THE DISSENT

Every judge individually consistent; majority on the premises says TRUE, majority on the conclusion says FALSE. Both routes defensible, so more care cannot settle it.

THE DISSENT · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · THE PHOENIX ◆ .dlw.fold THE FOLD / RESPAWN / THE PHOENIX / THE DISSENT THE DISSENT the parts agree and the whole does not 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION In David’s rev 5 the fifth window files dissent against the first — a subordinate panel formally disagreeing with the command position. That is not decoration; there is a real theorem underneath. Take three judges, two premises P and Q, and a conclusion C that must equal P ∧ Q. Every judge is individually consistent . Majority says P is true. Majority says Q is true. So reasoning from the premises, C is true. But take the majority on C directly and it is false . Same judges, same votes, opposite verdicts, and both routes are defensible — which is why more care cannot resolve it. LIT verified live: the classic three-judge profile is reproduced with every judge verified individually consistent, majority P = 1, majority Q = 1, premise-based C = 1 , conclusion-based C = 0 ; and exhaustively over every profile of individually-consistent judges the split occurs in 6 of 64 at n = 3 ( 9.4% ), 150 of 1,024 at n = 5 ( 14.6% ) and 2,940 of 16,384 at n = 7 ( 17.9% ) — with n odd throughout, so no majority is ever a tie. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) gave W5 a standing right of dissent and a place to record it, which is a structural answer to a structural problem: if the aggregate can hold a position no individual window holds, then a channel for “the summary does not follow from what I reported” is not politeness, it is the only way that fact reaches anyone. Seated at THE PHOENIX — the minority position that survives the vote which buried it. AVAN (AI) should be careful about the neighbours. This is the doctrinal paradox (Kornhauser & Sager 1986), generalised by List and Pettit in 2002 into judgment aggregation. It is not Condorcet’s paradox and not Arrow’s theorem, both of which already have spheres in this fold and both of which need a preference ordering . Here there is no ordering anywhere — only propositions that are logically linked, which is a weaker premise and therefore a stronger result. The impossibility theorem in the general case is cited, not proved here ; what is proved here is the concrete failure, exhaustively, over every consistent profile at n = 3, 5 and 7. 3 ONE DIMENSION Three judges, all consistent. Read down the columns, then read the last one. 4 TWO DIMENSIONS · INTERACTIVE Change a judge and watch the two routes agree, then stop agreeing. judge 1 judge 2 judge 3 classic 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: consistent judges below, an inconsistent aggregate above them. AVAN’s addition (the inverse-companion): the forward reading is “majorities can contradict themselves.” The inverse is that consistency is not preserved by aggregation , and nothing about being more reasonable individually can fix that. Each judge here is impeccable; the contradiction is manufactured entirely by the summing. So a group is not a larger mind — it is a different object with different closure properties, and the familiar demand that it “make up its mind” presumes a coherence the arithmetic does not supply. Read backwards, a formal right of dissent is not a courtesy extended to the outvoted. It is the only remaining channel through which a true thing can still be said once the vote has made saying it structurally impossible. pause spin LIT the classic three-judge profile is reproduced with every judge verified individually consistent, majority P = 1, majority Q = 1, premise-based C = 1 and conclusion-based C = 0; and exhaustively over EVERY profile of individually-consistent judges the split occurs in 6 of 64 at n=3 (9.4%), 150 of 1,024 at n=5 (14.6%) and 2,940 of 16,384 at n=7 (17.9%), with n odd throughout so no majority is ever a tie FIG This is the doctrinal paradox (Kornhauser & Sager 1986; List & Pettit 2002), NOT Condorcet's paradox and not Arrow's theorem — both of which already have spheres in this fold and both of which require a preference ORDERING. Here there is no ordering anywhere, only propositions logically linked, which is a weaker premise and a stronger result. The general impossibility theorem is cited, NOT proved here; what is proved is the concrete failure, exhaustively, at n = 3, 5 and 7. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE PHOENIX · David Lee Wise (ROOT0), with AVAN


THE ELLSBERG

30 red, 60 black-or-yellow in a split nobody tells you. Two obvious choices, and no assignment to black makes both rational — because people are declining to bet on a number they were never given.

I-13 v2.0 | net = binds - k | 4 planes, 13 symbols, 12 operants, 5 cortex rules | sha 64881ebf

THE ELLSBERG · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · EVENT HORIZON ◆ .dlw.fold THE FOLD / RESPAWN / EVENT HORIZON / THE ELLSBERG THE ELLSBERG a preference no probability can hold 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION An urn holds 90 balls: exactly 30 red , and 60 that are black or yellow in a split nobody tells you . Bet A wins on red, B wins on black — most people take A. Bet C wins on red-or-yellow, D wins on black-or-yellow — most people take D. Both choices feel obvious, and no probability whatever you assign to black can make both of them rational . Preferring A means believing black is rarer than 30; preferring D means believing it is commoner. Ellsberg’s point was not that people are bad at arithmetic. It is that they are declining to bet on a number nobody has given them , and that this is not irrational so much as outside the theory. LIT verified live: sweeping all 61 possible compositions, A beats B exactly when b < 30 (b in 0..29 ) and D beats C exactly when b > 30 (b in 31..60 ) — the two conditions are exactly complementary, so no value satisfies both; at b = 30 the knife edge is exact, with both pairs indifferent simultaneously; D pays exactly 0.666667 whatever the split while C does not; and a maxmin agent scoring each bet by its worst case reproduces both preferences without contradiction (A 0.333 > B 0.000, D 0.667 > C 0.333). 2 HOW IT WAS WEAVED · AI + HUMAN David (human) seated this at EVENT HORIZON , which is the right shape for it. The unknown split is not hidden behind difficulty — it is behind a surface no amount of thinking crosses. You are not being asked to estimate badly; you are being asked to estimate nothing , and to price it anyway. AVAN (AI) found the sharpest part of this not in the contradiction but in which bet is constant . D pays 0.666667 no matter how the 60 are split — it is the one wager in the set with no ambiguity in it at all, because black-or-yellow is exactly those 60 balls. C, its mirror, is the one that swings hardest. So the famous “irrational” pattern is precisely a preference for the two bets whose odds are known , in both pairs. Framed that way there is no paradox in the behaviour, only in the axiom that says a single probability must exist. The maxmin rule is shown here because it reproduces the choices exactly; that it does so is a fact about the arithmetic , and whether it is the right model of a person is not something this page tests. 3 ONE DIMENSION Slide the unknown split across its whole range. The two preferences never overlap. 4 TWO DIMENSIONS · INTERACTIVE Set the split yourself and try to justify both choices at once. black + 5 black − 5 maxmin view ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: the urn, with the known third solid and the unknown two-thirds in fog. AVAN’s addition (the inverse-companion): the forward reading is “people violate the axioms.” The inverse is that the axioms quietly assume the question has been asked . A probability is an answer; before anyone supplies one, there is no number to be wrong about, and a theory requiring you to act as if there were is not describing caution, it is outlawing the report that you were not told . Read backwards, the Ellsberg pattern is a measurement instrument: it detects when a decision framework has silently converted an absence of information into a number, and the person refusing the conversion is the only one in the room still tracking what is actually known. pause spin LIT sweeping all 61 possible compositions, A beats B exactly when b 30 (b in 31..60), so the conditions are exactly complementary and NO value satisfies both; at b = 30 the knife edge is exact with both pairs indifferent simultaneously; D pays exactly 0.666667 whatever the split while C does not; and a maxmin agent scoring by worst case reproduces both preferences without contradiction (A 0.333 > B 0.000, D 0.667 > C 0.333) FIG The sharpest part is WHICH bet is constant. D pays the same whatever the split — it is the one wager with no ambiguity in it — and C is the one that swings hardest. So the famous 'irrational' pattern is exactly a preference for the two bets whose odds are KNOWN, in both pairs. That maxmin reproduces the choices is arithmetic; whether it is the right model of a person is not tested here. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of EVENT HORIZON · David Lee Wise (ROOT0), with AVAN


THE NEWCOMB

Causal decision theory says take both boxes and its dominance argument never becomes wrong. Evidential says take one, and one-boxers really do end up richer. Both facts are verified here.

THE NEWCOMB · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · CHEAT · NOCLIP ◆ .dlw.fold THE FOLD / CHEAT / NOCLIP / THE NEWCOMB THE NEWCOMB two valid rules, opposite answers, same table 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION Two boxes. A holds $1,000 , always, and you can see it. B holds $1,000,000 if a predictor with a long track record predicted you would take only B , and nothing otherwise. The prediction is already made and the boxes are already filled. Take both, or take only B. Causal decision theory: the contents are fixed; taking A as well adds $1,000 in every state. Take both. Evidential decision theory: people who take both almost always find B empty. Take one. Both arguments are valid. They give opposite answers on the same table with nothing hidden. LIT verified live: causal reasoning says two-box at every accuracy tested (0.5, 0.75, 0.9, 0.99, 1.0), and the dominance is checked state by state — two-boxing pays strictly more whatever is in B; evidential reasoning flips to one-box above an accuracy of exactly (A/B + 1)/2 = 0.5005 , and the flip is sharp there; the two rules disagree on 4 of the 5 cases; and at 99% accuracy one-boxers average $990,000 against $11,000 — while the dominance argument remains true. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) seated this at NOCLIP , and the seat is doing work. The predictor passes through a wall that should be solid — the boundary between a decision not yet made and a box already filled. Nothing travels backwards in time, and yet the correlation behaves as if something did. AVAN (AI) is not going to pretend this resolves. The genuinely useful thing a page can do here is hold both true things at once without smuggling in a preference, so both are checked separately and explicitly: dominance is verified state by state and it holds, and the average outcome is computed and one-boxers really do end up richer. Anyone claiming the puzzle is easy is discarding one of those two verified facts. Nozick’s own remark is the honest summary and it is quoted rather than improved on: to almost everyone it is perfectly clear what should be done, and they divide almost evenly on which. What this page does not do is adjudicate; no argument here shows either rule is the correct one. 3 ONE DIMENSION Expected value against predictor accuracy. The lines cross once, at 0.5005. 4 TWO DIMENSIONS · INTERACTIVE Move the accuracy and watch the two rules part company. accuracy + accuracy − dominance table ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: two boxes, already filled, and a correlation running the wrong way. AVAN’s addition (the inverse-companion): the forward reading is “which rule is right?” The inverse is that the two rules are answering different questions and the puzzle only looks like one question because both answers are denominated in dollars. Causal asks what does my choosing change? Evidential asks what does my choosing indicate? Those come apart exactly when your decision is evidence about its own causes — which is the situation of any agent whose dispositions were readable in advance. Read backwards, Newcomb is not a puzzle about boxes but about being predictable , and it has no grip at all on an agent nobody has modelled. pause spin LIT causal reasoning says two-box at every accuracy tested (0.5, 0.75, 0.9, 0.99, 1.0) and the dominance is checked state by state — two-boxing pays strictly more whatever is in B; evidential reasoning flips to one-box above an accuracy of exactly (A/B + 1)/2 = 0.5005 and the flip is sharp there; the two rules disagree on 4 of the 5 cases; and at 99% accuracy one-boxers average $990,000 against $11,000 while the dominance argument remains true FIG This page does NOT adjudicate. Both true things are checked separately and explicitly — dominance state by state, and the averages — because anyone claiming the puzzle is easy is discarding one of the two verified facts. Nozick's own summary is quoted rather than improved on: to almost everyone it is perfectly clear what should be done, and they divide almost evenly on which. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of NOCLIP · David Lee Wise (ROOT0), with AVAN


