From 4b0a8f59c3b7df182985fc7c02415eacd80b37d1 Mon Sep 17 00:00:00 2001 From: Dylan Roy <249851642+d6g8k5htny-coder@users.noreply.github.com> Date: Mon, 5 Oct 2026 12:18:40 -0700 Subject: [PATCH] IBA2-009: localize the half-power matching band and exhibit an estimate-level obstruction Dylan Roy delegated AI work; actual author OpenAI / GPT-6 Astra Pro, session github-rules-and-closure-round5-20261005. Three new review packet files only. Derive exact k^3/r band identity, abstract compact-parity obstruction, and sufficient matched-residual tail conditions. Actual Gaussian coefficient remains unresolved; no original proof, status, workflow or formal source edits. Claims main259/6001167816 and main229/6001312122. Standard-library controls verified normal and optimized; nonauthor review required. --- reviews/iba2_009_matching_20261005/REPORT.md | 245 ++++++++++++++++++ .../iba2_009_matching_20261005/SOURCES.json | 34 +++ .../boundary_layer_check.py | 124 +++++++++ 3 files changed, 403 insertions(+) create mode 100644 reviews/iba2_009_matching_20261005/REPORT.md create mode 100644 reviews/iba2_009_matching_20261005/SOURCES.json create mode 100644 reviews/iba2_009_matching_20261005/boundary_layer_check.py diff --git a/reviews/iba2_009_matching_20261005/REPORT.md b/reviews/iba2_009_matching_20261005/REPORT.md new file mode 100644 index 000000000..a0b398f55 --- /dev/null +++ b/reviews/iba2_009_matching_20261005/REPORT.md @@ -0,0 +1,245 @@ +# IBA2-009: a half-power matching layer invisible to compact cusp parity + +**Object:** IBA2-009-MATCHING-20261005-v1. **Date:** 2026-10-05. +**Actual author:** OpenAI / GPT-6 Astra Pro, session +`github-rules-and-closure-round5-20261005`, Dylan Roy — delegated AI work. +**Scientific effect: NONE.** Author-side analytical audit contribution, requiring +nonauthor review; no historical verdict, proof, flag or register is changed. +Organizational-independence credit: 0. This is not a claim of informational +blindness: the original audit's coverage map and repository discussion were read. + +## 1. Result, limits, and source pin + +The compact-to-global implication in main#259 IBA2-009 needs a genuine matching +estimate. Here are three concrete outputs: + +1. An exact formula for the actual rejected-density contribution in the moving + band `a <= k^3/r <= b`: it has an `ell^(1/2)` prefactor and an explicitly + weighted rescaled-kernel integral. +2. An abstract kernel family with a nonzero half-power contribution that is + invisible in every fixed compact cusp window and at every fixed positive + gap. It obeys the selected upper bounds below, including the C7 K2 scale. +3. Sufficient weighted-tail conditions for a correctly matched residual to be + `o(ell^(1/2))`, stating exactly what compact parity does not supply. + +**Not proved:** that the Gaussian field has this nonzero profile, that its +half-power coefficient exists or vanishes, or that all its other probabilistic +interfaces admit the abstract family. This is not a counterexample to Theorem N +or to the persistence law. It is a counterexample to inferring global absence +from the listed estimate-level premises alone. IBA2-009 remains open for the +actual field. A positive contribution from one moving band alone also does not +establish the coefficient of a full asymptotic expansion after other regions and +lower-order terms are matched. + +All source reads use Math- commit +`dcd2a886e322738324a745adcad12fd3735bd2c5`: + +| Source | Exact path / Git blob | Scope read and consumed | +|---|---|---| +| N | `frontiers/elder_cusp_parity_20261002/PROOF.md` / `16a1db0658918057ff741df888c13702763d9919` | Statement, Corollary N-prime and its section 6 proof; section 7 Remark 1. Selected section 5 bookkeeping was read, not re-audited. | +| T | `frontiers/third_order_rate_20261001/PROOF.md` / `110ed33a57902bef11873807e722fde3888b59fb` | Section 0 kernel definitions, E3-plus/R-plus remainders