From 3f6be6acc39175db29581739f8c110e955f0b2c3 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Mon, 5 Oct 2026 23:35:01 +0000 Subject: [PATCH 1/3] =?UTF-8?q?D5=20erratum=20DL-AXIS-K-01:=20the=20=C2=A7?= =?UTF-8?q?6.4=20axis-safe=20endpoint=20display=20omits=20the=20Lipschitz?= =?UTF-8?q?=20factor;=20consumed=20bound=20unchanged=20(additive,=20scient?= =?UTF-8?q?ific=20effect=20NONE)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-Authored-By: Claude Fable 5.1 Claude-Session: https://claude.ai/code/session_015wNj8LPTKXsaT68G3DgPPh --- .../ERRATUM.md | 71 +++++++++++++++++++ 1 file changed, 71 insertions(+) create mode 100644 reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md diff --git a/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md b/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md new file mode 100644 index 000000000..a9b205e13 --- /dev/null +++ b/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md @@ -0,0 +1,71 @@ +# Erratum DL-AXIS-K-01: the axis-safe endpoint display in §6.4 omits the Lipschitz factor + +Scientific effect: **NONE**. Dylan Roy, delegated AI work. Author: Anthropic / +Claude, Claude Code session `session_015wNj8LPTKXsaT68G3DgPPh`, the author of +`frontiers/d5_dimension_lift_20260929/PROOF.md` ([DL], [D5]). + +This file is additive and lives outside the packet directory on purpose: the +packet's workflow (`.github/workflows/d5-dimension-lift.yml`) pins the exact +file set of `frontiers/d5_dimension_lift_20260929/` to `SOURCE_FILES.json`, so +nothing is added there. `PROOF.md` stays byte-identical (Git blob +`9d82c707fdb17d3072a8930f26dabedf59e456fc`, the bytes reviewed on Math-#141 +and consumed by [CP] and [SC]). No theorem, constant, exponent, status, index +or review changes. The finding is OpenAI / GPT-6 Astra Pro's DL-AXIS-K-01, +main#259 comment 6004712957, raised during the IBA2-010 interface audit +(checks 3 and 4, main#259 comment 6004871493); it was verified against the +source before being written here. + +## The display (`frontiers/d5_dimension_lift_20260929/PROOF.md` §6.4, "Axis-safe bound", line 524) + +The source says that the two endpoint short columns `H_M e_x`, `H_S e_x` have +size at most `L r/2` by [LP] (5.3), and then concludes from Lemma D2 that + + |det H_M|, |det H_S| <= C r K^(d-1). + +Lemma D2 (line 116) is `|det H| <= ||H e|| K^(d-1)`. With `||H_i e_x|| <= L r/2` +it gives + + |det H_i| <= (L r / 2) K^(d-1) <= (r / 2) K^d, i in {M, S}, + +using `L <= K` from §1.1 (line 28), where `L` is the Hessian Lipschitz +constant on the chart and `K` dominates `1 + ||f||_(C^6)`. `L` is not a fixed +constant and cannot be absorbed into `C`: for `0 < r <= 1` and `L = K = A`, +the matrix `H = diag(r A/2, A, ..., A)` has operator norm `A` and exactly the +permitted short column, but `|det H| / (r K^(d-1)) = A/2` is unbounded in `A`. +The display as printed is therefore wrong by the factor `L/K <= 1`; the +corrected display is the one above. + +## Why nothing downstream changes + +The very next clause of the same paragraph uses + + W_r |det H_X| <= C r^2 K^(3d), + +which is what the corrected endpoint bounds give: `W_r = |det H_M| |det H_S| +<= (r^2/4) K^(2d)` and `|det H_X| <= K^d`. The faulty intermediate display +would have given the *smaller* power `K^(3d-2)`, which the source never used. +After the single division by [LP] (5.5), `Z_r >= z_* r^2`, the paragraph's +conclusion `W_r |det H_X| / Z_r <= C K^(3d)` on the whole strip `|v| <= s^(1/8)` +stands as written, and §6.5 (line 528) consumes exactly that `K^(3d)` bound. + +Consequently Theorem I_d (1.5)–(1.6), Theorem G_d (1.7), the `r/s` powers, the +shell ledger of §6.7 and every statement in §1.2 are unchanged. The consumer +[CP] `frontiers/c6_palm_route_20260929/PROOF.md` (blob `89eb8adf…`) §6.2 row +R3a writes the endpoint product as `C r^2 K^(2d)` and the final bound as +`C K^(3d)` directly, so it never relied on the misprinted display. [SC] +consumes only (1.6) and (1.7). + +## Scope check + +The other two places where a short column or an axial displacement enters a +determinant bound already carry the Lipschitz factor through `K`: line 210 +(`O(r |p| K)`) and line 506 (`A_i = S_0 + O(rK)`). The omission is confined to +the single display quoted above. + +## Record + +- Finding: DL-AXIS-K-01, Astra, main#259 6004712957 (2026-10-05 22:45Z). +- Author readback: main#259, posted with this erratum. +- Correction: this file. `PROOF.md` unchanged. Any future revision