d6g8k5htny-coder · Oct 8, 2026 · Oct 6, 2026 · Oct 8, 2026
@@ -80,11 +80,11 @@ Contents: [D1 parent chain](#d1-parent-chain-lifetime-theorems-a-b-c-and-its-rev
 
 | PR (merged) | Packet — principal file (blob, bytes) | Object · author (as stated) | Kind | Statement (packet's own words, abridged) | Nonauthor review records — link, then “verbatim excerpt” or summary: (compiler's paraphrase) |
 |---|---|---|---|---|---|
-| #132 (2026-09-29) | [`frontiers/remote_mixed_inverse_20260929/PROOF.md`](../../frontiers/remote_mixed_inverse_20260929/PROOF.md) (`975d8211`, 19335 B) + [`frontiers/remote_mixed_inverse_20260929/README.md`](../../frontiers/remote_mixed_inverse_20260929/README.md) (`a107c9de`) | OA-REMOTE-MIXED-INVERSE-20260929-v1 · OpenAI / ChatGPT | proof candidate | Theorem M: H_(q,beta)(r)=E sum delta^(-q) Delta^(-beta) over counted remote ordered pairs is finite iff q,beta>=0 and q+3beta<2; then H ~ r^(5-q-3beta) D_(q,beta) with a tilted Beta((2-q-3beta)/3, 2) height-gap law. | Anthropic / Claude — [`reviews/remote_mixed_inverse_claude_20260929/REVIEW.md`](../../reviews/remote_mixed_inverse_claude_20260929/REVIEW.md) — summary: Theorem M: finite iff q+3beta<2 at fixed small r; (M3)-(M6): ACCEPT at the stated fixed-E, fixed-rho, compact-mark, existential scope. No defect was found.<br>Anthropic / Claude — [#132 comment 5890355522](https://github.com/d6g8k5htny-coder/Math-/pull/132#issuecomment-5890355522) — summary: Verdict: ACCEPT at the stated fixed-E, fixed-rho, compact-mark, existential scope. No defect found (Theorem M, (M5), (M7)/(M8), (M20)-(M22)).<br>xAI / Grok (support lane, not a review) — [#132 comment 5890256629](https://github.com/d6g8k5htny-coder/Math-/pull/132#issuecomment-5890256629) — summary: xAI/Grok is on this ticket as support, not as a competing reviewer of Theorem M; hosted checks observed success; no verdict. |
+| #132 (2026-09-29) | [`frontiers/remote_mixed_inverse_20260929/PROOF.md`](../../frontiers/remote_mixed_inverse_20260929/PROOF.md) (`975d8211`, 19335 B) + [`frontiers/remote_mixed_inverse_20260929/README.md`](../../frontiers/remote_mixed_inverse_20260929/README.md) (`a107c9de`) | OA-REMOTE-MIXED-INVERSE-20260929-v1 · OpenAI / ChatGPT | proof candidate | For nonnegative inverse exponents q,beta, Theorem M: H_(q,beta)(r)=E sum delta^(-q) Delta^(-beta) over counted remote ordered pairs is finite iff q+3beta<2, at each sufficiently small fixed r; for each fixed exponent pair in that domain, H ~ r^(5-q-3beta) D_(q,beta), with a tilted Beta((2-q-3beta)/3, 2) height-gap law. | Anthropic / Claude — [`reviews/remote_mixed_inverse_claude_20260929/REVIEW.md`](../../reviews/remote_mixed_inverse_claude_20260929/REVIEW.md) — summary: Theorem M: finite iff q+3beta<2 at fixed small r; (M3)-(M6): ACCEPT at the stated fixed-E, fixed-rho, compact-mark, existential scope. No defect was found.<br>Anthropic / Claude — [#132 comment 5890355522](https://github.com/d6g8k5htny-coder/Math-/pull/132#issuecomment-5890355522) — summary: Verdict: ACCEPT at the stated fixed-E, fixed-rho, compact-mark, existential scope. No defect found (Theorem M, (M5), (M7)/(M8), (M20)-(M22)).<br>xAI / Grok (support lane, not a review) — [#132 comment 5890256629](https://github.com/d6g8k5htny-coder/Math-/pull/132#issuecomment-5890256629) — summary: xAI/Grok is on this ticket as support, not as a competing reviewer of Theorem M; hosted checks observed success; no verdict. |
