Papanokechi

Resurgence by Galois conjugation for a second-order operator over Q(√3): Stokes data and a Hankel integral

We study a second-order linear differential operator over the field generated by the square root of three. At the origin it has a divergent power-series solution and a second formal solution with an irrational exponent. We prove that the series of the second solution is the Galoi...

Numerical identification of the error expansion of Brouncker's continued fraction for 4/π.

A short computational note on Brouncker's continued fraction 4/π = 1 + 1²/(2 + 3²/(2 + 5²/(2 + …))). With e_N the error after N partial quotients, the note determines numerically that (−1)^(N+1)·N·e_N tends to 4/π², and that the next coefficients of the expansion in 1/N are polyn...

The "if" direction of Conjecture 1.4 of arXiv:2111.04468: factorial reduction for the Eq. 6 and Eq. 7 families

Status: PROVED modulo pinned statements (listed in §3, each quoted with theorem/page number from the primary source). Reviewed by independent AI agents only; not yet reviewed by a human expert. Comments welcome. Conjecture 1.4 of Ben David, Nimri, Mendlovic, Manor, De la Cruz Men...

The Edge-Borel growth constant is a non-classical exponential period: an SL(2) monodromy on the Painleve III(D8) surface and a conditional transcendence theorem

v1.1 correction notice. This version corrects the identification of κ as a Stokes multiplier, withdraws the conditional transcendence theorem (Theorem 4) that the title refers to, and corrects four smaller statements, after an independent re-audit that recomputed the Stokes jump...

An explicit exponential-period representation of the V_quad connection coefficient

Correction notice (v1.4). This version withdraws the main identity and records the completed withdrawal of the journal submission. The text of version 1.3 follows this notice unchanged, except that the identity and the v1.3 list of unchanged results are marked in place. Journal s...

An Edge–Borel Radius Theorem for Positive Polynomial Continued Fractions

[2026-09-23] Scope correction — the “no logarithmic factor” clause. This record states the coefficient asymptotic g_n ∼ C R^{−n} n^{γ−1} with no logarithmic factor, and separately identifies the arithmetic subvariety γ ∈ ℤ as the locus where the singularity is a pole rather than...

The EBR Amplitude as a Connection Coefficient: Characterization and a Rigidity Dividing-Line Conjecture

[2026-09-23] Erratum — the logarithm at s = R. This record states that the local expansion at the dominant singularity s = R carries a logarithm arising from a resonance between the exponent −γ and the integer exponents {0, …, 2d−2}. That statement is withdrawn as an unconditiona...

Four Rounds of Adversarial Audit on a Quantitative Hypothesis: Definitional Invariances, Bound Echoes, and an Identifiability Limit — A Case Study

A case study in epistemic governance. Four rounds of adversarial audit applied to one quantitative hypothesis: a publicly presented model (G. Drumm, "Land of Khem") proposing that Egyptian pyramids operated as industrial-scale chemical plants. The pyramid model is the test object...

Four Rounds of Adversarial Audit on a Quantitative Hypothesis: Definitional Invariances, Bound Echoes, and an Identifiability Limit — A Case Study

A case study in epistemic governance. Four rounds of adversarial audit applied to one quantitative hypothesis: a publicly presented model (G. Drumm, "Land of Khem") proposing that Egyptian pyramids operated as industrial-scale chemical plants. The pyramid model is the test object...

The least-gated channel: unobserved values in a research pipeline

A methodological field note on a class of defect that no instrument in its pipeline could see: a value that enters from prose rather than from the object it describes, becomes load-bearing, and is never checked against that object. The note opens with a measurement rather than a...

The least-gated channel: unobserved values in a research pipeline

A methodological field note on a class of defect that no instrument in its pipeline could see: a value that enters from prose rather than from the object it describes, becomes load-bearing, and is never checked against that object. The note opens with a measurement rather than a...

Quasi-periodic prefactor at golden slope: period-2 structure, Zeckendorf-phase clustering, and separation from two controls

This record reports the prefactor at the GOLDEN slope. It is a companion computation to the A076227 software deposit (Zenodo 22121363), on a different slope and a different sequence; it is not a new version of that record and retracts nothing in it. The same exact-integer dynamic...

Reference-locked criteria in a single-instance research pipeline: four mechanisms, and two that compose

A pipeline validated on a single instance accumulates criteria keyed to that instance. This note separates four such classes by mechanism — shape lock, coefficient lock, hard-coded target, and screen-to-gate promotion — and reports that two of them compose into a failure neither...

An explicit exponential-period representation of the V_quad connection coefficient

Correction notice (v1.3). This version withdraws a claim. Through v1.2 the Discussion stated that this paper “completes part (ii)(a) for d=2” of the master conjecture of the Sakai stratification (10.5281/zenodo.20694840). Part (ii)(a) concerns the Edge–Borel coefficient, a differ...

Rank of the period matrix M_p mod p for periodic continued-fraction operators: 430 members proven nonzero, and three scoped negatives

Version 2 of this record. ADDITIVE: nothing in version 1 is retracted, corrected, or weakened. Every sentence of v1 remains true as written. Readers holding v1 do not need to discard anything. A note on the version number: "2.0.0" is not semantic versioning. It records the scale...

A closed evaluation of tr M_p mod p for periodic continued-fraction operators

A pre-registered computational run (PCF-ORBIT-SCHEMA) asking whether a four-step proof schema — rank-one deflation, an algebraic generating function from Lagrange–Bürmann, a combinatorial interpretation, and a free Z/p action — generalises across an 874-member class of continued-...

Enrollment is not coverage: integrity gates, their measured detection rates, and the limits of self-checking documentation

This is an experience report with n = 1, self-reported: the same author wrote the documents, the gates that check them, and this account of what the gates found, and no independent party re-ran anything. Every structural failure it describes was found by the apparatus catching it...