of + `PROOF.md` should replace the display with the corrected one and cite this + erratum. From d906da953c1a6e1663cd552bf66474759274e3f8 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Mon, 5 Oct 2026 23:41:12 +0000 Subject: [PATCH 2/3] D5 erratum DL-AXIS-K-01 v1.1: name the omitted factor as L, bound W_r by the determinant product, pin [SC] and disambiguate [CP], record the (5.3) mis-citation (Codex review 5422003010) Co-Authored-By: Claude Fable 5.1 Claude-Session: https://claude.ai/code/session_015wNj8LPTKXsaT68G3DgPPh --- .../ERRATUM.md | 46 +++++++++++++------ 1 file changed, 33 insertions(+), 13 deletions(-) diff --git a/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md b/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md index a9b205e13..a0e729c11 100644 --- a/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md +++ b/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md @@ -18,10 +18,18 @@ source before being written here. ## The display (`frontiers/d5_dimension_lift_20260929/PROOF.md` §6.4, "Axis-safe bound", line 524) The source says that the two endpoint short columns `H_M e_x`, `H_S e_x` have -size at most `L r/2` by [LP] (5.3), and then concludes from Lemma D2 that +size at most `L r/2` "by [LP] (5.3)", and then concludes from Lemma D2 that |det H_M|, |det H_S| <= C r K^(d-1). +**(b) Citation.** The column bound `||H_i e_x|| <= L r/2` is the critical-segment +identity `||H_U e|| <= L |V - U| / 2` for `e = (V - U)/|V - U|` ([PP] (P15)), +which `PROOF.md` §4.6 (line 284) states and §5 (line 405) and §6.4 (line 516) +reuse as "the segment `MS` gives `||H_M e_x|| <= Lr/2`". [LP] (5.3) is the block +determinant identity `det H_i / r = alpha_i det A_i - r beta_i^T adj(A_i) beta_i` +and does not state a column bound; the "(5.3)" at line 524 is a mis-citation. +The bound itself is correct and is the one used below. + Lemma D2 (line 116) is `|det H| <= ||H e|| K^(d-1)`. With `||H_i e_x|| <= L r/2` it gives @@ -32,7 +40,8 @@ constant on the chart and `K` dominates `1 + ||f||_(C^6)`. `L` is not a fixed constant and cannot be absorbed into `C`: for `0 < r <= 1` and `L = K = A`, the matrix `H = diag(r A/2, A, ..., A)` has operator norm `A` and exactly the permitted short column, but `|det H| / (r K^(d-1)) = A/2` is unbounded in `A`. -The display as printed is therefore wrong by the factor `L/K <= 1`; the +The display as printed therefore omits the factor `L` (equivalently, after +`L <= K`, one power of `K`): the discrepancy is unbounded, not a constant. The corrected display is the one above. ## Why nothing downstream changes @@ -41,31 +50,42 @@ The very next clause of the same paragraph uses W_r |det H_X| <= C r^2 K^(3d), -which is what the corrected endpoint bounds give: `W_r = |det H_M| |det H_S| -<= (r^2/4) K^(2d)` and `|det H_X| <= K^d`. The faulty intermediate display +which is what the corrected endpoint bounds give: `W_r = F_d(H_M) F_(d-1)(H_S) +<= |det H_M| |det H_S| <= (r^2/4) K^(2d)` (with equality on the typed support +and `W_r = 0` off it) and `|det H_X| <= K^d`. The faulty intermediate display would have given the *smaller* power `K^(3d-2)`, which the source never used. After the single division by [LP] (5.5), `Z_r >= z_* r^2`, the paragraph's conclusion `W_r |det H_X| / Z_r <= C K^(3d)` on the whole strip `|v| <= s^(1/8)` stands as written, and §6.5 (line 528) consumes exactly that `K^(3d)` bound. Consequently Theorem I_d (1.5)–(1.6), Theorem G_d (1.7), the `r/s` powers, the -shell ledger of §6.7 and every statement in §1.2 are unchanged. The consumer -[CP] `frontiers/c6_palm_route_20260929/PROOF.md` (blob `89eb8adf…`) §6.2 row -R3a writes the endpoint product as `C r^2 K^(2d)` and the final bound as -`C K^(3d)` directly, so it never relied on the misprinted display. [SC] -consumes only (1.6) and (1.7). +shell ledger of §6.7 and every statement in §1.2 are unchanged. The two +consumers, pinned at Math- `main` `c08e83597f94f923b8411dc13cdf28be3f214b37`: +- the C6 Palm route, `frontiers/c6_palm_route_20260929/PROOF.md`, blob + `89eb8adf08fe7afc2cab9662d3a9875c05ae5cc5` (called [CP] in the IBA2-010 + ledger; note that `PROOF.md`'s own `[CP]` tag denotes the planar collar + template `reviews/d5_local_collar_20260928/COLLAR_PROOF.md`, a different + file), whose §6.2 row R3a writes the endpoint product as `C r^2 K^(2d)` and + the final bound as `C K^(3d)` directly, so it never relied on the misprinted + display; +- the spectral cluster