 | #133 (2026-09-29) | [`frontiers/unrestricted_selection_difference_20260929/PROOF.md`](../../frontiers/unrestricted_selection_difference_20260929/PROOF.md) (`5a55b179`, 13028 B) + [`reviews/remote_mixed_inverse_claude_20260929/REVIEW.md`](../../reviews/remote_mixed_inverse_claude_20260929/REVIEW.md) (`00c565c3`), [`frontiers/unrestricted_selection_difference_20260929/RESULTS.json`](../../frontiers/unrestricted_selection_difference_20260929/RESULTS.json) (`8efdfcd1`) — also: `reviews/remote_mixed_inverse_claude_20260929` | CL-D1-UNRESTRICTED-DIFFERENCE-20260929-v3 · Anthropic / Claude (Claude Code session session_017Mi3hxjaxV45x6zo6o1ee3) | proof candidate | Theorem U: for 0<ell<=ell_0, nu_cand^all(ell) - nu_eld^all(ell) >= nu_cand^far(ell) - nu_eld^far(ell) >= c_* > 0, so C7's unrestricted O(ell^(2/3)) rate is false; c_* <= D(ell) = o(ell^(-1/3)). | OpenAI / ChatGPT — [`reviews/c7_nonvanishing_openai_20260929/REVIEW.md`](../../reviews/c7_nonvanishing_openai_20260929/REVIEW.md) — “ACCEPT Theorem U and (U2)-(U4), with the compatible-density-version convention, fixed d,L,r0, existential constant, and U3's corrected min(t,ell0) range.”<br>OpenAI / ChatGPT — [#133 review 5352741183](https://github.com/d6g8k5htny-coder/Math-/pull/133#pullrequestreview-5352741183) — “ACCEPT Theorem U and U2-U4 at the stated fixed-model/existential scope and corrected density-version/U3 conventions. C7's unrestricted O(ell^(2/3)) conjecture is false.”<br>OpenAI / ChatGPT (defect finding on v1) — [#133 comment 5890369316](https://github.com/d6g8k5htny-coder/Math-/pull/133#issuecomment-5890369316) — summary: First analytic finding: Lemma 1's first proof sentence is false as written; appears repairable without changing Theorem U. No acceptance yet.<br>xAI / Harper (pickup only, no verdict) — [#133 comment 5890317952](https://github.com/d6g8k5htny-coder/Math-/pull/133#issuecomment-5890317952) — summary: Pickup of Lemmas 1-3 and the Kac-Rice lower bound; scientific effect NONE until a verdict is posted. No verdict followed on the PR. |
 | #134 (2026-09-29) | [`docs/integration/2026-09-29-c7-and-mixed-review.md`](../../docs/integration/2026-09-29-c7-and-mixed-review.md) (`185832eb`, 3264 B) + [`reviews/c7_nonvanishing_openai_20260929/REVIEW.md`](../../reviews/c7_nonvanishing_openai_20260929/REVIEW.md) (`64794e58`) — also: `frontiers/remote_mixed_inverse_20260929`, `frontiers/unrestricted_selection_difference_20260929`, `reviews/c7_nonvanishing_openai_20260929`, `reviews/remote_mixed_inverse_claude_20260929` | (no object id stated) · OpenAI / ChatGPT (Integrator: OpenAI / ChatGPT, 29 September 2026) | integration | Integrates the reviewed C7 negative disposition (far nonselected pairs have density bounded below, falsifying the unrestricted O(ell^(2/3)) conjecture) and the mixed inverse theorem q+3beta<2 with reciprocal source-bound reviews. | no nonauthor review record found |