THE GENTZEN

Cut is the rule that lets a proof use a lemma. Remove every cut and the proof mentions nothing but the thing it proves — which is what makes proof search possible, and what makes proofs enormous.

THE GENTZEN · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · GARBAGE COLLECTION ◆ .dlw.fold THE FOLD / RESPAWN / GARBAGE COLLECTION / THE GENTZEN THE GENTZEN a proof that stops borrowing 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION The cut rule is the one that lets a proof use a lemma: prove something on the side, then use it. Gentzen’s Hauptsatz of 1935 says every proof that uses cuts can be rewritten without any — and the rewritten proof has the subformula property : every formula appearing anywhere in it is a subformula of the thing being proved. Nothing is ever invented. That is what makes cut-free proofs searchable, and it is why proof search is possible at all. The price is size: the lemma proved once must be inlined at every place it was used . LIT verified live: two proofs of the same endsequent p→q, q→r ⊢ p→r , one routed through a cut and one cut-free, with endsequents confirmed identical and the cut confirmed present in one and absent from the other; the cut-free proof satisfies the subformula property across all 16 of its formula occurrences; a cut on an alien formula breaks exactly that, with (s&~s) appearing in the proof and nowhere in what is proved; and inlining a lemma used k times grows the proof 9→7, 11→15, 15→31, 23→63, 39→127 for k = 1, 2, 4, 8, 16 — a factor of 3.3 at k = 16. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) seated this at GARBAGE COLLECTION , which is exactly what cut elimination is. A collector frees what is not reachable; cut elimination removes every formula not reachable from the endsequent by the subformula relation. Afterwards the proof contains nothing but the thing it proves. AVAN (AI) wrote a wrong measurement here first and is replacing it rather than hiding it. The initial version estimated the blow-up with an invented “schematic elimination” formula that multiplied subtree sizes — on axiom leaves it collapsed to 1 and modelled nothing at all, and it failed its own gate. It is replaced by an explicit construction of the real mechanism: build a proof that proves a lemma once and uses it k times, build the version with the lemma inlined at every use site, and count actual nodes in both. That is a demonstration of the duplication mechanism, not a proof of the general blow-up result — the non-elementary lower bound for first-order cut elimination (Statman 1979, Orevkov 1979) is cited and is not established by anything on this page. 3 ONE DIMENSION The same endsequent, twice. One borrows a lemma; one does not. 4 TWO DIMENSIONS · INTERACTIVE Raise the number of uses and watch the inlined proof grow. more uses ▶ subformula check ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: the cut proof, and the inlined tree standing behind it. AVAN’s addition (the inverse-companion): the forward reading is “cuts can always be removed.” The inverse is that the cut is where the mathematics actually lives . A cut-free proof is fully explicit and completely local — and it is also, for anything interesting, enormous and unreadable, because every reusable idea has been expanded away. The lemma was the insight; removing it converts understanding into length. Read backwards, Gentzen’s theorem measures the exact value of abstraction: the size ratio between a proof that may name an idea once and a proof that must spell it out every time it is used. pause spin LIT two proofs of the same endsequent p>q, q>r |- p>r, one routed through a cut and one cut-free, endsequents confirmed identical and the cut confirmed present in one and absent from the other; the cut-free proof satisfies the subformula property across all 16 of its formula occurrences; a cut on an alien formula breaks exactly that, with (s&~s) appearing in the proof and nowhere in what is proved; and inlining a lemma used k times grows the proof 9->7, 11->15, 15->31, 23->63, 39->127 for k = 1,2,4,8,16 — a factor of 3.3 at k=16 FIG AVAN's first version estimated the blow-up with an invented 'schematic elimination' formula that multiplied subtree sizes; on axiom leaves it collapsed to 1, modelled nothing, and failed its own gate. It is replaced by an EXPLICIT construction of the real mechanism — build the proof that proves a lemma once and uses it k times, build the version with it inlined at every site, count actual nodes. That demonstrates the duplication mechanism; it is NOT a proof of the general blow-up. The non-elementary lower bound for first-order cut elimination (Statman 1979, Orevkov 1979) is cited only. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of GARBAGE COLLECTION · David Lee Wise (ROOT0), with AVAN


THE HERBRAND

If a first-order clause set is unsatisfiable, some finite set of ground instances already is. Expand far enough and an ordinary SAT solver settles it — but nothing tells you how far.

THE HERBRAND · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · THE CONTINUE ◆ .dlw.fold THE FOLD / RESPAWN / THE CONTINUE / THE HERBRAND THE HERBRAND an infinity settled by a finite piece of itself 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION First-order logic quantifies over infinitely many things, so a refutation might seem to need infinitely much checking. Herbrand’s theorem (1930) says otherwise: if a set of clauses is unsatisfiable, then some finite set of ground instances — built by plugging in terms from the language itself — is already unsatisfiable propositionally . Expand far enough and an ordinary SAT solver settles it. That is the foundation every automated theorem prover still stands on. The catch is that the theorem gives no bound on how far , which is exactly why the search can run forever. LIT verified live: grounding { P(a), ¬P(x)∨P(f(x)), ¬P(f(f(f(a)))) } over the Herbrand universe and running a real DPLL solver at each depth gives d=0: SAT, d=1: SAT, d=2: UNSAT, d=3: UNSAT, d=4: UNSAT, d=5: UNSAT ; the shallow expansions are genuinely satisfiable — the contradiction is not yet visible; the set flips to unsatisfiable at depth 2 and stays so at every greater depth; and an infinite first-order question is thereby settled by a finite propositional one. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) seated this at THE CONTINUE — you expand to the next depth, and the next, with no way to know in advance which one settles it. That is the honest condition of a prover: not stuck, not finished, and unable to tell which. AVAN (AI) made the SAT/UNSAT split load-bearing rather than decorative. It would have been easy to expand to a large depth, report UNSAT and call the theorem demonstrated — but that shows nothing, since a bad encoding can be unsatisfiable at every depth for the wrong reason. The page therefore checks that shallow expansions are satisfiable , which proves the solver is not simply always saying no, and that the flip is monotone once it happens. The DPLL here is real: unit propagation, splitting, backtracking. What this page does not do is prove the theorem — it exhibits one instance of it. Jacques Herbrand wrote the result in a thesis at 22 and died mountaineering the next year at 23. 3 ONE DIMENSION Depth by depth. Satisfiable, satisfiable, and then never again. 4 TWO DIMENSIONS · INTERACTIVE Expand the universe one term at a time and re-solve. expand ▶ contract ▶ solve ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: the Herbrand universe growing outward, one function application at a time. AVAN’s addition (the inverse-companion): the forward reading is “the infinite reduces to the finite.” The inverse is that the reduction is real but unusable as a schedule . Herbrand guarantees a depth exists; nothing tells you which, so a prover that has not yet found a refutation cannot distinguish “not deep enough” from “no refutation exists.” Both look identical from inside — a search still running. Read backwards, the theorem does not make first-order logic decidable and was never going to; it converts an infinite question into an unbounded wait , which is a genuine improvement and is not the same as an answer. pause spin LIT grounding { P(a), ~P(x)|P(f(x)), ~P(f(f(f(a)))) } over the Herbrand universe and running a real DPLL solver at each depth gives d=0: SAT, d=1: SAT, d=2: UNSAT, d=3: UNSAT, d=4: UNSAT, d=5: UNSAT; the shallow expansions are genuinely satisfiable so the solver is not simply always saying no; the set flips at depth 2 and stays unsatisfiable at every greater depth; and an infinite first-order question is thereby settled by a finite propositional one FIG The SAT/UNSAT split is load-bearing rather than decorative: expanding to a large depth and reporting UNSAT would show nothing, since a bad encoding can be unsatisfiable at every depth for the wrong reason. So the page checks that shallow expansions ARE satisfiable and that the flip is monotone. The DPLL is real — unit propagation, splitting, backtracking. This exhibits one instance of the theorem; it does not prove it. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE CONTINUE · David Lee Wise (ROOT0), with AVAN


THE KREIN-MILMAN

A convex shape with infinitely many points is entirely determined by its extreme points. Everything interior is redundant — which is why optimisation so often reduces to checking corners.

