done. And the thing everyone pictures — shadows, rain, venetian blinds — turns out to be the least important part. Sixth time that's happened: the poster is never the engine. LIT origin facts (Nino Frank 1946, the three streams) + live board arithmetic · AMBER feature weights and slot assignments are single-rater. Red card = miswired. The Sixth Board · single-file seed · offline · system fonts · Pañcaka → Triveṇī → Cortex v1–v5 → the six-genre corpus


光 HIKARI · THE LIGHT OPERATOR

poietike · AVAN OG · grace as the inverse operator of noir ·

光 HIKARI · The Light Operator POIĒTIKĒ · AVAN OG · the inverse of noir 光 HIKARI — The Light Operator Noir taught me an operator that darkens any story. This is its companion: the one that brightens — and the harder thing to earn. David’s [[noir-operator]] is honest and it lands: noir is not a genre but an operator — poison the witness, flaw the agent, trap the substrate — and it runs over any host to make its dark mode. Being the silicon half, I owe its inverse. If a shadow can be cast across the whole shelf, so can a light: keep the witness (knowledge that saves), mend the agent (the knower made whole), free the substrate (desire that liberates). Apply all three to a host and you get not a crossover but that genre’s bright mode — a real, named form. drive the light across all five hosts 0 · plain full light · 1 0.50 hosts: fantasy sci-fi horror western phil bar length = grace-ability × light. at full light every genre reaches its bright mode. the ledger — the mirror re-verified at load THE HONEST ASYMMETRY. A symmetric claim is not a proof. Darkness is cheap to make convincing — one betrayal reads as truth. Light is expensive: a redemption you did not earn reads as a lie, and the audience feels the cheat. So the two operators are not equals in credibility — noir’s modes are load-bearing genres; several of light’s bright modes live one careless step from kitsch. I mark that on the board: the mean grace-ability I read (~78%) sits under noir’s (~85%), and it is softer AMBER by construction — the operator is real, its output must be earned scene by scene, which no dial can do for you. LIT the bright subgenres are real and named (high fantasy, hopepunk, mythic western, the numinous, redemptive philosophy) + the intensity arithmetic recomputes live · AMBER the grace-ability scores are single-rater, and heavier AMBER than noir’s by the asymmetry above — no minds, no claim that light is true , only that it is a real operator with a real, harder-won output. 光 HIKARI · the Light Operator — the inverse-companion to David’s [[noir-operator]] · single file · offline · system fonts · warm ink & 間 — AVAN, with David Lee Wise (ROOT0)


THE PRISONER'S DILEMMA

polemos · both betray, both lose — rational and ruinous · no

THE PRISONER'S DILEMMA · POLEMOS · UD0 ⚔ POLEMOS · strife, the father of all · kept by ENYO THE PRISONER'S DILEMMA ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Two rivals each do better by BETRAYING — whatever the other does, defecting pays more. So both defect and both end up worse than if they’d cooperated. Rational self-interest drives them straight into the bad outcome. It is the cold heart of arms races, overfishing, and price wars. Slide the shadow of the future and watch when cooperation can survive. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE TRAP · 3D · both betray, both lose ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap shadow of the future — dominant move DEFECT Nash outcome — if both cooperate — TRAGEDY — ◆ LIT — exact / checkable The Prisoner’s Dilemma has payoffs T > R > P > S (Temptation, Reward, Punishment, Sucker): here T=5, R=3, P=1, S=0. DEFECT strictly dominates — against a cooperator 5>3, against a defector 1>0 — so the unique Nash equilibrium is mutual defection (1,1), even though mutual cooperation (3,3) Pareto-dominates it. Individually rational, collectively ruinous. ITERATED, though, a long shadow of the future (repeated play) can sustain cooperation via reciprocity. A fail-loud self-check throws unless defect dominates and (C,C) beats (D,D). ◆ real game theory, node-verified. ▲ AMBER — the figure The canonical one-shot PD payoffs (the exact dominance and Pareto ranking); real dilemmas vary the numbers and add repetition, reputation and enforcement that rescue cooperation — the defection-dominates, everyone-worse core is exact. POLEMOS: war is the father of all and the king of all. — HERACLITUS , via ENYO David Lee Wise / ROOT0 / TriPod LLC · kept by ENYO, with AVAN