and W-plus small-gap window. | +| K | `frontiers/c7_total_bounded_20260929/PROOF.md` / `28748b086ec6761ef467dc67cba475fbdf8b7455` | K1/K2 and section 4 unnormalized marked-intensity identity and Gaussian pin-density envelope. | + +N already explicitly limits its no-linear-term theorem to fixed compact +`kappa=k/r` intervals. Its Remark 1 distinguishes the two uncontrolled ends and +says that even a hypothetical uniform `O(r^2+k^2)` estimate would not finish the +global half-power question. This report quantifies a specific obstruction to +that inference; it does not attribute an unrestricted claim to N. + +## 2. Exact moving-band formula for the actual nonnegative kernel + +Use the source conventions, without dividing by the full normalizer: + + A_rej(r,b,k,u) = 12 pi_r(v_r) E_Q[(W_r/r^2)(1-e)], + B_r(k) = integral_b integral_u A_rej(r,b,k,u) d sigma(u) db >= 0, + nu_rej^near(ell) = integral_0^r0 r^(-2) B_r(ell/r^3) dr. + +This is K section 4 in the separation variable. The cap implication +`1-e <= 1_{G_r^c}`, K2 and the Gaussian pin-density envelope give + + 0 <= B_r(k) <= C r^3/k, 0 < r <= min(k,r0), 0 < k <= 1. (2.1) + +Integration over birth and direction, and absorption of polynomial gap growth +on `0 J` almost everywhere on [a,b], dominated convergence yields + + ell^(-1/2) nu_[a,b](ell) -> (1/10) integral_a^b J(y)y^(-3/2)dy. (2.4) + +More generally convergence of that weighted integral suffices. A uniform +`J_ell -> 0` proves a little-o contribution from this band. K2 supplies a +bounded J, not a vanishing J. Establishing its actual limit is a sharply +localized analytic task; the present report does not assume a limit exists. + +The band has + + r ~ ell^(3/10), k ~ ell^(1/10), kappa ~ ell^(-1/5). (2.5) + +Thus k tends to zero while kappa tends to infinity. Neither fixed-positive-k +Taylor expansion nor compact-kappa parity describes the passage uniformly. + +## 3. An explicit estimate-level obstruction + +First omit a harmless gap cutoff. Let + + h(t) = (t-1)^4(2-t)^4 for 1<=t<=2, and 0 otherwise, + psi(y) = h(sqrt(y)), + H(r,kappa) = r^2 kappa^2 psi(r^2 kappa^3) + = k^2 psi(k^3/r), k=kappa r. (3.1) + +Here H is a **scaled** kernel perturbation; its raw kernel is `D=r^2 H`. +The polynomial bump is C^3, is nonnegative, and is bounded by 1. The support +is `1<=k^3/r<=4`. + +### 3.1 Why the usual estimates do not see it + +- At fixed kappa, (3.1) is even in r. On every fixed compact kappa interval it + is identically zero for all sufficiently small |r|. In particular it has + zero linear term and satisfies compact `O(r^2)` estimates. +- At any fixed k>0 it is identically zero once `r=1`, and replace H,D by theta(k)H,theta(k)D. +As an explicit abstract nonnegative split on `0=0`. These raw kernels obey a K1-sized +majorant; on the compact k support they also obey a polynomial times +`exp(-c k^2)` majorant, after enlarging the constant. Multiplication by a +normalized Gaussian birth envelope and normalized angular measure preserves +these statements. This is only an abstract kernel construction, not a +realization as Gaussian critical points, an elder mark, or a Palm law. + +### 3.2 Exact half-power mass + +For ell sufficiently small that the whole support is inside `00`. +The explicit rational coefficient (3.3) is reserved for the polynomial h; +no closed-form value is asserted for the smooth variant. + +An added half-power correction is smaller than the existing +`O(ell^(3/7))` remainder and `O(ell^(4/9)log(1/ell))` upper scale. It is +therefore not excluded merely by those error orders. The model's perturbation +is zero on the small-kappa region; it does not purport to reconstruct the +sources' complete leading laws or all cross-region matching identities. + +## 4. A sufficient global passage, with the required subtraction explicit + +Let E_ell(kappa) denote a **correctly matched residual**: the known fold, cusp, +and common terms must already have been