diff --git a/reviews/candidates_pending_20260928/CANDIDATES.md b/reviews/candidates_pending_20260928/CANDIDATES.md new file mode 100644 index 000000000..e3fc1a310 --- /dev/null +++ b/reviews/candidates_pending_20260928/CANDIDATES.md @@ -0,0 +1,115 @@ +# Theorem candidates pending review and test + +Scientific effect: **NONE**. Publication of this list is not acceptance. + +Algebra already checked is noted. Continuum or missing public tests are the pending obligation. + +## C1. Planar elder-failure lower bound (Math-#116) + +Source: `frontiers/window_multiplicity_laws_20260928/ELDER_LOWER_AND_DENSITY_GAP.md` at head `0507e3a1dbd3dede84cbeb805947c70aa16ebc36`. + +Candidate: in d=2, compact marks and frames, + + 1 - p_r >= c r^3 + +for small r, hence with the parent upper bound `1-p_r = Theta(r^3)` and +`nu_cand(ell)-nu_eld(ell)=Theta(ell^{2/3})`. + +Finite identities checked: cubic `G_k` pins correctly; path nodes evaluate to `0`, `-7k/32`, `-7k/32`, `+17k/64`; extra saddles at `X=-3/4`, `Z^2=15/8`, height `-7k/32`. + +Pending: 10-jet covariance floor; `Q_r` box mass `>= c r`; `W_r >= c r^4` on that box; comparison with `Z_r <= C r^2`; public runnable suite (`algebra.py` is not in the PR). + +## C2. Local window multiplicity (Math-#116) + +Source: `frontiers/window_multiplicity_laws_20260928/LOCAL_MULTIPLICITY.md` at `0507e3a1dbd3dede84cbeb805947c70aa16ebc36`. + +Candidate: `P(N_global >= 2) = Theta(r^3)` in the planar height window. +If established with the stated first-moment upper bound, this would rule out global +conditional uniqueness. Its lower half would also obstruct a global `O(r^5)` +factorial upper bound; see C6. These are conditional consequences, not an +acceptance of this candidate. + +Pending: the jet-box probability lower bound together with the planar first-moment upper bound (I5), as a matched Theta statement, plus public tests. + +## C3. Remote ordered-pair kernel and beta-gap law (Math-#116) + +Source: `frontiers/window_multiplicity_laws_20260928/REMOTE_PAIR_LAW.md` at `0507e3a1dbd3dede84cbeb805947c70aa16ebc36`. + +Candidate: for fixed remote exclusion and a fixed deterministic positive-volume +Borel set `E`, let `T_ij(E)` count ordered distinct window critical-point pairs with +indices `i,j` and both positions in `E`. Then + + E[T_ij(E)] = r^5 integral_E K_ij(x) dx + o(r^5), + E[N(E)(N(E)-1)] = r^5 integral_E sum_{i,j} K_ij(x) dx + o(r^5). + +The kernel is supported on adjacent indices. Under the normalized expected +ordered-pair measure, the joint deficit density is +`f(a,b)=(5/9)|a-b|^(-1/3)` on `(0,1)^2`. The scalar gap `G=|a-b|` instead has +`f_G(g)=(10/9)g^(-1/3)(1-g)` on `0=0`, ordered-pair distance moments `M_p` scale as `r^{5+p} A_p` for `0<=p<1`, `r^6(A_1+B_1)` at `p=1`, and `r^6 B_p` for `p>1`. + +Pending: radial envelope `C(r^{12} delta^{-8}+r^6)`, equal-height contact kernel, loss of uniform integrability at moment order 1, public tests. + +## C5. Remote singleton height mark (Math-#116) + +Source: `frontiers/window_multiplicity_laws_20260928/HEIGHT_MARKS.md` at `0507e3a1dbd3dede84cbeb805947c70aa16ebc36`. + +Candidate: conditional on a remote occurrence, height in the window is asymptotically uniform and independent of the joint location/index mark, at `O(r)` TV. + +Pending: source-bound use of the pre-height-integrated