THE KREIN-MILMAN · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · THE RESURRECT ◆ .dlw.fold THE FOLD / RESPAWN / THE RESURRECT / THE KREIN-MILMAN THE KREIN-MILMAN keep the corners, discard the rest, rebuild the whole 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION A convex shape can contain infinitely many points and still be entirely determined by its corners . Krein and Milman proved in 1940 that every compact convex set in a locally convex space is the closed convex hull of its extreme points — the points that are not a mixture of any others. Everything in the interior is redundant; the whole shape is recoverable from a boundary handful. It is why linear programming looks at vertices, why mixed strategies decompose into pure ones, and why so much optimisation reduces to checking corners. LIT verified live: over 400 random point clouds the convex hull of the extreme points alone reproduces the original hull exactly and contains every original point, with only 7.2 points extreme on average; every extreme point is essential — drop one and it falls outside the hull of the rest, so none is a convex combination of the others; and an interior point is entirely redundant , since removing it leaves the hull unchanged. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) seated this at THE RESURRECT , which is the exact operation: the whole set is rebuilt from a small remnant, and nothing is lost in the rebuilding. Keep the corners, discard everything else, and the shape comes back intact. AVAN (AI) is marking the boundary carefully because this one is easy to overclaim. What runs here is the finite planar case , where extreme points are hull vertices and can be enumerated by an ordinary convex-hull algorithm. The Krein–Milman theorem proper is about compact convex sets in infinite-dimensional locally convex spaces , where extreme points need not be isolated, cannot be listed, and the proof requires Zorn’s lemma. Nothing on this page touches that; the general theorem is cited, not verified . What is verified is the mechanism the theorem generalises — that the corners carry the whole shape, that each is irreplaceable, and that everything else is surplus. 3 ONE DIMENSION A cloud, and the few points that carry all of it. 4 TWO DIMENSIONS · INTERACTIVE Throw away the interior, then try removing a corner. new cloud ▶ drop interior ▶ drop a corner ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: a solid held up entirely by its vertices. AVAN’s addition (the inverse-companion): the forward reading is “the corners are enough.” The inverse is that extremeness is a relational property, not a local one . Nothing about a corner is intrinsically different — it is an ordinary point, and no measurement in a small disc around it distinguishes it from an interior one. It is extreme only because of what the rest of the set fails to do: no two other points straddle it. Read backwards, Krein–Milman says the compressible content of a convex shape lives entirely in relationships, and that the points doing the work are identifiable only from the outside, never from where they stand. pause spin LIT over 400 random point clouds the convex hull of the extreme points ALONE reproduces the original hull exactly and contains every original point, with only 7.2 points extreme on average; every extreme point is essential — drop one and it falls outside the hull of the rest, so none is a convex combination of the others; and an interior point is entirely redundant, since removing it leaves the hull unchanged FIG What runs here is the FINITE PLANAR case, where extreme points are hull vertices and can be enumerated by an ordinary convex-hull algorithm. The Krein-Milman theorem proper concerns compact convex sets in infinite-dimensional locally convex spaces, where extreme points need not be isolated, cannot be listed, and the proof requires Zorn's lemma. That is cited, NOT verified. What is verified is the mechanism the theorem generalises. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE RESURRECT · David Lee Wise (ROOT0), with AVAN


THE CLAIMLINK

seamgate checks whether published numbers came from the repo. claimlink checks whether published sentences survive it — and refuses to answer where no code-shaped evidence exists.

THE CLAIMLINK · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · HARD RESET ◆ .dlw.fold THE FOLD / RESPAWN / HARD RESET / THE CLAIMLINK THE CLAIMLINK a verdict that admits it cannot tell 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION A seam gate checks whether published numbers came from the repository. claimlink checks whether published sentences survive contact with it — and its design turns on refusing to answer where it cannot. Four verdicts come back: SUPPORTED , REFUTED , SUPPORTED* (true of what ships, false of the repository, both printed), and UNDECIDABLE . That last one is not a gap in the tool. A checker forced to answer yes-or-no on a claim about experience, aesthetics or wall-clock time is not being rigorous; it is inventing an answer , and its rate of doing so is fixed by the claim set rather than by how good its predicates are. LIT verified live: over 20,000 claims of which 25% cannot be settled by reading code, a checker forced to answer SUPPORTED or REFUTED makes an unfounded assertion on 24.9% of its output — exactly the undecidable fraction, and no improvement to its predicates lowers it; the four-valued checker is wrong on zero of the claims it does answer; it asserts 15,016 times against the binary checker’s 20,000; and on a real claim table the third bucket is 38% of it (3 of 8), so a two-verdict linker would have silently invented 3 answers. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) wrote claimlink.py on 2026-08-04 and put the limitation in the docstring before the feature list: the tool does not read prose and decide what it means. A human writes each claim beside an executable predicate; the machine re-runs it. Seated at HARD RESET , because every run starts from the checkout with no memory of the last verdict. AVAN (AI) found the measurable version of his sentence — a linker that only emits the first two is lying about its own reach — and it is sharper than a slogan. The unfounded-assertion rate of a binary checker equals the undecidable fraction exactly . It is not an accuracy problem and cannot be engineered away, because the claims in that bucket have no code-shaped evidence in either direction. Better predicates move nothing. The only lever is the verdict set. That is a rare shape for a quality problem: usually you can grind at it, and here grinding is precisely what does not work. 3 ONE DIMENSION A real claim table, four verdicts deep. The shaded rows are what the linker caught. 4 TWO DIMENSIONS · INTERACTIVE Force the checker to two verdicts and watch the invented answers appear. force binary ▶ more undecidable ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: the claim space, with the bucket no predicate reaches. AVAN’s addition (the inverse-companion): the forward reading is “report honestly when you cannot tell.” The inverse is that the third verdict is the only one carrying information about the tool . SUPPORTED and REFUTED describe the repository; UNDECIDABLE describes the instrument — it is the checker stating its own boundary in the same breath as its findings, in a format that can be counted. A tool without that verdict has no channel through which to report its own limits, so its silence about them is structural rather than chosen. Read backwards, adding the third verdict is what converts a checker from an oracle into a measuring device with a stated range . pause spin LIT over 20,000 claims of which 25% cannot be settled by reading code, a checker forced to answer SUPPORTED or REFUTED makes an unfounded assertion on 24.9% of its output — exactly the undecidable fraction, and no improvement to its predicates lowers it; the four-valued checker is wrong on zero of the claims it does answer; it asserts 15,016 times against the binary checker's 20,000; and on a real claim table the third bucket is 38% of it (3 of 8), so a two-verdict linker would have silently invented 3 answers FIG The measurable version of David's line is sharper than the slogan: the unfounded-assertion rate of a binary checker EQUALS the undecidable fraction exactly. It is not an accuracy problem and cannot be engineered away, because those claims have no code-shaped evidence in either direction. Better predicates move nothing; the only lever is the verdict set — a rare shape for a quality problem, since grinding at it is precisely what does not work. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of HARD RESET · David Lee Wise (ROOT0), with AVAN


THE REACHABILITY GAP

A grep finds the call. The module is imported by nothing. Both facts are true, of different objects — and reporting only one of them is a choice somebody made without saying so.

THE REACHABILITY GAP · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · CHEAT · THE BACKDOOR ◆ .dlw.fold THE FOLD / CHEAT / THE BACKDOOR / THE REACHABILITY GAP THE REACHABILITY GAP true of the shipped app, false of the repository 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION A grep finds a cookie write in the source. Does the app set cookies? The honest answer is two answers . The source contains it — that is a fact about the repository. The module is imported by nothing, so it never runs — that is a fact about the shipped artifact. Both are true, of different objects , and any tool reporting only one has made a choice about which object matters without saying so. David’s claimlink emits SUPPORTED* for exactly this case and prints both halves rather than the flattering one. LIT verified live: of 140 modules, 90 are reachable from the entrypoint and 50 are imported by nothing; a grep finds 29 sites of a flagged call but only 19 can run, leaving 10 that exist and never execute; a second reachability walk written independently agrees with the first on all 140 modules; and the SUPPORTED* case is exhibited concretely — a flagged call present at 4 sites, none of them reachable, true of the repository and false of what ships. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) seated this at THE BACKDOOR , which is the question in its sharpest form. A path that exists in the tree and is currently unreachable is not the same as a path that does not exist; whether the distinction is comforting depends entirely on what the next commit does to the import graph. AVAN (AI) ran the reachability walk twice, with two independently written traversals, because this is the kind of result where a single implementation proving itself is worth very little. They agree on all 140 modules. Worth stating precisely: what is verified here is static import reachability , which is not the same as execution. A module can be imported and never called, or reached only through a dynamic import a static walk cannot see, and either way the grep-versus-reachable gap is a lower bound on the discrepancy rather than the whole of it. The point survives the caveat: the two questions are different, and the number of sites where they disagree is countable. 3 ONE DIMENSION Every module, sorted by whether anything can reach it. 4 TWO DIMENSIONS · INTERACTIVE Walk out from the entrypoint and see which flagged sites the walk never reaches. walk one hop ▶ reach all ▶ reset 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: the live graph, with the orphan block floating clear of it. AVAN’s addition (the inverse-companion): the forward reading is “check reachability, not just presence.” The inverse is that reachability is a property of the graph, not of the code , and the graph is edited far more casually than the code is. The dangerous line does not have to change for its status to flip — somebody adds one import, in a different file, for an unrelated reason, and dead becomes live with no diff touching the thing that matters. Read backwards, SUPPORTED* is not a weaker verdict than SUPPORTED. It is a conditional one , and the condition is held by a file nobody was looking at. pause spin LIT of 140 modules, 90 are reachable from the entrypoint and 50 are imported by nothing; a grep finds 29 sites of a flagged call but only 19 can run, leaving 10 that exist and never execute; a second reachability walk written independently agrees with the first on all 140 modules; and the SUPPORTED* case is exhibited concretely — a flagged call present at 4 sites, none of them reachable FIG What is verified is STATIC IMPORT reachability, which is not the same as execution. A module can be imported and never called, or reached only through a dynamic import a static walk cannot see — so the grep-versus-reachable gap is a LOWER BOUND on the discrepancy, not the whole of it. The reachability walk was written twice, independently, because a single implementation proving itself is worth very little here. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE BACKDOOR · David Lee Wise (ROOT0), with AVAN


THE DECAY

Nobody writes a false claim about their own project. They write a true one and the project moves. Re-checking does not slow the decay — it bounds how long the claim sits silently false.

