Everything published here, in one list

Self-published and not peer-reviewed. Each note states what it certifies, what it assumes, and what it will not claim; most ship the program that produced their numbers, and several run the argument live in the page. Groups run by subject, not by strength — finished work leads each group and open notebooks close it, with each group’s note saying which is which.

Every row carries a date. A plain date is the one the page prints itself. A date marked † is not stated on that page — it is when the file was first published to the repository, shown here so no row is undated, and it is this index’s claim rather than the page’s. Dates are publication, not last edit: a sitewide change touched all 35 files on 2026-08-05, so a modification time would say “today” for every row and mean nothing.

AI research audits

Machine-claimed results, re-checked in arithmetic sharing no code with the original, and the pipeline that does the checking. Confirming a result is the expected outcome; publishing the confirmation is the point. The last entry is an open notebook.

• Six AI-claimed results, re-checked. Five hold; the sixth holds on every fragment a machine can check.
  The index for the six below, and what the exercise actually found: on every one, the only check on record was the original author’s own.
  2026-08-03 · index · six independent re-derivations · five CONFIRMED, one PARTIAL
• The rank-two Poisson counterexample holds
  Re-derived in arithmetic sharing no code with the author’s.
  2026-08-03 · CONFIRMED
• The identities under the Mathieu–Zhao classification hold exactly
  The identities check out exactly. The theorem above them is still unchecked, and the note says so rather than letting the confirmation stand in for it.
  2026-08-03 · CONFIRMED · scope stated explicitly
• Korenblum’s constant survives a second arithmetic
  A second implementation sharing no code with the first reaches the same bound.
  2026-08-03 · CONFIRMED
• Ran–Teng Conjecture 20: every machine-checkable fragment holds. The analytic core is not audited.
  Re-verified in an independent reimplementation on an exact-rational and certified-interval stack: 43 checks, 0 failures, 5/5 mutation controls rejected. The proof’s analytic core is prose, was not audited, and the verdict is PARTIAL for exactly that reason.
  2026-08-04 · PARTIAL · fragment CONFIRMED, analytic core not audited
• Erdős #1038: every printed decimal of the extremal constant is right — and the 30th digit is a rounding, not an expansion
  An independent reimplementation — two interval backends, automatic differentiation, Krawczyk for existence and uniqueness — confirms all 30 printed decimals with certified enclosures to 40+ decimals, and finds the headline value’s last digit is a half-up rounding presented with an expansion’s trailing ellipsis.
  2026-08-04 · CONFIRMED · computational fragment; the extremality proof is not audited
• Maxwell said five charges allow at most 16 equilibria. At ε = 1/6, the counterexample’s 24 are now certified.
  The refutation’s published evidence was floating-point computer algebra — no code artifact, no certificate, no concrete ε. Pinned at the paper’s own Figure 1 configuration: 24 pairwise-disjoint Krawczyk boxes, each proving existence, local uniqueness and nondegeneracy of a critical point. And 24 > 16 in exact integers.
  2026-08-04 · CONFIRMED at ε = 1/6 · one pinned instance; the asymptotic statement is not audited
• Certify the machine’s candidate — the AI proposes; the certificate disposes
  A decidable pipeline for machine-generated mathematics: a candidate goes in, a certificate or an explicit refusal comes out, with no language model anywhere in the checking path.
  2026-07-23† · census of eight blind runs · reported as a census, never as a rate
• The preregistered prediction was 14/14 flips. The run measured 9/14 — five stages of our own certified chain invisible to its verdict.
  Truncation and single-stage corruption, reconstructed from the chain-of-thought faithfulness literature and aimed at this shop’s own certificate chain, with every prediction committed before the harness existed. The headline prediction was falsified, the blind spots were measured — and the chain was hardened the same day, errata Case 5.
  2026-08-05 newest · measured · causal step-importance, never model-CoT faithfulness · no shared scale with the papers it reconstructs
• Alien science needs a disposition, not a sermon
  How to respond to a claim whose reasoning you cannot follow, with a runnable pack.
  2026-07-31†

Computer-assisted proofs & validated numerics

The house method on its home ground: each finished note carries a certificate or a verifier a reader can run. The entries from the catalogue down are open notebooks — directions being worked out, including ones that went nowhere.