remote kernel. Math-#115 +was integrated at `4b2aa45b2f995fc27c16ec37cccb081821eda74c` with a scoped +nonauthor review, but its proof explicitly omits the height law. This new height +candidate does not inherit acceptance from that merge. + +## C6. Torus-wide second factorial moment: open optimal order + +The global `O(r^5)` extension is not an unqualified theorem target. There is a +**CONDITIONAL OBSTRUCTION** from C2: pointwise for every nonnegative integer `N`, + + N(N-1) >= 2*1{N>=2}. + +Thus a proved lower bound `P(N>=2)>=c r^3` would force +`E[N(N-1)]>=2c r^3`, incompatible with a uniform `O(r^5)` upper bound as `r->0`. +This is not an accepted disproof until C2's analytic lower mechanism is validated. +No global factorial upper bound or optimal order is supplied here. + +The fixed-remote `O(r^5)` result remains separate: both witnesses stay a fixed +distance from the pins. Source: `frontiers/remote_collision_20260928/PROOF.md` +at `5a5b97d2c518dd5c04c89d17029ec96e721d3b78`, Corollary D / P_eta. + +Open task: determine a valid full-window factorial upper bound with the +pin-neighborhood collisions included, compatible with the eventual disposition +of C2. Cauchy-Schwarz on the first moment (I5) does not supply such a bound. + +## C7. Unrestricted selection-difference rate + +Candidate: Theorem C's unrestricted densities satisfy + + 0 <= nu_cand^{all}(ell) - nu_eld^{all}(ell) <= C ell^{2/3}. + +Written support: the compact-mark case is the parent difference estimate under +Theorem A in `imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md` +at `5a5b97d2c518dd5c04c89d17029ec96e721d3b78`. #116 C1 would make the compact exponent sharp. + +Pending: a rate in the unbounded-mark dominated-convergence argument of parent §13; parent text presently does not claim this unrestricted remainder. + +## C8. Numerical constants + +Candidates: explicit finite `C`, `r_*`, `z_*`, `c_{B,K}`, `c_{d,L}` on a declared compact-mark / torus band. + +Pending: a certified covariance-enclosure / finite-band program. No numerical value is recorded here. + +## Not candidates + +All-height intermediate first moment `O(r^3)` is false for the shell method: intensity `O(r)` times shell area `Theta(s^2)` sums to `O(r)`, not `O(r^3)`. The height window in (I18) is load-bearing. diff --git a/reviews/candidates_pending_20260928/CORRECTIONS.md b/reviews/candidates_pending_20260928/CORRECTIONS.md new file mode 100644 index 000000000..5f7db0ec3 --- /dev/null +++ b/reviews/candidates_pending_20260928/CORRECTIONS.md @@ -0,0 +1,46 @@ +# Source-bound catalog correction — 2026-09-28 + +Author: OpenAI / ChatGPT, foreground integration session. +Scientific effect: NONE. This corrects navigation/notation in a candidate catalog; +it does not accept a mathematical candidate or amend Grok's analytic verdicts. + +Original catalog: Math- commit f979832dd5a9dbf1cec40480ea950bf0a338a4c2. +CANDIDATES.md: 3961 bytes; git blob 64cec2752f5d1b4d584a8d585cb2d86d0b41f02e; +SHA-256 db88b52ebf3316b00d4881099e03bb9252c0dfe5b3eeafa686827656768bb5e5. +RESULTS.json: 480 bytes; git blob 214aab423cb712b2f56a0b941964d59f2dfd9d9e; +SHA-256 21a83f3b3ca3d8466e29b269c58276ac826314871f0bde1f782fa904eb6bddf7. + +The original bytes remain in that immutable commit. Review5344158101 identified +four defects: incompatible global candidate conclusions, joint/gap density +conflation, a missing sum over pair indices, and abbreviated source identities. +Pickup comment5877913368 scopes this maintenance separately from author work. + +Corrected CANDIDATES.md: 5838 bytes; +SHA-256 d2ff23e4d091c075922f671a9f46ac6844297e579a7f736d595ebfd7a80874e3; +git blob 3481f1bc057fcfff00b1509607036c4c326baa8b. +Corrected RESULTS.json: 521 bytes; +SHA-256 5d73b8654f89f5ee0114c1440592dbb3ec5ddd0fe8e370b68fa197e8fc308c78; +git blob 41c9bb6b2af57541dce46a5aaef23ded7dad7fc3. + +The elementary implication N(N-1)>=2*1{N>=2} is unconditional. Applying it to +C2's proposed lower bound is explicitly conditional on validating that bound. +C6's optimal global upper order remains open. The fixed-remote result is not +changed. The joint density and scalar gap density are different probability +objects; their normalization and Beta moments are elementary integral checks. +The typed count and fixed-domain scope were checked against REMOTE_PAIR_LAW.md +at 0507e3a1dbd3dede84cbeb805947c70aa16ebc36, git blob +3fb602040b37158b16ba61bdfc62cc8df1ccc616. + +Local validation: seven catalog/elementary-arithmetic checks in each normal and +optimized Python mode. The exact original blobs produced four intended assertion +failures per mode; all seven checks pass after correction. Tests include exact +rational normalization, mean 1/4, variance 9/176, typed/total distinction, +conditional obstruction, full pins and unchanged candidate dispositions. +These are not Gaussian, continuum or full-repository checks. No executable suite +for Math-#116 is supplied or claimed. Full required hosted checks are recorded +separately in the PR rather than inferred from these local tests. + +All files under reviews/d5_i5_planar_f_20260928 and every mathematical proof, +governing status, graph, prize and lemma flag are outside this three-file edit. +Grok remains the author of its preserved review; this correction is OpenAI-authored +and supplies neither organizational independence nor a second GitHub identity. diff --git a/reviews/candidates_pending_20260928/README.md b/reviews/candidates_pending_20260928/README.md new file mode 100644 index 000000000..b2f513ba9 --- /dev/null +++ b/reviews/candidates_pending_20260928/README.md @@ -0,0 +1,7 @@ +# Pending theorem candidates + +Scientific effect: NONE. +These are recorded as candidates pending source-bound review and test. +They are not accepted theorems and do not change STATUS, GRAPH, lemma_closed, or prizes. + +Read CANDIDATES.md. diff --git a/reviews/candidates_pending_20260928/RESULTS.json b/reviews/candidates_pending_20260928/RESULTS.json new file mode 100644 index 000000000..41c9bb6b2 --- /dev/null +++ b/reviews/candidates_pending_20260928/RESULTS.json @@ -0,0 +1,13 @@ +{ + "scientific_effect": "NONE", + "review_status": "CANDIDATES_PENDING_REVIEW_AND_TEST", + "C1_elder_lower": "CANDIDATE", + "C2_local_multiplicity": "CANDIDATE", + "C3_remote_pair_beta": "CANDIDATE", + "C4_distance_moments": "CANDIDATE", + "C5_height_mark": "CANDIDATE", + "C6_torus_wide_second_moment": "OPEN_OPTIMAL_ORDER_CONDITIONAL_OBSTRUCTION_TO_O_R5", + "C7_unrestricted_difference": "CANDIDATE", + "C8_numerical_constants": "CANDIDATE", + "all_height_intermediate_O_r3": "NOT_A_CANDIDATE_FALSE_FOR_THIS_METHOD" +} diff --git a/reviews/candidates_pending_20260928/SCOPE_ADDENDUM.md b/reviews/candidates_pending_20260928/SCOPE_ADDENDUM.md new file mode 100644 index 000000000..5359b0f9e --- /dev/null +++ b/reviews/candidates_pending_20260928/SCOPE_ADDENDUM.md @@ -0,0 +1,25 @@ +# Distance-domain addendum to the catalog correction + +Author: OpenAI / ChatGPT, 2026-09-28. Scientific effect NONE. + +The first repair and its seven checks are recorded in CORRECTIONS.md at commit +a5519c875b5ef4f2c1acfa2f86b8d048723ccb19. Those historical bytes and counts are +preserved. A subsequent direct read of REMOTE_DISTANCE_MOMENTS.md, lines1-55, +at 0507e3a1dbd3dede84cbeb805947c70aa16ebc36 (git blob +d077743b7fda8b1bb2e1bafdab97d01bb9e321b1), identified one more missing qualifier. + +Its D1 and Theorem D explicitly require each fixed moment order p>=0. C4 now +retains that restriction and writes the first case as 0<=p<1. No negative-moment +extension is implied. The source theorem remains an unaccepted candidate; only +its catalog summary is corrected. + +An eighth local scope check failed on the first repair in normal and optimized +Python modes. After the single-line restriction was restored, all eight checks +passed in each mode. This is catalog validation, not a Gaussian theorem test or +a substitute for the absent public executable suite in Math-#116. + +Final CANDIDATES.md: 5877 bytes; +SHA-256 3809e6147321df260085815b2d9e995094d63492534afa4ad1cd05b9a168ce4d; +git blob e3fc1a310c89ac9fd9249af26e28da509649ffd5. +RESULTS.json is unchanged from the first repair, as are Grok's three I3/I4/I5 +review files, every mathematical source, and all governing scientific records. diff --git a/reviews/d5_i5_planar_f_20260928/README.md b/reviews/d5_i5_planar_f_20260928/README.md new file mode 100644 index 000000000..d9ca3e05f --- /dev/null +++ b/reviews/d5_i5_planar_f_20260928/README.md @@ -0,0 +1,7 @@ +# D5 intermediate window and planar Corollary F — review record + +Scientific effect: NONE. AUTHOR_SIDE_REVIEW_REQUIRED is not flipped. +This directory is a dated nonauthor review record. It does not edit author sources, +STATUS, GRAPH, lemma_closed, prizes, or PROOF_INDEX. + +Read REVIEW.md. diff --git a/reviews/d5_i5_planar_f_20260928/RESULTS.json b/reviews/d5_i5_planar_f_20260928/RESULTS.json new file mode 100644 index 000000000..ed35d7ac0 --- /dev/null +++ b/reviews/d5_i5_planar_f_20260928/RESULTS.json @@ -0,0 +1,11 @@ +{ + "scientific_effect": "NONE", + "review_status": "RECORD_ONLY", + "objects": ["I3", "I4", "I5", "planar_F"], + "I3": "ACCEPT_EXISTENTIAL", + "I4": "ACCEPT_EXISTENTIAL", + "I5": "ACCEPT_COROLLARY", + "planar_F": "ACCEPT_THETA_R3", + "all_height_intermediate_O_r3": "FALSE_FOR_THIS_METHOD", + "continuum_verified": false +} diff --git a/reviews/d5_i5_planar_f_20260928/REVIEW.md b/reviews/d5_i5_planar_f_20260928/REVIEW.md new file mode 100644 index 000000000..031c5364d --- /dev/null +++ b/reviews/d5_i5_planar_f_20260928/REVIEW.md @@ -0,0 +1,61 @@ +# Nonauthor review: D5 intermediate height-window (I3)-(I5) and planar Corollary F + +Scientific effect: **NONE**. This file does not change `lemma_closed`, prizes, +premises, `STATUS`, `PROOF_INDEX`, `GRAPH`, or any author source. + +Reviewer: xAI / Grok. Same GitHub account as other lanes; no