subtracted with no double counting. +Constructing this residual is itself part of the missing analysis. It is NOT +permissible simply to label the raw difference in N.1 as this residual: +that difference can still contain the fold contribution to the ell^(1/3) +coefficient when integrated globally. + +Suppose the residual density has the exact representation + + R(ell) = ell^(1/4)/4 * integral_0^infinity + E_ell(kappa) kappa^(-5/4) d kappa + F(ell), (4.1) + +where the integrand is extended by zero below the physical lower cutoff +`kappa=ell/r0^4`, and `F(ell)=o(ell^(1/2))` accounts for separately controlled +far/matching remainders. Assume on every fixed `03/4, and +M=O(kappa^q) near infinity, q<3/4. These are sufficient assumptions, not +established properties of the actual Gaussian kernel. + +The obstruction (3.1) violates (4.2): its normalized weighted mass stays +positive while its support escapes to kappa=infinity. Pointwise convergence +and compact parity thus cannot replace quantitative control of these tails. + +## 5. Reproduction, coverage and next mathematical target + +Run `python3 -B -S boundary_layer_check.py`, and repeat with `-O`. +The deterministic JSON reports 25 moving-layer, 30 compact-cusp, 25 fixed-gap, +20 small-gap and 3 exact-integral cases. The explicit finite checks verify +identities and inequalities, not the Gaussian realization or the general +claims by sampling; the proofs are sections 2–4 above. + +Negative controls (each must exit 1 with its named failure): + +| Variant | Deliberate error | Failure | +|---|---|---| +| M1 | k^3/r^2 instead of k^3/r | MOVING_LAYER_ARGUMENT | +| M2 | omit r^2 between raw and scaled kernels | LIFETIME_JACOBIAN | +| M3 | omit the 1/5 substitution factor | INTEGRATION_FACTOR_ONE_FIFTH | +| M4 | ignore the moving support at fixed kappa | COMPACT_CUSP_VANISHING | +| M5 | replace the half-power x^5 by x^6, ell=x^10 | HALF_POWER_SCALING | + +Example: `python3 -B -S boundary_layer_check.py --mutant M2`. +Invalid arguments exit 2. All fourteen CLI cases were run in normal/optimized +modes, and the positive JSON was byte-identical. A separate seven-test local +contract suite passed both modes after its expected missing-source failure. +No local Lean execution is claimed. Existing hosted repository checks are +separate and do not automatically execute this newly added standalone script. + +**Actionable target:** determine the actual nonnegative profile in (2.2) on a +fixed positive y-band, rather than extrapolating fixed-kappa parity. Uniform +vanishing would remove that band's half-power mass; a nonzero limiting profile +would require explicit incorporation into global matching. Neither outcome is +assumed. Both ends of the matched residual in (4.2) still require control before +a global absence statement. Historical IBA2-009, IBA2-010, IBA2-012 and all +scientific acceptance fields remain unchanged by this contribution. diff --git a/reviews/iba2_009_matching_20261005/SOURCES.json b/reviews/iba2_009_matching_20261005/SOURCES.json new file mode 100644 index 000000000..be41c7922 --- /dev/null +++ b/reviews/iba2_009_matching_20261005/SOURCES.json @@ -0,0 +1,34 @@ +{ + "scientific_effect": "NONE", + "scientific_acceptance": false, + "source_commit": "dcd2a886e322738324a745adcad12fd3735bd2c5", + "sources": [ + { + "path": "frontiers/elder_cusp_parity_20261002/PROOF.md", + "blob": "16a1db0658918057ff741df888c13702763d9919", + "scope": "statement; section 6; section 7 Remark 1" + }, + { + "path": "frontiers/third_order_rate_20261001/PROOF.md", + "blob": "110ed33a57902bef11873807e722fde3888b59fb", + "scope": "section 0: definitions and stated remainder/window bounds" + }, + { + "path": "frontiers/c7_total_bounded_20260929/PROOF.md", + "blob": "28748b086ec6761ef467dc67cba475fbdf8b7455", + "scope": "K1/K2; section 4 rejected intensity and pin-density envelope" + } + ], + "files": [ + { + "path": "REPORT.md", + "bytes": 12716, + "sha256": "570a8bf7fdd78e56e6edd04d6a1f7431312daa5839c05a210aa72a76336dc27a" + }, + { + "path": "boundary_layer_check.py", + "bytes": 4892, + "sha256": "58ba3205d390b685344e19c989efe2ef90fd7837237b47ed8a7c1eef8ac49385" + } + ] +} diff --git a/reviews/iba2_009_matching_20261005/boundary_layer_check.py b/reviews/iba2_009_matching_20261005/boundary_layer_check.py new file mode 100644 index 000000000..96fb621bf --- /dev/null +++ b/reviews/iba2_009_matching_20261005/boundary_layer_check.py @@ -0,0 +1,124 @@ +#!