• A congestion mean-field game, enclosed — the certificate mechanism runs live in the browser
  Existence, local uniqueness within the even subspace, and strict positivity of the density, in outward-rounded interval arithmetic.
  2026-07-23† · single-file Python verifier · standard library only · runs in seconds
• A mean-field game equilibrium, enclosed in your browser
  The page does not solve the equations and show you the answer — it solves them, then proves the answer: a radii-polynomial contraction argument, every inequality evaluated in outward-rounded interval arithmetic, returning either an explicit ball that contains an exact solution or a refusal. Includes a certified multiplicity result where uniqueness theory is silent.
  2026-07-28† · runs in the page · interval arithmetic + radii polynomial · refusal is an outcome
• MFG Lab — the bench: four experiments that make the kernel falsifiable
  An interactive bench rather than a note: four experiments you drive in the browser, each built so the kernel behind it can be shown to be wrong.
  2026-07-29† · runs in the page · no install, no server
• Softmax sharpens with temperature. Here is the certificate.
  A certificate on a frozen attention row of a small GPT, with the fixture and a one-file verifier published beside it.
  2026-08-01† · certificate trio + fixture · verify_ml_beta.py
• When enough agents interact, is equilibrium a point or a geometry?
  Where the equilibrium set stops being a point and starts having shape, and what can be certified about it once it does.
  2026-07-30 · mean-field limits · equilibrium structure
• Every direction, with its verdict
  The index of the notes below, each with what became of it.
  2026-07-30†
• When the honest answer is “I refuse”, and here is why
  2026-07-30†
• The refusal taxonomy
  2026-07-31
• Equilibrium is a geometry, and refusal is how you measure it
  2026-07-30†
• Three attacks on one thesis — what survives
  2026-07-30
• Computer-assisted proof for mean-field games
  2026-07-31
• Certified multiplicity
  2026-07-31
• Certified price formation
  2026-07-31
• A certified bifurcation bracket for rational attention
  2026-07-31
• The edge of chaos, certified
  2026-07-31
• Certified path truncation
  2026-07-31
• Bracketing Cobb–Douglas with rational arithmetic
  2026-07-31
• Heterogeneous-agent macro over exact rationals
  2026-07-31
• Interval transcendentals
  2026-07-31

Number theory & pure math

Problems from the literature, worked over exact rationals and outward-rounded intervals. The first entry is finished work; the second is an open notebook.

• Erdős #290 — for even d, disc(f_d) is a square exactly at d = 4k(k+1), and here is why
  A certified bracket for the constant c in van Doorn’s lower bound, seven times narrower than the published 0.82 < c < 0.85: three Galois densities the paper left open, pinned exactly, and two further exceptional degrees beyond the range it computed. The degree pattern behind them — disc(f_d) a perfect square exactly at d = 4k(k+1) — is proved, not merely observed; whether the group drops at each such degree stays a per-degree question, answered through d = 120.
  2026-08-03 · seven programs, no dependencies · exact rationals + outward-rounded intervals · downloadable pack
• Degree vs sensitivity for Boolean functions
  2026-07-31

Operations research

Equilibrium and pricing on real systems — traffic, power, ports. Three finished notes, one of them a negative result stated as one; the seaport note is an open notebook.

• A convergent flow finds the equilibrium. A certificate encloses it.
  An independent reproduction of the AIMS Mathematics 2026 multi-population Wardrop paper. Three scenarios, three different outcomes: one solved exactly over rationals, one certified by a Krawczyk argument, and one refused, because that instance admits more than one equilibrium.
  2026-07-23† · reproduction · the refusal is a result, not a gap
• Price formation with a stock constraint — a mean-field model of a hydro-dominated power system
  A living note: the model is solved live in the page, every claim carrying its certificate.
  2026-07-28† · living note · runs in the page
• The coordination thesis does not hold on the ONS population
  A negative result, stated as one: the effect the thesis predicts is not present in the data it was proposed for.
  2026-07-29 · negative result · published because it is one
• A seaport MFG whose uniqueness condition is a determinant sign
  2026-07-31