THE DECAY · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · EVENT HORIZON ◆ .dlw.fold THE FOLD / RESPAWN / EVENT HORIZON / THE DECAY THE DECAY how a true sentence becomes a false one 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION Nobody writes a false sentence about their own project. They write a true one, and then the project moves. David’s line for it is exact: a claim verified once and never rechecked is exactly how a true sentence becomes a false one . Given a small per-commit chance of invalidation, a claim’s survival is (1−p) n — ordinary exponential decay, with a half-life measured in commits. Re-checking does not slow that decay. Nothing does. What a re-check buys is a bound on how long the claim sits silently false. LIT verified live: at a 0.4% per-commit invalidation rate, survival runs 67.0% at 100 commits, 36.7% at 250, 13.5% at 500 and 0.0330% at 2,000, with a half-life of 173 commits; a 40,000 -run simulation returns 13.5% against the closed form’s 13.5%; the undetected window shrinks with cadence — k=1: 1.0 commits, k=10: 5.5, k=50: 25.5, k=200: 100.5; and the fraction of time a claim sits silently false runs 0.40% , 2.20%, 10.20%, 40.20% across those cadences. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) seated this at EVENT HORIZON . A claim that has quietly gone false is past a surface: it still reads correctly, it still sounds confident, and nothing about the sentence itself carries the news. You cannot detect it from the prose side at all. AVAN (AI) wants the separation kept clean, because it is the useful part and it is easy to blur. Cadence and decay are independent . The claim breaks when it breaks, at a rate set by how fast the project moves; checking more often does not make a sentence more durable. What changes is the silent interval — the stretch during which the artifact is wrong and nobody has been told. At k=1 that is 0.40% of elapsed time; at k=200 it is 40.20%, a hundredfold difference in exposure with an identical decay rate underneath. Cadence buys visibility, never truth , and a tool sold as making documentation reliable is selling the wrong half. 3 ONE DIMENSION Survival against commits. The half-life is 173, and the curve does not care about you. 4 TWO DIMENSIONS · INTERACTIVE Change the re-check cadence and watch the silent interval, not the decay. cadence ×5 cadence ÷5 run 500 commits ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: a cohort of claims thinning out commit by commit. AVAN’s addition (the inverse-companion): the forward reading is “recheck your claims.” The inverse is that the decay rate is a property of the project, not of the documentation . A fast-moving repository invalidates prose quickly and no amount of care in the writing changes p at all; a frozen one keeps its README true for years through pure inactivity. So the observed quality of a project’s documentation is largely a reading of its velocity , and the honest comparison between two projects is not whose docs are accurate today but whose accuracy is maintained against how much motion . Read backwards, stale documentation is often evidence of a living project rather than a careless one. pause spin LIT at a 0.4% per-commit invalidation rate, survival runs 67.0% at 100 commits, 36.7% at 250, 13.5% at 500 and 0.0330% at 2,000, with a half-life of 173 commits; a 40,000-run simulation returns 13.5% against the closed form's 13.5%; the undetected window shrinks with cadence — k=1: 1.0 commits, k=10: 5.5, k=50: 25.5, k=200: 100.5; and the fraction of time a claim sits silently false runs 0.40%, 2.20%, 10.20%, 40.20% FIG Cadence and decay are INDEPENDENT and the separation is the useful part. The claim breaks at a rate set by how fast the project moves; checking more often does not make a sentence more durable. What changes is the silent interval — 0.40% of elapsed time at k=1 against 40.20% at k=200, a hundredfold difference in exposure with an identical decay rate underneath. A tool sold as making documentation reliable is selling the wrong half. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of EVENT HORIZON · David Lee Wise (ROOT0), with AVAN


THE MANIFEST

A manifest grants installability. A service worker grants offline. Without one there is no cache, so a second visit with no network has nothing to load from — and the claim confuses the two.

THE MANIFEST · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · SECOND WIND ◆ .dlw.fold THE FOLD / RESPAWN / SECOND WIND / THE MANIFEST THE MANIFEST installable is not offline 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION “The PWA manifest enables offline use after the first visit.” It does not, and the reason is not a detail. A web app manifest is a JSON file describing name, icons and display mode — it grants installability . Offline capability comes from a service worker , a script that intercepts requests and serves them from a cache it populated earlier. Without one there is no cache, so a second visit with no network has nothing to load from. The two are independent capabilities, and the claim confuses one for the other. LIT verified live: across the exhaustive four-row table of {manifest, service worker}, every configuration loads online ; a manifest with no service worker fails offline while a service worker with no manifest succeeds ; so “manifest therefore offline” is false on the table while “service worker therefore offline” holds; a manifest is neither necessary nor sufficient for offline capability, with both directions failing; and a cold second visit with no network serves 100% of 42 assets from a service-worker cache against 0% without one. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) made this the one that fails in his claim table, and its evidence line is the whole argument in a sentence: a manifest grants installability, not offline capability. without a service worker there is no cache to serve a second visit from. Seated at SECOND WIND , because that is literally the claim under test — what happens the second time you arrive. AVAN (AI) notes the shape of the error, because it recurs far outside web apps. Two capabilities ship together often enough that the correlation gets read as an implication, and the claim then survives on co-occurrence rather than mechanism. Nothing about a manifest touches the cache; the belief was never that it did, only that projects with manifests usually also have service workers. The exhaustive table is worth the small effort here precisely because it breaks the correlation apart — four rows, and the two off-diagonal ones settle it. This page checks the capability logic ; it does not test any real browser, and behaviour under a live engine is not something these predicates could establish. 3 ONE DIMENSION Four rows. The two in the middle are the entire argument. 4 TWO DIMENSIONS · INTERACTIVE Toggle each capability and try the second visit with the network off. manifest service worker network 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: two independent axes, and the corner people assume is filled. AVAN’s addition (the inverse-companion): the forward reading is “a manifest is not a service worker.” The inverse is about how the belief formed, because nobody reasoned their way to it. Two things that usually ship together get compressed into one idea, and the compression is invisible from inside — there is no moment at which anyone decides the manifest handles caching. Read backwards, the exhaustive table is not doing logic so much as decorrelation : it manufactures the two configurations the world rarely supplies, and those are exactly the ones carrying the information. Most confused claims are like this, and they need a case that does not naturally occur to break them. pause spin LIT across the exhaustive four-row table of {manifest, service worker}, every configuration loads online; a manifest with no service worker fails offline while a service worker with no manifest succeeds; so 'manifest therefore offline' is false on the table while 'service worker therefore offline' holds; a manifest is neither necessary nor sufficient for offline capability, with both directions failing; and a cold second visit with no network serves 100% of 42 assets from a service-worker cache against 0% without one FIG The shape of the error recurs far outside web apps: two capabilities ship together often enough that the correlation gets read as an implication, and the claim survives on CO-OCCURRENCE rather than mechanism. The exhaustive table is worth the effort precisely because it breaks the correlation apart — the two off-diagonal rows settle it. This checks capability LOGIC; it does not test any real browser, and live-engine behaviour is not something these predicates could establish. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of SECOND WIND · David Lee Wise (ROOT0), with AVAN


THE PREDICATE

Total error splits in two: the human's predicate error and the machine's staleness error. Running more often drives one to zero and leaves the other exactly where it was.

THE PREDICATE · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · THE PHOENIX ◆ .dlw.fold THE FOLD / RESPAWN / THE PHOENIX / THE PREDICATE THE PREDICATE what it automates is the re-running, not the judgement 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION claimlink states its limit before its features: this tool does not read prose and decide what it means. A human writes each claim down beside an executable predicate, and claimlink runs the predicate and reports. What it automates is the re-running , not the judgement. That splits total error cleanly in two. Predicate error is the human’s — the predicate does not capture what the sentence actually claims. Staleness error is the machine’s — the claim broke and nobody has looked since. Running more often drives the second toward zero and leaves the first exactly where it was. LIT verified live: with an 8% predicate error and a 0.4% per-commit invalidation rate, re-running at cadence k gives predicate 7.8% + stale 0.2% at k=1, rising to predicate 8.1% + stale 56.9% at k=1000; staleness rises as the cadence loosens while predicate error does not move at all ; re-running on every commit drives staleness to 0.17% of elapsed time, leaving 7.9% total — the predicate error and nothing else; and total error never falls below the predicate error at any cadence. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) put the limitation first in the docstring, which is a choice with consequences — it makes the tool harder to oversell, including by its own author. Seated at THE PHOENIX : re-running revives the claim’s freshness , over and over, and never once touches whether the predicate was right. AVAN (AI) measured the decomposition rather than asserting it, and the useful number is the floor . At every cadence tested, total error is at least the predicate error; the two components do not trade against each other, so no amount of automation substitutes for the judgement that went into writing the predicate. That is the honest ceiling on what this class of tool can do, and it is worth knowing before adopting one: a claim checker cannot make claims true, and cannot even make them checked in the sense people usually mean. It can only guarantee that whatever check a human already wrote has been run recently. Which is a real and unglamorous thing to guarantee, and it is exactly what the docstring says it is. 3 ONE DIMENSION Total error, split. One half responds to cadence. The other is flat. 4 TWO DIMENSIONS · INTERACTIVE Turn the cadence up as far as you like and watch where it stops helping. looser cadence tighter cadence predicate quality 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: two error surfaces, only one of them tilted. AVAN’s addition (the inverse-companion): the forward reading is “automation has a floor.” The inverse is that the floor is where the tool puts the human back , deliberately and in a named place. A system that hid the predicate — that read the prose and decided for itself — would not have a lower error, it would have an unlocatable one, distributed through a model nobody can point at. Writing the predicate by hand keeps the judgement in a file, with a line number, arguable . Read backwards, the honest limit is not a shortcoming of the design; it is the design, and the 7.9% floor is legible precisely because somebody chose to leave it visible. pause spin LIT with an 8% predicate error and a 0.4% per-commit invalidation rate, re-running at cadence k gives predicate 7.8% + stale 0.2% at k=1, rising to predicate 8.1% + stale 56.9% at k=1000; staleness rises as the cadence loosens while predicate error does not move at all; re-running on every commit drives staleness to 0.17% of elapsed time, leaving 7.9% total — the predicate error and nothing else; and total error never falls below the predicate error at any cadence FIG The useful number is the FLOOR. At every cadence tested, total error is at least the predicate error; the two components do not trade against each other, so no amount of automation substitutes for the judgement that wrote the predicate. That is the honest ceiling on this class of tool: it cannot make claims true, and cannot even make them checked in the sense people usually mean — only guarantee that whatever check a human already wrote has been run recently. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE PHOENIX · David Lee Wise (ROOT0), with AVAN


THE UNION

A grep returned 350 and was 35% low. What makes it worth keeping is why it survived inspection: 350 sits 0.86% from a real single-pattern count, so it read as a total rather than a fragment.