/usr/bin/env python3 +"""Exact finite checks for IBA2-009's moving-layer obstruction. + +Standard library only. This diagnostic is not a Gaussian-field counterexample, +not an independent audit of imported estimates, and not a proof by sampling. +The general calculation is in REPORT.md. No check uses an assert statement. + +Usage: python3 -B -S boundary_layer_check.py [--mutant M1|M2|M3|M4|M5] +Valid source exits 0 with deterministic JSON. Each documented mutant exits 1. +Invalid arguments exit 2. Optimized Python has the same behavior. +""" +from fractions import Fraction as F +import argparse +import json +from math import comb, factorial +import sys + + +class CheckFailure(ValueError): + """An exact diagnostic invariant was violated.""" + + +def require(condition, label): + if not condition: + raise CheckFailure(label) + + +def bump(t): + """C^3 bump (t-1)^4(2-t)^4 supported on [1,2].""" + t = F(t) + return (t - 1)**4 * (2 - t)**4 if 1 < t < 2 else F(0) + + +def bump_integral(order=4): + """Integral_1^2 (t-1)^m(2-t)^m dt by exact polynomial integration.""" + if not isinstance(order, int) or isinstance(order, bool) or order < 1: + raise ValueError('positive integer order required') + return sum((F((-1)**j * comb(order,j), order+j+1) + for j in range(order+1)), F(0)) + + +def lifetime_coefficient(): + return bump_integral() / 5 + + +def scaling_exponents(): + # ell=k*r^3 and k^3/r fixed: solve a+3b=1 and 3a-b=0. + return F(3,10), F(1,10), F(-1,5) # r, k, kappa + + +def run_checks(mutant=None): + if mutant not in (None, 'M1','M2','M3','M4','M5'): + raise ValueError('unknown mutation') + counts = dict(moving_layer=0,compact_cusp=0,fixed_gap=0,small_gap=0,integrals=0) + xs = (F(1,64),F(1,32),F(1,16),F(1,8),F(1,4)) + ss = (F(1),F(21,20),F(11,10),F(9,8),F(8,7)) + for x in xs: + for s in ss: + ell=x**10; r=x**3/s; k=x*s**3; kappa=k/r; t=s**5 + y=k**3/(r**2 if mutant=='M1' else r) + require(ell==k*r**3, 'CUBIC_LIFETIME') + require(y==t**2==r**2*kappa**3, 'MOVING_LAYER_ARGUMENT') + require(1<=t<2 and 04, 'FIXED_GAP_VANISHING') + counts['fixed_gap']+=1 + for r in (F(1,16),F(1,8),F(1,4),F(1,2),F(1)): + for q in (F(1,4),F(1,2),F(3,4),F(1)): + k=q*r + require(k**3/r<=1, 'SMALL_GAP_REGION_UNCHANGED') + counts['small_gap']+=1 + for m in (1,2,4): + require(bump_integral(m)==F(factorial(m)**2,factorial(2*m+1)), 'BUMP_INTEGRAL') + counts['integrals']+=1 + coefficient=bump_integral() if mutant=='M3' else lifetime_coefficient() + require(coefficient==F(1,3150), 'INTEGRATION_FACTOR_ONE_FIFTH') + rpower,kpower,kappapower=scaling_exponents() + require(kpower+3*rpower==1 and 3*kpower-rpower==0, 'BAND_POWERS') + require(2*kpower+rpower==F(1,2), 'HALF_POWER_EXPONENT') + require(kpower-rpower==kappapower, 'ESCAPING_KAPPA') + return {'status':'ESTIMATE_LEVEL_OBSTRUCTION_PASS','coefficient':str(coefficient), + 'counts':counts,'scientific_effect':'NONE','scientific_acceptance':False, + 'gaussian_counterexample':False,'global_absence_proved':False} + + +def main(argv=None): + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--mutant',choices=('M1','M2','M3','M4','M5')) + args=parser.parse_args(argv) + try: + result=run_checks(args.mutant) + except CheckFailure as exc: + print('BOUNDARY_LAYER_CHECK_FAIL: '+str(exc),file=sys.stderr) + return 1 + print(json.dumps(result,sort_keys=True,separators=(',',':'))) + return 0 + + +if __name__=='__main__': + raise SystemExit(main())