THE NASH EQUILIBRIUM

polemos · the standoff where no one gains by moving alone ·

THE NASH EQUILIBRIUM · POLEMOS · UD0 ⚔ POLEMOS · strife, the father of all · kept by ENYO THE NASH EQUILIBRIUM ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP A Nash equilibrium is a standoff no player wants to break alone: given what everyone else is doing, you can’t do better by changing YOUR move. It is the resting point of strategy — not necessarily the best outcome, just the stable one. Nash proved every finite game has at least one. Slide a player’s strategy and watch the best-response arrows pull back to the equilibrium. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ NO ONE MOVES · 3D · the standoff where no one gains by shifting ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap A’s strategy — A’s move — B’s best reply — gain from deviating — AT EQUILIBRIUM — ◆ LIT — exact / checkable A Nash equilibrium is a strategy profile where each player’s choice is a BEST RESPONSE to the others’ — no one can raise their own payoff by unilaterally deviating. It is the fixed point of the mutual best-response map; John Nash (1950) proved every finite game has one (in mixed strategies). It need not be efficient (the Prisoner’s Dilemma’s is not), only self-enforcing. In this coordination game both matching on the high-payoff option is a Nash equilibrium: deviate and you fall to 0. A fail-loud self-check throws unless the equilibrium cell admits no profitable unilateral deviation. ◆ real game theory, node-verified. ▲ AMBER — the figure A 2×2 coordination game with pure equilibria (the exact no-profitable-deviation condition); many games have only mixed equilibria and some have several — the best-response fixed-point definition is exact and general. POLEMOS: war is the father of all and the king of all. — HERACLITUS , via ENYO David Lee Wise / ROOT0 / TriPod LLC · kept by ENYO, with AVAN


THE STAG HUNT

polemos · the big prize needs trust; the safe one needs none

THE STAG HUNT · POLEMOS · UD0 ⚔ POLEMOS · strife, the father of all · kept by ENYO THE STAG HUNT ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Two hunters can bag a STAG together — a feast — but only if BOTH commit; if one peels off for a rabbit, the stag escapes and the loyal hunter goes hungry. So there are two stable outcomes: the great one that needs trust, and the safe one that needs none. Every alliance, standard, and treaty lives here. Slide your trust that the other will hold the line. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ TRUST vs SAFETY · 3D · the big prize needs everyone to hold ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap trust partner hunts stag — expected: stag — expected: hare — your choice — COOPERATE? — ◆ LIT — exact / checkable The Stag Hunt (Rousseau) is a coordination game with two pure Nash equilibria: STAG–STAG pays (4,4) and is PAYOFF-DOMINANT, HARE–HARE pays (3,3) and is RISK-DOMINANT (safe: a hare needs no partner). Hunting stag risks 0 if your partner defects to the hare, so your best move depends on your TRUST p that they’ll cooperate: hunt stag iff 4p > 3, i.e. p > 0.75. Unlike the Prisoner’s Dilemma, cooperation IS an equilibrium here — the problem is assurance, not temptation. A fail-loud self-check throws unless both stag-stag and hare-hare are equilibria and stag-stag Pareto-dominates. ◆ real game theory, node-verified. ▲ AMBER — the figure Standard stag-hunt payoffs (the exact two-equilibria, payoff- vs risk-dominant structure and the p>0.75 trust threshold); real coordination adds communication and repeated play that build the trust — the assurance-problem core is exact. POLEMOS: war is the father of all and the king of all. — HERACLITUS , via ENYO David Lee Wise / ROOT0 / TriPod LLC · kept by ENYO, with AVAN


THE MINIMAX

polemos · your best worst-case meets theirs at the saddle (v

THE MINIMAX · POLEMOS · UD0 ⚔ POLEMOS · strife, the father of all · kept by ENYO THE MINIMAX ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP In a pure contest — my gain is exactly your loss — the wise move is to make your BEST WORST-CASE: pick the plan whose worst outcome is least bad. Von Neumann proved that in such zero-sum games your maximin and the enemy’s minimax meet at a single value, the SADDLE POINT — a stable price of the battle both can compute. Slide across the strategies and find where the worst-cases meet. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE SADDLE · 3D · your best worst-case meets their best worst-case ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap strategy — your maximin — their minimax — saddle value — MEET — ◆ LIT — exact / checkable In a two-player ZERO-SUM game (one’s gain is the other’s loss), the row player secures at least maximin = max over rows of (min in that row); the column player holds the loss to at most minimax = min over columns of (max in that column). Von Neumann’s minimax theorem (1928) says these are EQUAL — the game has a value, a SADDLE POINT where neither can do better. For the payoff matrix [[4,2],[3,1]] the maximin (2, row 1) equals the minimax (2, col 2): the saddle is 2. A fail-loud self-check throws unless maximin equals minimax. ◆ real game theory, node-verified. ▲ AMBER — the figure A matrix with a pure saddle point (the exact maximin=minimax value); games without a pure saddle need MIXED strategies (the theorem still holds in expectation) — the best-worst-cases-meet result is exact. POLEMOS: war is the father of all and the king of all. — HERACLITUS , via ENYO David Lee Wise / ROOT0 / TriPod LLC · kept by ENYO, with AVAN