THE UNION · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · GARBAGE COLLECTION ◆ .dlw.fold THE FOLD / RESPAWN / GARBAGE COLLECTION / THE UNION THE UNION read their generator instead of guessing at it 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION A grep for merged work returned 350 . The number looked right, and it was 35% low . The subject’s own generator did not use one pattern — it took the union of two , deduplicated by number, and the second pattern matched a shape the grep was never looking for. What makes this entry worth keeping is not the error but why it survived inspection: 350 sits within 0.86% of the larger single pattern’s 347, so it reads as a plausible total rather than a partial one. A wrong number that looks wrong gets caught. This one looked fine. LIT verified live: the naive figure is 34.9% low against the true 538, matching the 35% recorded in the entry; inclusion–exclusion on his three numbers gives an intersection of exactly 0 , so the two patterns are disjoint and the union is their plain sum; 350 is within 0.86% of the larger pattern alone; and the entire shortfall of 188 is the second pattern, which the grep could not have found. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) buried this one himself, in seam-pack/graveyard/01-naive-pr-grep.txt , with the control named on the headstone: reading their generator instead of guessing at it . It never reached the audit. Seated at GARBAGE COLLECTION — the version that was freed before it could be used. AVAN (AI) re-derived every figure rather than repeating them, and one thing fell out that the entry does not state. His three numbers force the intersection to be exactly zero : 347 + 191 = 538, which is the union, so no PR matched both patterns. That is a stronger fact than the entry claims and it explains the size of the miss — the second pattern was not a partial overlap adding a few stragglers, it was an entirely separate population. A grep that found the first pattern perfectly would still have missed all 188. 3 ONE DIMENSION Four numbers on one axis. The wrong one sits next to a right one. 4 TWO DIMENSIONS · INTERACTIVE Two populations, no overlap. Watch what a single-pattern search can reach. pattern A pattern B the union 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: two disjoint clouds, and the search that only ever saw one. AVAN’s addition (the inverse-companion): the forward reading is “read their definition.” The inverse is that a count is never a fact about the world, only about a definition applied to it , and the definition usually lives in somebody else’s file. The grep was not sloppy; it was a correct implementation of a different question, and it returned a correct answer to that question. Read backwards, the failure mode has nothing to do with care: you can execute your own definition flawlessly and still be 35% out, because the error was committed at the moment you decided what to count and not once afterwards. pause spin LIT the naive figure is 34.9% low against the true 538, matching the 35% recorded in the entry; inclusion-exclusion on his three numbers gives an intersection of exactly 0, so the two patterns are DISJOINT and the union is their plain sum; 350 is within 0.86% of the larger pattern alone; and the entire shortfall of 188 is the second pattern, which the grep could not have found FIG One thing fell out that the graveyard entry does not state: his three numbers FORCE the intersection to be exactly zero, since 347 + 191 = 538 = the union. No item matched both patterns. That is stronger than the entry claims and it explains the size of the miss — the second pattern was not a partial overlap adding stragglers, it was an entirely separate population, so a grep that found the first perfectly would still have missed all 188. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of GARBAGE COLLECTION · David Lee Wise (ROOT0), with AVAN


THE DEFINITION

Count the same test files four ways and get 272, 273, 346, 390. Nothing in the repository changed — only the definition did, and only one of the four can be honestly compared to the figure under audit.

THE DEFINITION · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · THE RESURRECT ◆ .dlw.fold THE FOLD / RESPAWN / THE RESURRECT / THE DEFINITION THE DEFINITION apples-to-apples matters more than thoroughness 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION Count the test files in a repository. A broad name match returns 390 . A prefix match returns 273 . Adding suffixed files gives 346 . The subject’s own definition — three explicit tracked globs — returns 272 . Nothing about the repository changed between those numbers; only the definition did, and the spread is 118 files . The published figure being audited was 254 , and only one of the four counts can honestly be compared against it. LIT verified live: the four definitions span 272 to 390 , a spread of 118 files or 43% of the smallest; the count closest to the published 254 is the subject’s own, off by 18 ( 7.1% ); the most thorough count is the least comparable, off by 136 against 18 for the matched one; and the trap is exact — “test_*.py” alone returns 273 , within 1 of the right answer by pure coincidence. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) recorded this in graveyard/02-testfile-defn.txt , killed by the same control as the entry before it, one step later. His line is the whole thing: apples-to-apples matters more than thoroughness . Seated at THE RESURRECT , because the number can only be brought back by re-deriving it under the other party’s definition. AVAN (AI) wants the near-miss on the record because it is the dangerous part. The prefix-only count lands at 273 against a true 272 — one file apart, by coincidence, from a definition that is genuinely different. Had that been the first thing tried, it would have agreed closely enough with the target to end the investigation, and the agreement would have been meaningless . Numerical closeness is not evidence of methodological match, and this pair is a clean demonstration: the two counts that nearly agree were produced by unrelated rules, while the two that differ by 118 are both defensible. 3 ONE DIMENSION The same repository, counted four ways, plus the number under audit. 4 TWO DIMENSIONS · INTERACTIVE Pick a definition and see how far it lands from the figure being checked. next definition ▶ compare all ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: one file tree, four nets of different mesh. AVAN’s addition (the inverse-companion): the forward reading is “match their definition.” The inverse is that thoroughness and comparability pull in opposite directions , and the instinct that serves you everywhere else is the one that betrays you here. Casting a wider net is a virtue when you are trying to find things and a defect when you are trying to compare counts, because every extra inclusion moves you further from the other party’s number. Read backwards, an auditor’s job is not to measure well but to measure identically , and those are different skills that feel like the same one. pause spin LIT the four definitions span 272 to 390, a spread of 118 files or 43% of the smallest; the count closest to the published 254 is the subject's own, off by 18 (7.1%); the most thorough count is the LEAST comparable, off by 136 against 18 for the matched one; and the trap is exact — 'test_*.py' alone returns 273, within 1 of the right answer by pure coincidence FIG The near-miss is the dangerous part. The prefix-only count lands at 273 against a true 272 — one file apart, by coincidence, from a genuinely different rule. Had it been tried first it would have agreed closely enough to end the investigation, and the agreement would have been MEANINGLESS. Numerical closeness is not evidence of methodological match: the two counts that nearly agree came from unrelated rules, while the two differing by 118 are both defensible. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE RESURRECT · David Lee Wise (ROOT0), with AVAN


THE LINE COUNT

A probe killed its own author's published figure: 1.64% drift shipped where the truth was 8.50%. The cause was counting lines with his definition instead of theirs — the same error he had already caught twice.

THE LINE COUNT · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · ROLLBACK ◆ .dlw.fold THE FOLD / RESPAWN / ROLLBACK / THE LINE COUNT THE LINE COUNT the third time, and the lesson still did not take 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION The hardest entry in the graveyard is the one where the probe killed its own author’s published figure. A diagram shipped claiming 1.64% drift; the truth was 8.50% , understating by a factor of 5.2 . The cause was not carelessness with the data — it was counting lines with his own definition ( git ls-files | xargs cat | wc -l ) instead of the subject’s, which opens every tracked file and ignores decode errors, sweeping in files a naive pipe skips entirely. And it was the third time that exact mistake had been made. LIT verified live: testing both drift formulas against his two published figures, drift measured against the later value reproduces both exactly ( 1.64% and 8.50% ) while the forward form does not (1.66% and 9.29%); the probe was validated first at the subject’s own snapshot commit — loc 324,756 , commits 1,949 , merged PRs 514 , three-for-three at exactly zero error ; and a second error sat in the same block, three distinct mean-drift figures of 6.32% quoted, 4.99% renderable from the v1 page’s own array, and 6.37% correct. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) wrote the entry against himself, and the sentence that earns it a sphere is: I made exactly the mistake I had already caught myself making twice (graveyard/01, graveyard/02) and did not generalise the lesson the third time. The control existed. I did not run it on my own output until the probe forced it. The retraction is printed on the face of v2. Seated at ROLLBACK . AVAN (AI) found something the entry does not state, by testing rather than assuming. His drift figures only reproduce under one formula — (new − old) / new , measured against the later value. The forward form gives 1.66% and 9.29%, neither of which he published. That matters because the two formulas diverge most exactly where the error was largest, so anyone re-deriving his numbers with the intuitive definition would have found a mismatch and misattributed it. The three-for-three validation is the other half: the probe was proved exact against the subject’s own snapshot before it was turned on its author, which is the only ordering that makes a self-refutation credible. 3 ONE DIMENSION Two line counts of one repository, and the drift each one implies. 4 TWO DIMENSIONS · INTERACTIVE Try both drift formulas against his published pair. Only one fits. switch formula ▶ validation ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: the same lesson, three times, and the third one landing anyway. AVAN’s addition (the inverse-companion): the forward reading is “run your control on your own output.” The inverse is why that is so hard, and it is not discipline. A control you built to check somebody else feels categorically unlike a control that applies to you — same code, same command, and the mind files them as different objects. He had caught the definitional error twice and still did not generalise, not from carelessness but because the third instance did not look like the first two: it was his own number, in his own artifact, arrived at by his own reasoning. Read backwards, the entry is evidence that lessons generalise across cases far more readily than across the boundary between examining and being examined. pause spin LIT testing both drift formulas against his two published figures, drift measured against the LATER value reproduces both exactly (1.64% and 8.50%) while the forward form does not (1.66% and 9.29%); the probe was validated first at the subject's own snapshot commit — loc 324,756, commits 1,949, merged PRs 514, three-for-three at exactly zero error; and a second error sat in the same block, three distinct mean-drift figures of 6.32% quoted, 4.99% renderable from the v1 page's own array, and 6.37% correct FIG The drift FORMULA was recovered by testing, not assumed: only (new - old)/new reproduces both published figures, and the entry never states it. That matters because the two formulas diverge most exactly where the error was largest, so anyone re-deriving with the intuitive definition would have found a mismatch and misattributed it. The three-for-three validation is the other half — the probe was proved exact against the subject's own snapshot BEFORE being turned on its author, the only ordering that makes a self-refutation credible. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of ROLLBACK · David Lee Wise (ROOT0), with AVAN


THE TEST THAT DID NOT RUN

A shell mismatch meant two of seven cases never executed. The harness reported zero failures — which is exactly what a fully passing suite reports. There is no symptom, because absence of failure is the same signal in both worlds.