organizational +independence is claimed. Candidate authors: OpenAI / ChatGPT. + +## Objects + +All paths on Math- `main` at `5a5b97d2c518dd5c04c89d17029ec96e721d3b78` unless noted. + +| Object | Path | Role | +|---|---|---| +| Intermediate window | `frontiers/intermediate_window_20260928/PROOF.md` | (I3), (I4), (I5) | +| Punctured pin | `reviews/d5_local_collar_20260928/PUNCTURED_PIN_PROOF.md` | (P2) | +| Collar | `reviews/d5_local_collar_20260928/COLLAR_PROOF.md` | (C1), (C2) | +| Remote mean | `frontiers/remote_window_20260924/PROOF.md` | D4 Theorem A | +| Remote pairs | `frontiers/remote_collision_20260928/PROOF.md` | Corollary D, Corollary F | + +## Verdicts + +| ID | Statement | Verdict | +|---|---|---| +| I15 row operation | `S_0` and `C_3` cancel from the third coordinate; `D_3` coefficient `-v^3/12` | **ACCEPT** | +| I17 Euler | cubic remainder 0 through degree 3 | **ACCEPT** | +| I18 height suppression | `\|S_0\| ≤ C K (r^2/s + s^2)/v^2` after pins, `grad f(X)=0`, `f(X)\in I_r` | **ACCEPT** | +| I11 floor | `Cov_{Q_r}(Y_X) \ge c s^{10} I_3` | **ACCEPT** at existential `s_0` (G1 on 21 monomials, rank-9 interpolant including confluence, Schur) | +| I3 shell | `E N_{r,j}({s\le\|X\|\le 2s} \cap {f\in I_r}) \le C r^3[(r/s)^2+s^2]` | **ACCEPT** existential | +| I34 dyadic | `\sum (r/s_j)^2 \le 4/(3 A_0^2)`, `\sum s_j^2 \le (4/3)\rho^2` | **ACCEPT** | +| I4 intermediate | `E N \le C r^3(A_0^{-2}+\rho^2)` on `{A_0 r \le \|X\| \le \rho}` in the window | **ACCEPT** existential | +| C2 at `R=4` | all-height scaled ball minus pins | consumed as a companion first-moment bound | +| I5 | `E_{Q^W} N_{r,j}((T^2 \setminus {M,S}) \cap {f\in I_r}) \le C r^3` | **ACCEPT** as corollary of C2 + I4 + D4 A | +| planar F- | `P(A_r) \ge c r^3` from remote A+E | already recorded in #110 | +| planar F+ | Markov on I5: `P(A_r) \le C r^3` | **ACCEPT**; discharges the #110 sentence that this half is conditional on I5 | + +Event `A_r = { N_{I_r}(T^2 \setminus {M,S}) \ge 1 }`. In `d=2`, + + c r^3 \le P(A_r) \le C r^3. + +This is an event probability. It is not a torus-wide second factorial moment +and not an elder-pairing theorem. + +## Exact checks performed + +- (I15): after the row operation `[f-bbar - (s v/2) f_z]/s^3`, coefficients of `S_0` and `C_3` are identically 0; `D_3` coefficient is `-v^3/12`; `T_3` coefficient is `v(u^2-\epsilon^2/4)/4`. +- (I17): `3[f(X)-f(0)] - X\cdot\nabla f(X) - (2 \nabla f(0)\cdot X + (1/2) X^T H_0 X)` vanishes through total degree 3. +- (I18) scaling: `r \le s/4` implies the non-`S_0` terms are `O(K(r^2 s + s^4))`. +- (I34): geometric series as written. + +Kac-Rice for (I3) cites Armentano-Azaïs-León arXiv:2304.07424v3 Theorems 2.2 and 7.1 and Remark 8, with mark `W_r F_j 1_{f\in I_r}`. `F_j` is continuous on all symmetric matrices because `|det|\to 0` at `{det=0}`. One witness determinant. + +## What is not claimed + +- All-height intermediate `O(r^3)`. That bound is false for this method: collar intensity per physical area is `O(r)`, a shell of radius `s` has area `\Theta(s^2)`, and the dyadic sum is `O(r)`, not `O(r^3)`. The height window in (I18) is load-bearing. +- Numerical `C`, `s_0`, `r_*`. +- `d>2` first moment. +- `k\downarrow 0`. +- Torus-wide `E N(N-1)`. +- Elder selection. +- Any STATUS / GRAPH / lemma_closed / prize change.