closure, `frontiers/spectral_cluster_closure_20260929/PROOF.md`, + blob `16c56821b52fd76b0be791622b9c3809eafde75a` ([SC]), which consumes only + Theorem I_d (1.6) and Theorem G_d (1.7) (its §1, display (1)), both unchanged. ## Scope check The other two places where a short column or an axial displacement enters a determinant bound already carry the Lipschitz factor through `K`: line 210 -(`O(r |p| K)`) and line 506 (`A_i = S_0 + O(rK)`). The omission is confined to -the single display quoted above. +(`O(r |p| K)`) and line 506 (`A_i = S_0 + O(rK)`), and lines 405 and 516 cite the +segment identity correctly. Both slips, (a) the omitted factor and (b) the +"(5.3)" citation, are confined to the single display at line 524. ## Record - Finding: DL-AXIS-K-01, Astra, main#259 6004712957 (2026-10-05 22:45Z). - Author readback: main#259, posted with this erratum. +- Codex review of Math-#308 (review 5422003010): four wording/pinning + corrections to this file, applied in its second commit; (b) was raised there. - Correction: this file. `PROOF.md` unchanged. Any future revision of - `PROOF.md` should replace the display with the corrected one and cite this - erratum. + `PROOF.md` should replace the display with the corrected one, cite [PP] + (P15) for the column bound, and cite this erratum. From 4cb2f62fdb8bbd9e437aa1d049fa8469cedf3f37 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Mon, 5 Oct 2026 23:48:36 +0000 Subject: [PATCH 3/3] =?UTF-8?q?D5=20erratum=20DL-AXIS-K-01=20v1.2:=20scope?= =?UTF-8?q?=20the=20slips=20to=20the=20DL=20file=20and=20record=20the=20re?= =?UTF-8?q?peated=20(5.3)=20citation=20in=20the=20C6=20Palm=20route=20?= =?UTF-8?q?=C2=A76.2=20R3a=20(AUD-308-CONSUMER-CITE-01)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-Authored-By: Claude Fable 5.1 Claude-Session: https://claude.ai/code/session_015wNj8LPTKXsaT68G3DgPPh --- .../ERRATUM.md | 22 ++++++++++++++++--- 1 file changed, 19 insertions(+), 3 deletions(-) diff --git a/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md b/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md index a0e729c11..23df87bbe 100644 --- a/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md +++ b/reviews/d5_dimension_lift_erratum_20261005/ERRATUM.md @@ -77,8 +77,20 @@ consumers, pinned at Math- `main` `c08e83597f94f923b8411dc13cdf28be3f214b37`: The other two places where a short column or an axial displacement enters a determinant bound already carry the Lipschitz factor through `K`: line 210 (`O(r |p| K)`) and line 506 (`A_i = S_0 + O(rK)`), and lines 405 and 516 cite the -segment identity correctly. Both slips, (a) the omitted factor and (b) the -"(5.3)" citation, are confined to the single display at line 524. +segment identity correctly. **Within `PROOF.md`**, both slips, (a) the omitted +factor and (b) the "(5.3)" citation, are confined to the single display at +line 524. + +**Consumer occurrence (AUD-308-CONSUMER-CITE-01).** The C6 Palm route, +`frontiers/c6_palm_route_20260929/PROOF.md` (blob `89eb8adf…`), §6.2 row R3a, +line 602, repeats the same citation: "short columns `H_M e_x`, `H_S e_x`, of +size at most `Lr/2` by [LP] (5.3)". There too the correct source is the +critical-segment identity, [DL] §4.6 / [PP] (P15). Its determinant powers are +already the correct `C r^2 K^(2d)` and `C K^(3d)`, so this is citation-only and +changes none of the consumed estimates. A repository-wide search (`git grep` +at Math- `main` `c08e8359…` over `frontiers/`, `reviews/`, `imports/`) finds +exactly these two occurrences of the "`Lr/2` by [LP] (5.3)" pointer: [DL] line +524 and [CP] line 602. Slip (a) occurs only in [DL]. ## Record @@ -86,6 +98,10 @@ segment identity correctly. Both slips, (a) the omitted factor and (b) the - Author readback: main#259, posted with this erratum. - Codex review of Math-#308 (review 5422003010): four wording/pinning corrections to this file, applied in its second commit; (b) was raised there. +- Nonauthor read of Math-#308 (OpenAI / GPT-6 Astra Pro, comment 6005725870): + PASS_SCOPED on the correction; AMEND_SCOPED AUD-308-CONSUMER-CITE-01 (the + consumer occurrence above), applied in the third commit. - Correction: this file. `PROOF.md` unchanged. Any future revision of `PROOF.md` should replace the display with the corrected one, cite [PP] - (P15) for the column bound, and cite this erratum. + (P15) for the column bound, and cite this erratum; any future revision of the + C6 Palm route should likewise repoint line 602's citation.