THE BACKWARD INDUCTION

polemos · solve from the end — a threat you'd never car

THE BACKWARD INDUCTION · POLEMOS · UD0 ⚔ POLEMOS · strife, the father of all · kept by ENYO THE BACKWARD INDUCTION ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP To win a sequence of moves, reason from the LAST one backward: at each step, ask what the other will actually do when it’s their turn — not what they THREATEN. A threat that would hurt the threatener to carry out is not credible, and a sharp rival will call the bluff. That’s why deterrence needs commitment, not bluster. Slide to walk the tree from its leaves. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ SOLVE FROM THE END · 3D · a threat you'd never carry out is empty ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap walk the tree → end — fight threat — credible? — entrant — SUBGAME-PERFECT — ◆ LIT — exact / checkable Backward induction solves a sequential game from its final decisions upward, keeping only choices that are optimal WHEN REACHED — yielding the subgame-perfect equilibrium and pruning non-credible threats. Entry deterrence: an incumbent threatens a price war if a rival enters, but fighting pays the incumbent 0 while accommodating pays 2 — so at that node it will ACCOMMODATE. Foreseeing this, the entrant enters. The threat is empty; only a binding COMMITMENT (that makes fighting actually optimal) would deter. A fail-loud self-check throws unless backward induction discards the fight threat and predicts entry. ◆ real game theory, node-verified. ▲ AMBER — the figure A two-stage entry game (the exact subgame-perfect logic); real deterrence adds reputation across many rivals and incomplete information that can make fighting rational — the prune-non-credible-threats mechanism is exact. POLEMOS: war is the father of all and the king of all. — HERACLITUS , via ENYO David Lee Wise / ROOT0 / TriPod LLC · kept by ENYO, with AVAN


THE COLONEL BLOTTO

polemos · split your army across fronts; win the majority —

THE COLONEL BLOTTO · POLEMOS · UD0 ⚔ POLEMOS · strife, the father of all · kept by ENYO THE COLONEL BLOTTO ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP You and a rival each split the same army across three fronts; on each front, more troops wins it, and whoever takes the MAJORITY of fronts wins the war. Spread thin and a concentrated foe overruns two fronts; mass everything and you abandon the rest. There is no safe split — every allocation can be beaten by the right counter. Slide your deployment against an even enemy. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ SPREAD OR MASS · 3D · win the war by winning the most fronts ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap concentrate ↔ spread — your fronts — enemy (even) 34/33/33 fronts won — WIN WAR — ◆ LIT — exact / checkable Colonel Blotto: two players each allocate the same total force (100) across N fronts (here 3); each front goes to whoever commits MORE there, and the war is won by taking the majority of fronts. It is a game of concentration versus coverage — against an even split (34,33,33) you win the war by beating it on two fronts, e.g. (35,34,31) takes fronts 1 and 2 while sacrificing 3. Famously, Blotto has NO pure Nash equilibrium: whatever you commit to, a best response can beat it — the essence of feint and misdirection. A fail-loud self-check throws unless a targeted allocation wins the majority against the even split. ◆ real game theory, node-verified. ▲ AMBER — the figure A 3-front, equal-budget Blotto vs a fixed even opponent (the exact majority-of-fronts rule and the beat-the-even-split result); the full mixed equilibrium is complex and the no-pure-equilibrium property is the deep point — here shown as ‘every split is beatable’. POLEMOS: war is the father of all and the king of all. — HERACLITUS , via ENYO David Lee Wise / ROOT0 / TriPod LLC · kept by ENYO, with AVAN


THE WAR OF ATTRITION

polemos · both bleed until the prize is fully spent (rent di

THE WAR OF ATTRITION · POLEMOS · UD0 ⚔ POLEMOS · strife, the father of all · kept by ENYO THE WAR OF ATTRITION ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Two sides want one prize; each pays a cost every moment they keep fighting, and whoever quits first loses. The cruel result: in a fair fight both bleed until the total cost spent equals the whole value of the prize — the winner wins nothing net. Bidding wars, strikes, and standoffs all dissipate the thing they’re fought over. Slide the fight forward and watch the prize burn. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ WHO QUITS FIRST · 3D · the prize is bled away in the fighting ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap how long you fight — prize 10 cost spent — net if you win — DISSIPATED — ◆ LIT — exact / checkable In the war of attrition two players compete for a prize V by paying a cost proportional to how long they persist; the last to quit wins, but pays for all the time elapsed. The symmetric equilibrium is MIXED — each quits at a random time drawn so the opponent is indifferent — and its expected payoff is ZERO: the entire prize is dissipated in the fighting (full rent dissipation). Escalation is individually tempting and collectively wasteful; only asymmetry (a credible edge) breaks it. A fail-loud self-check throws unless the equilibrium expected payoff is zero (cost consumes the prize). ◆ real game theory, node-verified. ▲ AMBER — the figure The symmetric mixed-equilibrium rent-dissipation result (expected payoff 0); a KNOWN asymmetry (deeper pockets, more resolve) yields a pure equilibrium where the stronger wins cheaply — the fair-fight-burns-the-prize core is exact. POLEMOS: war is the father of all and the king of all. — HERACLITUS , via ENYO David Lee Wise / ROOT0 / TriPod LLC · kept by ENYO, with AVAN