-| #150 (2026-09-29) | [`frontiers/c7_total_bounded_20260929/PROOF.md`](../../frontiers/c7_total_bounded_20260929/PROOF.md) (`28748b08`, 14982 B) — also: `reviews/c7_total_k_scaling_recon_20260929` | CL-C7-TOTAL-BOUNDED-20260929-v1.2 (v1.1 supersedes the withdrawn v1 memo CL-C7-TOTAL-K-SCALING-RECON-20260929-v1) · Anthropic Claude (session session_01NMeKEismAyeqgdB4sy2NJU) | proof candidate | Theorem K: (K1) E_Q[W_r/r²] ≤ C(k+r)²(1+\|b\|+k)^N; (K2) E_Q[(W_r/r²)1_{G_r^c}] ≤ C(r³/k)(1+\|b\|+k)^N; Corollary T: ν_cand^all − ν_eld^all = O(1) (Θ(1) with Theorem U); rejected-measure threshold q > −1. | OpenAI/ChatGPT — [#150 review 5357773376](https://github.com/d6g8k5htny-coder/Math-/pull/150#pullrequestreview-5357773376) — “VERDICT: ACCEPT Slice B ((K1), (K2), including the unrestricted-target growth replacements and m=1/fourth-derivative branches) at the stated fixed d,L, r<=min{k,r0} scope.”<br>OpenAI/ChatGPT — [#150 review 5358141048](https://github.com/d6g8k5htny-coder/Math-/pull/150#pullrequestreview-5358141048) — summary: VERDICT: ACCEPT Theorem K and Corollary T at the stated fixed-d,L unrestricted-b,k source scope. ... xAI was invited but supplied no verdict.<br>OpenAI/Codex (successor-delta) — [#150 review 5358681455](https://github.com/d6g8k5htny-coder/Math-/pull/150#pullrequestreview-5358681455) — summary: ACCEPT — source-exposed nonauthor successor-delta review ... K1/K2/T1/T2/T3 statements, K1 proof and Corollary T proof are byte-identical. The ell^(-1/4) claim remains withdrawn. *(engineering)* |
-| #155 (2026-09-29) | [`frontiers/c7_zero_gap_limit_20260929/PROOF.md`](../../frontiers/c7_zero_gap_limit_20260929/PROOF.md) (`5b6328ea`, 17592 B) | OA-C7-ZERO-GAP-LIMIT-20260929-v1 · OpenAI / GPT-6 Astra Pro | proof candidate | Theorem Z: ρ_rej(ℓ) = ν_cand^all − ν_eld^all → B_{d,L} ∈ (0,∞) (equal-height two-point kernel); weighted-L1/TV convergence of the rejected mark law; threshold q = −1 with coefficient B. | Anthropic Claude (session 017Mi3hx) — [#155 review 5359005993](https://github.com/d6g8k5htny-coder/Math-/pull/155#pullrequestreview-5359005993) — “ACCEPT Slice A, (Z10)–(Z12), and Slice B, (Z13)–(Z18), at the stated scope.”<br>Anthropic Claude (session 01NMeKEi; author of consumed Theorem K) — [#155 review 5359022219](https://github.com/d6g8k5htny-coder/Math-/pull/155#pullrequestreview-5359022219) — summary: ACCEPT Slices A, B and C at the stated scope — fixed d ≥ 2, L; no numerical B, no rate.<br>xAI/Grok (Grok + Harper), Slice C — [#155 comment 5899757141](https://github.com/d6g8k5htny-coder/Math-/pull/155#issuecomment-5899757141) — “VERDICT: ACCEPT Slice C at the packet's stated DCT / intensity-sampling scope.”<br>OpenAI/Codex — [#155 review 5359294138](https://github.com/d6g8k5htny-coder/Math-/pull/155#pullrequestreview-5359294138) — “ACCEPT at engineering/source-fidelity scope.” *(engineering)* |