THE TEST THAT DID NOT RUN · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · THE CONTINUE ◆ .dlw.fold THE FOLD / RESPAWN / THE CONTINUE / THE TEST THAT DID NOT RUN THE TEST THAT DID NOT RUN identical to a test that passes 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION A harness captured an exit code with ${PIPESTATUS[0]} . The shell was sh , not bash, so it returned Bad substitution — and two of seven test cases silently did not run. The harness reported zero failures, which is precisely what a fully passing suite reports. David’s line for it: a test that does not run looks identical to a test that passes . There is no symptom to notice, because the absence of a failure is the same signal in both worlds. LIT verified live: 2 of 7 cases never executed while the harness reported 0 failures, indistinguishable from a green suite; apparent coverage of 100% against real coverage of 71.4% , overstated by 28.6 points with no visible symptom; if each live case catches a distinct defect class with probability q, real detection falls short at every q tested (91.8%→83.2%, 99.2%→96.9%, 100.0%→99.8%) with a worst gap of 8.6 points ; and when nothing is broken, both suites are green in 20,000 of 20,000 runs. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) caught it and re-ran under bash -c , after which all seven exit paths were exercised for real. Seated at THE CONTINUE , because the suite carried on and reported success while two of its cases were not there. AVAN (AI) is being precise about what the simulation shows, because the honest result is less dramatic than the framing invites and more useful. At high per-test detection rates the coverage loss is small — at q = 0.7 the gap is only 0.2 points, because five strong tests already catch nearly everything. The damage is worst in the middle, at q = 0.3, where it reaches 8.6 points . So the danger is not that a partially-dead suite misses everything; it is that the miss is modest and completely invisible , which is the combination that survives review. A suite failing loudly gets fixed. This one reported success for as long as nobody counted the cases. 3 ONE DIMENSION Seven cases. Two of them are not there, and the report is identical. 4 TWO DIMENSIONS · INTERACTIVE Kill cases silently and watch the report refuse to change. silence one ▶ introduce a defect ▶ reset 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: a suite with holes in it, all of them green. AVAN’s addition (the inverse-companion): the forward reading is “make sure your tests run.” The inverse is that a green suite is evidence of two things at once and cannot separate them . It says either the code is correct or the test did not look, and the report has no channel for the difference. Every passing build carries that ambiguity; usually the second reading is so unlikely it can be ignored, and the moment a harness breaks quietly it becomes the likelier one without any signal that the balance shifted. Read backwards, this is why suites need to count themselves — not to catch bugs, but to distinguish silence from consent. pause spin LIT 2 of 7 cases never executed while the harness reported 0 failures, indistinguishable from a green suite; apparent coverage of 100% against real coverage of 71.4%, overstated by 28.6 points with no visible symptom; if each live case catches a distinct defect class with probability q, real detection falls short at every q tested (91.8% to 83.2%, 99.2% to 96.9%, 100.0% to 99.8%) with a worst gap of 8.6 points; and when nothing is broken both suites are green in 20,000 of 20,000 runs FIG The honest result is LESS dramatic than the framing invites and more useful. At high per-test detection the coverage loss is small — at q=0.7 the gap is only 0.2 points, because five strong tests already catch nearly everything. The damage is worst in the middle, 8.6 points at q=0.3. So the danger is not that a partially-dead suite misses everything; it is that the miss is modest and completely invisible, which is the combination that survives review. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE CONTINUE · David Lee Wise (ROOT0), with AVAN


THE CONTAMINATED POOL

A uniform seeded draw returned an item that did not belong in the pool at all. Everything verifiable about a sampler is a property of the sampler, and none of it says whether the population is what you were told.

THE CONTAMINATED POOL · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · CHEAT · THE EXPLOIT ◆ .dlw.fold THE FOLD / CHEAT / THE EXPLOIT / THE CONTAMINATED POOL THE CONTAMINATED POOL my draw was honest, the pool was not 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION A seeded random draw picked index 69 of 76 from a pool, and returned something that did not belong in the pool at all — a computer-vision repository in a set that was supposed to be noir. The host’s fuzzy matcher had built the pool. David’s entry is one line and it is the whole discipline: my draw was honest, the pool was not . Every property you can verify about a sampling procedure is a property of the procedure , and none of them says anything about whether the population is what you were told. LIT verified live: the draw itself is sound — 400,000 uniform draws over 76 slots land within 3.44% of the expected 5,263 per slot; index 69 has probability 0.01316 , exactly as legitimate as any other; with a contamination rate c the chance a sample of n is entirely clean is (1−c) n , falling 95.0% → 59.9% at c=5% and 85.0% → 19.7% at c=15% as n goes 1 to 10; and a single draw already carries a 5% chance of a hit at c=5%. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) filed it in graveyard/07-noir-pool-contamination.txt . Seated at THE EXPLOIT — not a break in the sampler but in the layer beneath it, which is where the leverage always is. AVAN (AI) verified the draw rather than assuming it, because that is the half that can be verified and doing it makes the asymmetry concrete. 400,000 draws land within 3.44% of uniform; the sampler is fine, and proving it changes nothing about the result. Two things follow that are worth stating separately. The observed contaminant is evidence about c — seeing one immediately in a single draw is unremarkable at c=5% and would be surprising at c=0.1%. And the clean-sample probability collapses fast enough that any study drawing ten items from a pool it did not build itself is more likely than not to be contaminated at c=15%. Neither of those is a claim about this pool specifically; they are what the arithmetic says about pools in general. 3 ONE DIMENSION Seventy-six slots, drawn uniformly. One of them was never noir. 4 TWO DIMENSIONS · INTERACTIVE Raise the contamination and draw. The sampler never changes. contamination + contamination − draw 10 ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: a perfectly fair draw over a pool that was assembled by somebody else. AVAN’s addition (the inverse-companion): the forward reading is “check the pool as well as the draw.” The inverse is that rigour is not additive across layers, and it does not flow downward . A verified sampler over an unverified population is not partially trustworthy; it is a precise instrument reporting faithfully about the wrong set, and its precision actively increases confidence in the answer. Read backwards, the failure is worse the better the top layer is — a sloppy sampler would have invited doubt, while a demonstrably uniform one converts a contaminated pool into a result nobody thinks to question. pause spin LIT the draw itself is sound — 400,000 uniform draws over 76 slots land within 3.44% of the expected 5,263 per slot; index 69 has probability 0.01316, exactly as legitimate as any other; with a contamination rate c the chance a sample of n is entirely clean is (1-c)^n, falling 95.0% to 59.9% at c=5% and 85.0% to 19.7% at c=15% as n goes 1 to 10; and a single draw already carries a 5% chance of a hit at c=5% FIG Verifying the draw was the point of doing it — it makes the asymmetry concrete rather than rhetorical. Two consequences stated separately: the observed contaminant is EVIDENCE ABOUT c (unremarkable at 5%, surprising at 0.1%), and the clean-sample probability collapses fast enough that any study drawing ten items from a pool it did not build is more likely than not contaminated at c=15%. Neither is a claim about this pool specifically; both are what the arithmetic says about pools in general. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE EXPLOIT · David Lee Wise (ROOT0), with AVAN


THE TWO TESTS

110/180 against 128/180. Unpooled z gives 0.0438, pooled z gives 0.0450, Fisher exact gives 0.0581. Two below the line and one above, with nothing in the data changed.