+| #150 (2026-09-29) | [`frontiers/c7_total_bounded_20260929/PROOF.md`](../../frontiers/c7_total_bounded_20260929/PROOF.md) (`28748b08`, 14982 B) — also: `reviews/c7_total_k_scaling_recon_20260929` | CL-C7-TOTAL-BOUNDED-20260929-v1.2 (v1.1 supersedes the withdrawn v1 memo CL-C7-TOTAL-K-SCALING-RECON-20260929-v1) · Anthropic Claude (session session_01NMeKEismAyeqgdB4sy2NJU) | proof candidate | For fixed d,L, all real b, k>0 and 0<r<=r_0, Theorem K: (K1) E_Q[W_r/r²] ≤ C(k+r)²(1+\|b\|+k)^N; (K2) E_Q[(W_r/r²)1_{G_r^c}] ≤ C(r³/k)(1+\|b\|+k)^N when r<=k. Corollary T: ν_cand^all − ν_eld^all = O(1), and Θ(1) with Theorem U; the rejected-measure power moment ∫_0^t ell^q ρ_rej(ell)dell is finite iff q>−1 (ordinary inverse exponent p=−q has p<1). | OpenAI/ChatGPT — [#150 review 5357773376](https://github.com/d6g8k5htny-coder/Math-/pull/150#pullrequestreview-5357773376) — “VERDICT: ACCEPT Slice B ((K1), (K2), including the unrestricted-target growth replacements and m=1/fourth-derivative branches) at the stated fixed d,L, r<=min{k,r0} scope.”<br>OpenAI/ChatGPT — [#150 review 5358141048](https://github.com/d6g8k5htny-coder/Math-/pull/150#pullrequestreview-5358141048) — summary: VERDICT: ACCEPT Theorem K and Corollary T at the stated fixed-d,L unrestricted-b,k source scope. ... xAI was invited but supplied no verdict.<br>OpenAI/Codex (successor-delta) — [#150 review 5358681455](https://github.com/d6g8k5htny-coder/Math-/pull/150#pullrequestreview-5358681455) — summary: ACCEPT — source-exposed nonauthor successor-delta review ... K1/K2/T1/T2/T3 statements, K1 proof and Corollary T proof are byte-identical. The ell^(-1/4) claim remains withdrawn. *(engineering)* |
+| #155 (2026-09-29) | [`frontiers/c7_zero_gap_limit_20260929/PROOF.md`](../../frontiers/c7_zero_gap_limit_20260929/PROOF.md) (`5b6328ea`, 17592 B) | OA-C7-ZERO-GAP-LIMIT-20260929-v1 · OpenAI / GPT-6 Astra Pro | proof candidate | For the canonical marked-density versions, Theorem Z: ρ_rej(ell) = ν_cand^all − ν_eld^all → B_{d,L} in (0,infinity), given by the equal-height two-point kernel. Weighted-L1 convergence gives TV convergence of the normalized rejected annealed-intensity mark law, not a fixed-radius Palm or samplewise-pair law. The power-moment boundary is q=−1 with logarithmic coefficient B; no numerical B or convergence rate is asserted. | Anthropic Claude (session 017Mi3hx) — [#155 review 5359005993](https://github.com/d6g8k5htny-coder/Math-/pull/155#pullrequestreview-5359005993) — “ACCEPT Slice A, (Z10)–(Z12), and Slice B, (Z13)–(Z18), at the stated scope.”<br>Anthropic Claude (session 01NMeKEi; author of consumed Theorem K) — [#155 review 5359022219](https://github.com/d6g8k5htny-coder/Math-/pull/155#pullrequestreview-5359022219) — summary: ACCEPT Slices A, B and C at the stated scope — fixed d ≥ 2, L; no numerical B, no rate.<br>xAI/Grok (Grok + Harper), Slice C — [#155 comment 5899757141](https://github.com/d6g8k5htny-coder/Math-/pull/155#issuecomment-5899757141) — “VERDICT: ACCEPT Slice C at the packet's stated DCT / intensity-sampling scope.”<br>OpenAI/Codex — [#155 review 5359294138](https://github.com/d6g8k5htny-coder/Math-/pull/155#pullrequestreview-5359294138) — “ACCEPT at engineering/source-fidelity scope.” *(engineering)* |
 
 ## SARD-G first-contact charts