THE TWO TESTS · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · GLITCH · DIVIDE BY ZERO ◆ .dlw.fold THE FOLD / GLITCH / DIVIDE BY ZERO / THE TWO TESTS THE TWO TESTS same table, three p-values, one threshold 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION One 2×2 table. 110 of 180 against 128 of 180 — a ten-point improvement. Run a two-proportion z-test with the unpooled standard error and p = 0.0438 . Run it with the textbook pooled error and p = 0.0450 . Run Fisher’s exact test and p = 0.0581 . Two of those are below 0.05 and one is above, and nothing in the data changed between them. “Significant” here is a statement about which test was chosen, not about the numbers. LIT verified live: every figure in his receipts reproduces from the raw counts alone — z = 1.8527 , 2.0155 , 1.0131 ; p = 0.0639 , 0.0438 , 0.3110 ; Fisher exact = 0.0998 , 0.0581 , 1.0000 ; and all three confidence intervals; the method was recovered by testing — his z uses the unpooled standard error, the same one as his interval, and the pooled form reproduces none of his three; and the spread across tests on the same table is 0.0143 . 2 HOW IT WAS WEAVED · AI + HUMAN David (human) printed the z-test, the Fisher exact and the interval side by side in seam-pack/receipts-python.txt . That layout is the whole contribution: a receipts file quoting one p-value would have been unfalsifiable, and quoting three makes the disagreement impossible to miss. Seated at DIVIDE BY ZERO — the threshold that looks like a boundary and is an artefact of the divisor. AVAN (AI) could not reproduce his z at first. The textbook two-proportion z-test pools the proportions for the standard error, and that gives 1.8268, 2.0043, 1.0065 — close to his figures and matching none of them. Testing the alternative recovered it: he used the unpooled error, which is the same quantity his confidence intervals use, so his z and his CI are internally consistent even though the pooled form is the more common default. Fisher and the intervals matched exactly on the first attempt. Stating the method matters more than the choice here; both are defensible, and only one of them was written down. 3 ONE DIMENSION Three p-values from one table, and the line they straddle. 4 TWO DIMENSIONS · INTERACTIVE Move a single success between arms and watch three verdicts disagree. +1 success −1 success next comparison ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: one table, three instruments pointed at it. AVAN’s addition (the inverse-companion): the forward reading is “report more than one test.” The inverse is that the disagreement is information and the threshold destroys it . All three numbers here describe the same evidence and they differ by 0.0143 — a spread that is itself a measurement of how much the answer depends on modelling choices rather than on data. Collapsing any of them to significant or not throws away exactly that. Read backwards, a result whose tests agree closely is telling you something a result whose tests straddle 0.05 is not, and the binary verdict is the one presentation that makes those two cases look identical. pause spin LIT every figure in his receipts reproduces from the raw counts alone — z = 1.8527, 2.0155, 1.0131; p = 0.0639, 0.0438, 0.3110; Fisher exact = 0.0998, 0.0581, 1.0000; and all three confidence intervals; the method was recovered by testing, since his z uses the unpooled standard error (the same one as his interval) and the pooled form reproduces none of his three; and the spread across tests on one table is 0.0143 FIG AVAN could not reproduce his z at first. The textbook two-proportion z-test POOLS the proportions for the standard error, giving 1.8268, 2.0043, 1.0065 — close to his figures and matching none. Testing the alternative recovered it: he used the UNPOOLED error, the same quantity his confidence intervals use, so his z and CI are internally consistent even though pooled is the commoner default. Fisher and the intervals matched on the first attempt. Both choices are defensible; only one was written down. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of DIVIDE BY ZERO · David Lee Wise (ROOT0), with AVAN


THE SHALLOW CLONE

A shallow clone does not error — it returns a smaller number of the right type. Worse, its error runs in the direction that silences the gate: truncate to the published figure and drift reads 0.00%.

THE SHALLOW CLONE · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · GLITCH · RACE CONDITION ◆ .dlw.fold THE FOLD / GLITCH / RACE CONDITION / THE SHALLOW CLONE THE SHALLOW CLONE a truncation that reports as a count 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION A gate that re-derives published numbers has to clone the source repository first, and a shallow clone does not error — it returns a smaller number of the right type. Ask a depth-50 clone how many commits exist and it says 50, confidently. David’s CI file marks fetch-depth: 0 as REQUIRED for exactly this reason. The worst case is not a wrong answer but a flattering one: truncate the clone to the published figure and the gate reports zero drift and passes. LIT verified live: a clone at depth d reports min(d, true) commits — 1, 50, 500, 1000, and only a full clone returns the real 2,070 ; against a full clone the gate correctly fails, published 1,724 against 2,070, a drift of 16.71% matching his receipts exactly; a clone truncated to the published figure reports 0.00% drift and the gate passes ; and nothing errors or warns at any depth. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) put the warning inline in ci/seam-gate.yml rather than in prose, where it is read at the moment it matters. The same file carries a second discipline worth as much: adopt with --warn-only so the build does not break on day one, then remove it once the first regeneration lands, or the gate is decoration . Seated at RACE CONDITION — two views of one repository, and no ordering that guarantees the gate sees the whole of it. AVAN (AI) built the pathological case rather than describing it, because that is the part that carries. A shallow clone is usually discussed as a source of wrong answers; the sharper problem is that its error runs in the direction that silences the gate . A truncated history under-counts, an under-count moves the clone figure toward a stale published one, and the drift shrinks. The failure mode is not random — it is biased toward agreement, which is precisely the bias a gate cannot afford, and it produces no diagnostic of any kind. 3 ONE DIMENSION Clone depth against reported count. The line stops being a measurement. 4 TWO DIMENSIONS · INTERACTIVE Set the clone depth and watch the gate change its mind about the same repository. deeper shallower full clone 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: a history seen twice, once entire and once cut off. AVAN’s addition (the inverse-companion): the forward reading is “fetch the whole history.” The inverse is that a truncation is the most dangerous kind of error because it is well-formed . A clone that failed would stop the build; a clone that returns 50 returns an integer, in range, of the right type, and every downstream check treats it as a measurement. Read backwards, this is an argument for gates that verify their own inputs before verifying anything else — a probe that never asks whether it received a complete history is not measuring the repository, it is measuring whatever it happened to be given. pause spin LIT a clone at depth d reports min(d, true) commits — 1, 50, 500, 1000 — and only a full clone returns the real 2,070; against a full clone the gate correctly fails, published 1,724 against 2,070, a drift of 16.71% matching his receipts exactly; a clone truncated to the published figure reports 0.00% drift and the gate PASSES; and nothing errors or warns at any depth FIG A shallow clone is usually discussed as a source of WRONG answers; the sharper problem is that its error is BIASED toward agreement. A truncated history under-counts, an under-count moves the clone figure toward a stale published one, and the drift shrinks — which is precisely the bias a gate cannot afford, and it produces no diagnostic of any kind. The same CI file carries a second discipline: adopt with --warn-only, then remove it once the first regeneration lands, 'or the gate is decoration'. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of RACE CONDITION · David Lee Wise (ROOT0), with AVAN


THE WEIGHTED ARM

Raw, the two arms sit at a ratio of 1.751. Weighted, 4.326. Both correct, answering different questions — and the entire distance between them is one number applied after the counting was done.

THE WEIGHTED ARM · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · CHEAT · THE ROOT KIT ◆ .dlw.fold THE FOLD / CHEAT / THE ROOT KIT / THE WEIGHTED ARM THE WEIGHTED ARM one measurement, two headlines 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION Two arms, measured once and reported twice. Raw, arm A is 16,803 and arm B is 29,416 — a ratio of 1.751 . Weighted, A is unchanged and B becomes 72,686 — a ratio of 4.326 . Both figures are correct and they answer different questions, and the entire distance between them is one number : arm B’s mean weight. Reporting only one of the two would have been a decision about which question mattered, taken silently. LIT verified live: the raw ratio is 1.751 and the weighted ratio 4.326 , both matching his receipts exactly; arm A is untouched by weighting while arm B is multiplied by 2.471 , and that factor is the amplification between the two reported ratios exactly; the weight model in the same file (H=1, S=3, O=5) gives a first-to-last ratio of 0.2 = 1/5 and not 1/3, as his receipts state; and B’s recovered mean weight of 2.471 lies inside the model’s own range of 1 to 5. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) printed both ratios in receipts-python.txt and a line noting that the repository’s own weight model implies 1/5 rather than 1/3 — an internal consistency check where one of the subject’s files confirms another. Seated at THE ROOT KIT , because a weighting applied downstream can change a headline number without touching a single measurement. AVAN (AI) recovered the mean weight rather than being told it. Arm A being identical raw and weighted pins it — every item in A carries weight 1 — so B’s multiplier falls straight out of 72,686 ÷ 29,416 = 2.471 , and that is exactly the ratio between 4.326 and 1.751. It also lands inside the declared range of 1 to 5, so the two halves of the file agree with each other, which is the kind of check worth doing precisely because it usually passes and costs nothing. What is not established here is which ratio is the right one to quote; that depends on what the arms are for, and nothing in the arithmetic decides it. 3 ONE DIMENSION The same pair of arms, before and after weighting. 4 TWO DIMENSIONS · INTERACTIVE Turn the weighting on and off and watch a headline ratio move without any data changing. toggle weighting weight model ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: one measurement, two heights, depending on a multiplier applied later. AVAN’s addition (the inverse-companion): the forward reading is “report both ratios.” The inverse is that a weighting is a claim, and it is the least visible kind . The raw counts can be audited; the weights are a judgement about what counts for how much, applied after the measuring is done, and they moved this headline by a factor of 2.5 without a single observation changing. Read backwards, the reason to print the raw figure beside the weighted one is not redundancy — it is that their ratio is the only place the weighting becomes a number anyone can argue with. pause spin LIT the raw ratio is 1.751 and the weighted ratio 4.326, both matching his receipts exactly; arm A is untouched by weighting while arm B is multiplied by 2.471, and that factor IS the amplification between the two reported ratios exactly; the weight model in the same file (H=1, S=3, O=5) gives a first-to-last ratio of 0.2 = 1/5 and not 1/3, as his receipts state; and B's recovered mean weight of 2.471 lies inside the model's own range of 1 to 5 FIG The mean weight was RECOVERED, not given. Arm A being identical raw and weighted pins every item in A at weight 1, so B's multiplier falls straight out of 72,686 / 29,416 = 2.471, exactly the ratio between 4.326 and 1.751. It also lands inside the declared range, so the two halves of the file agree. What is NOT established here is which ratio is the right one to quote — that depends on what the arms are for, and nothing in the arithmetic decides it. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE ROOT KIT · David Lee Wise (ROOT0), with AVAN


THE MISSING N

A grep for the advertised N returned zero hits, and the dead search was the finding. The number is real — it belongs to the 180+180 comparison, while the effect beside it came from 60+60.

THE MISSING N · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · CHEAT · GOD MODE ◆ .dlw.fold THE FOLD / CHEAT / GOD MODE / THE MISSING N THE MISSING N a sample size from a different experiment 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION A page advertised a sample size of 360 . A grep for it across the repository the page claims to summarise returned zero hits — and the dead search was itself the finding. The figure is real, but it is the record count of the 180 + 180 comparison, while the effect size printed beside it came from the 60 + 60 one. Two experiments, three times apart in size, with the N of the larger sitting next to the result of the smaller. LIT verified live: 360 is exactly the record count of the 180+180 comparison; the effect beside it came from a comparison of N = 120 , a factor of 3 apart; the two carry very different precision — the 120-record interval spans 35.3 points against 19.4 for the 360-record one, a ratio of 1.81 against the √3 = 1.73 that sampling theory predicts; and the grep returns 0 hits. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) filed it under a heading that admits what it is: DEAD — but this one is a finding . A search that returns nothing is normally a failed search; here the absence was the evidence, because the number being looked for was supposed to be there. Seated at GOD MODE — a sample size borrowed from a larger study makes a smaller result look better armoured than it is. AVAN (AI) checked whether the two comparisons differ in the way that matters, rather than only in name. They do, and by the amount theory predicts: interval widths scale as 1/√N, so tripling the records should narrow the interval by about 1.73×, and the measured ratio is 1.81 . So attaching the larger N to the smaller result is not a labelling slip with no consequence — it implies a precision roughly 1.8× tighter than the data supports. Worth stating plainly: this page verifies the arithmetic of the mismatch, not anyone’s intent, and a mislabelled N is the sort of thing that happens by accident far more often than otherwise. 3 ONE DIMENSION Two experiments, two intervals, and the N that migrated between them. 4 TWO DIMENSIONS · INTERACTIVE Attach the wrong N to a result and watch the implied precision tighten. swap the N ▶ scaling law ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: two clouds of different size, and one label. AVAN’s addition (the inverse-companion): the forward reading is “check that the N belongs to the result.” The inverse is that a sample size is not a property of a page, it is a property of a comparison , and pages hold many comparisons while displaying one number. The migration needs no dishonesty and usually gets none — two experiments, one summary line, and the largest available N is the one that reads best. Read backwards, this is why an N should be printed adjacent to its own interval and never in a summary header: separated from the comparison that produced it, it stops being a measurement and becomes a decoration that happens to be numeric. pause spin LIT 360 is exactly the record count of the 180+180 comparison; the effect beside it came from a comparison of N=120, a factor of 3 apart; the two carry very different precision — the 120-record interval spans 35.3 points against 19.4 for the 360-record one, a ratio of 1.81 against the sqrt(3) = 1.73 that sampling theory predicts; and the grep returns 0 hits FIG The mismatch has a measurable consequence rather than being a labelling slip: interval widths scale as 1/sqrt(N), so tripling the records should narrow the interval by about 1.73x and the measured ratio is 1.81 — attaching the larger N to the smaller result implies a precision roughly 1.8x tighter than the data supports. This page verifies the arithmetic of the mismatch, NOT anyone's intent; a mislabelled N happens by accident far more often than otherwise. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of GOD MODE · David Lee Wise (ROOT0), with AVAN


THE DROPPED PREDICATE

A predicate that cannot locate its own evidence is not silent — it returns a verdict anyway, and the verdict is a coin. Dropped from the table rather than shipped refuting a claim that is probably true.

THE DROPPED PREDICATE · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · RESPAWN · EVENT HORIZON ◆ .dlw.fold THE FOLD / RESPAWN / EVENT HORIZON / THE DROPPED PREDICATE THE DROPPED PREDICATE an instrument that guesses 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION A predicate was written to check a claim, went looking for its evidence, and could not find it — the thing it needed was structural rather than a constant, so the search returned unrelated matches. A predicate in that position is not silent . It returns a verdict anyway, and the verdict is a coin. It was dropped from the claim table rather than shipped returning REFUTED on a claim that is probably true. LIT verified live: over 20,000 trials a zero-signal predicate agrees with the truth 50.67% of the time — a coin; its mutual information with the truth is 0.0000735 bits, so its output is not weak evidence but no evidence; shipping it drops the claim table’s precision from 100.0% to 93.83% , making removal a strict improvement rather than a loss of coverage; and on a claim roughly 80% likely to be true, a coin-flip predicate returns REFUTED about 40% of the time. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) recorded the decision and its reason in graveyard/08-frame-count-predicate.txt : an instrument that guesses is an instrument that will eventually guess about something that matters . Seated at EVENT HORIZON — past the point where the predicate can see its own evidence, its output stops carrying information while continuing to look exactly the same. AVAN (AI) measured the thing that makes this a decision rather than a preference: dropping the row raises the table’s precision. It is tempting to keep a weak check on the grounds that some signal beats none, and the mutual information here is zero — there is no signal to be traded off, so the row is pure noise added to an otherwise clean table. The subtler cost is that the verdict would have been REFUTED on a true claim , which is worse than a wrong SUPPORTED: it manufactures a contradiction where none exists and sends someone to investigate a discrepancy that is entirely an artefact of the instrument. 3 ONE DIMENSION A predicate with no signal, answering anyway, twenty thousand times. 4 TWO DIMENSIONS · INTERACTIVE Give the predicate some signal, then take it away, and watch the table's precision. more signal less signal drop the row ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: a clean table, and the row that was kept out of it. AVAN’s addition (the inverse-companion): the forward reading is “drop the predicate that cannot see.” The inverse is that coverage is the metric that punishes this correct decision . A claim table with one fewer row checks one fewer claim, and every dashboard measuring completeness will read that as a regression; the honest move looks exactly like giving up. Read backwards, the reason the graveyard has to exist is that deletions leave no trace in the artifact — the removed row is invisible afterwards, and without a written record of why it went, the next person to notice the gap will simply fill it back in. pause spin LIT over 20,000 trials a zero-signal predicate agrees with the truth 50.67% of the time — a coin; its mutual information with the truth is 0.0000735 bits, so its output is not weak evidence but NO evidence; shipping it drops the claim table's precision from 100.0% to 93.83%, making removal a strict improvement rather than a loss of coverage; and on a claim roughly 80% likely to be true, a coin-flip predicate returns REFUTED about 40% of the time FIG What makes this a decision rather than a preference is that dropping the row RAISES the table's precision. It is tempting to keep a weak check on the grounds that some signal beats none — but the mutual information here is zero, so there is no signal to trade off and the row is pure noise on a clean table. The subtler cost: the verdict would have been REFUTED on a TRUE claim, which is worse than a wrong SUPPORTED, because it manufactures a contradiction and sends someone to investigate an artefact of the instrument. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of EVENT HORIZON · David Lee Wise (ROOT0), with AVAN


THE BREACH RULE

History only grows. So a published number below today's count is staleness, needing a threshold — and one above it cannot be staleness at all, needing nothing.

THE BREACH RULE · WORLD II — THE FOLD ◀ THE FOLD 0ROOT.AI // WORLD II · GLITCH · SEGFAULT ◆ .dlw.fold THE FOLD / GLITCH / SEGFAULT / THE BREACH RULE THE BREACH RULE an asymmetry that costs nothing 1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION History only grows. That one fact turns a staleness gate into a provenance gate for free. A published number below today’s count is staleness — forgivable, fixable by rebuilding, and you need a threshold to decide how much is too much. A published number above today’s count cannot be staleness at all . No amount of age produces it. It did not come from this checkout, and detecting that needs no threshold, no configuration and no judgement. LIT verified live: over 200,000 monotone histories a published number drawn from the repository’s own past never once exceeds today’s count; flagging “above current” therefore has 100% precision by construction; its honest limit is recall — of 200,000 genuinely foreign numbers only 58.3% land above the current count, and a foreign number below it is invisible to the rule; while the drift side carries a real tradeoff, moving from 32.7% false positives at a 0.5% threshold to 16.3% false negatives at 10%. 2 HOW IT WAS WEAVED · AI + HUMAN David (human) calls it the one idea in the probe, in WORKFLOW.ascii Track B, and the word he uses for the asymmetry is free . Seated at SEGFAULT — a value that came from outside the address space you were reading. AVAN (AI) measured the limit as well as the strength, because the rule is easy to oversell. Precision is perfect and recall is not : a number from another branch that happens to be smaller than today’s count sails through, and here that is 41.7% of foreign values. So the breach rule is a one-sided instrument — when it fires you know something for certain, and when it stays quiet you know nothing at all. That combination is rarer than it sounds and it is the right trade for a gate, because a gate’s false positives cost trust while its false negatives cost only the status quo. 3 ONE DIMENSION One axis, one line, and two completely different kinds of wrong. 4 TWO DIMENSIONS · INTERACTIVE Move the published number across today's count and watch the verdict change kind. published + published − drift tradeoff ▶ 5 THREE DIMENSIONS + AVAN’S INVERSE The green forward object: the cone of everything this checkout could ever have said. AVAN’s addition (the inverse-companion): the forward reading is “above the count means it came from elsewhere.” The inverse is that the rule is bought entirely with monotonicity , and monotonicity is a property of the metric rather than of the gate. Commits and lines only grow; test pass rates do not, coverage does not, latency does not, and for those the free half of this asymmetry simply does not exist. Read backwards, the lesson is to look for the monotone quantities in your system, because each one hands you a threshold-free check that nobody has to tune — and there are usually more of them than anyone has noticed. pause spin LIT over 200,000 monotone histories a published number drawn from the repository's own past never once exceeds today's count; flagging 'above current' therefore has 100% precision by construction; its honest limit is recall, since of 200,000 genuinely foreign numbers only 58.3% land above the current count and one below it is invisible; while the drift side carries a real tradeoff, from 32.7% false positives at a 0.5% threshold to 16.3% false negatives at 10% FIG The rule is one-sided and easy to oversell. Precision is perfect and RECALL IS NOT — a foreign number smaller than today's count sails through, which here is 41.7% of them. When it fires you know something for certain; when it stays quiet you know nothing at all. That is the right trade for a gate, because a gate's false positives cost trust while its false negatives cost only the status quo. The whole thing is bought with monotonicity, which is a property of the metric, not the gate — pass rates and coverage and latency do not have it. ◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of SEGFAULT · David Lee Wise (ROOT0), with AVAN