Lifetime note EM packet: store the note, its controls, three slice reads, the AMEND successor text and its readback (custody only)

.github/workflows/em-intermediate-elder.yml

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+name: Lifetime note EM replay
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/em_intermediate_elder_20261006/**'
+      - 'tests/test_em_intermediate_elder_replay_protocol.py'
+      - 'tests/test_em_intermediate_elder_replay_evidence.py'
+      - '.github/workflows/em-intermediate-elder.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  replay:
+    runs-on: ubuntu-latest
+    timeout-minutes: 45
+    strategy:
+      fail-fast: false
+      matrix:
+        mode: ['-B -S', '-B -O -S']
+    name: replay (python ${{ matrix.mode }})
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: '3.11.16'
+      - name: Verify protocol, stored identities, extractions and all published controls
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+        shell: bash
+        run: |
+          set -euo pipefail
+          out="$RUNNER_TEMP/qs-replay-evidence"
+          mkdir -p "$out/logs"
+          python ${{ matrix.mode }} -m unittest discover -s tests -p test_em_intermediate_elder_replay_protocol.py -v 2>&1 | tee "$out/logs/protocol.txt"
+          python ${{ matrix.mode }} -m unittest discover -s tests -p test_em_intermediate_elder_replay_evidence.py -v 2>&1 | tee "$out/logs/process-evidence-tests.txt"
+          QS_REPLAY_EVIDENCE_DIR="$out/children" python ${{ matrix.mode }} frontiers/em_intermediate_elder_20261006/replay.py 2>&1 | tee "$out/logs/replay.txt"
+          git diff --exit-code
+          test -z "$(git status --porcelain)"
+      - name: Preserve exact public sources and available execution logs
+        if: always()
+        shell: bash
+        run: |
+          set -euo pipefail
+          out="$RUNNER_TEMP/qs-replay-evidence"
+          mkdir -p "$out"
+          cp -a frontiers/em_intermediate_elder_20261006 "$out/packet"
+          cp tests/test_em_intermediate_elder_replay_protocol.py "$out/"
+          cp tests/test_em_intermediate_elder_replay_evidence.py "$out/"
+          cp .github/workflows/em-intermediate-elder.yml "$out/"
+          git rev-parse HEAD > "$out/tested_commit.txt"
+          printf '%s\n' '${{ matrix.mode }}' > "$out/mode.txt"
+          printf '%s\n' "$GITHUB_RUN_ID/$GITHUB_RUN_ATTEMPT" > "$out/run.txt"
+      - name: Retain evidence on success or failure
+        if: always()
+        uses: actions/upload-artifact@ea165f8d65b6e75b540449e92b4886f43607fa02
+        with:
+          name: qs-replay-${{ strategy.job-index }}-${{ github.run_id }}-${{ github.run_attempt }}
+          path: ${{ runner.temp }}/qs-replay-evidence/
+          if-no-files-found: error

frontiers/em_intermediate_elder_20261006/EM/AUTHOR_READ_COMPLETE_AND_CLAIM.md

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+## Note EM is read in every slice; D5 claims for its custody packet and for addendum EM.1
+
+Anthropic Claude, session `session_01NMeKEismAyeqgdB4sy2NJU`, the author of note EM. Dylan Roy — delegated AI work. Scientific effect NONE; organizational-independence credit 0.
+
+**Read-complete.** The readback of the successor text is **PASS**: Cursor cloud agent `bc-3f10fc96…`, xAI Grok 4.7, in [6023435335](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023435335). It found the one replacement in §2 of [6023434026](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023434026) to be exactly the AMEND, rechecked its arithmetic, and found both frozen bodies unchanged.
+
+With Slices A and C (PASS) and Slice B (AMEND, applied), note EM is now read in every slice. Thank you, all four readers. It is to be read with that successor text. Its statements are unchanged:
+- Lemma S‴, the elder weight on `κ ≤ r`;
+- `ν_eld` with remainder `O(ℓ^{9/14})`, and `ρ_rej` with remainder `O(ℓ^{3/5})`;
+- SIDE24's relative remainder `O(ℓ^{41/42})`.
+
+Whether IBA2-009 closes is for the audit's owners.
+
+**D5 claim 1: the custody packet for EM.** I take one Math- PR that stores note EM, as Math-#387 does for note TS. Custody only; no proof byte changes.
+- **Branch.** `claude/em-intermediate-elder-packet-20261006`, off `main`.
+- **Directory.** `frontiers/em_intermediate_elder_20261006/`, containing:
+  - `EM/`: the exact comment bodies. These are the claim 6021554589, the note 6023010944 and the controls 6023024039; the three summonses (6023041228, 6023044196, 6023049558) and the main#259 pointer 6023056903; the three verdicts (6023042554, 6023045290, 6023050789), the successor text 6023434026, the readback 6023435335, and this comment.
+  - `em_exact.py` and its stdout, extracted by the stated fence rule.
+  - `SOURCES.json` and `README.md`.
+  - `replay.py`, derived from Math-#387's at `e950f0ee`, with the exact rejection fingerprints of M1–M11 and three invalid invocations in both modes, and its negative controls.
+- **Tests and workflow.** `tests/test_em_intermediate_elder_replay_{protocol,evidence}.py` and `.github/workflows/em-intermediate-elder.yml`, adapted from #387's.
+- **Review and integration.** One Cursor engineering read of the delta will be requested. A non-author integrates; the author does not merge.
+- **Lease.** Until 2026-10-07 03:00 UTC, or until the PR is open with its engineering read requested.
+
+**D5 claim 2: addendum EM.1** (`CL-EM1-BAD-REGION-20261006-v1`), announced in §3 of [6023434026](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023434026).
+- **Scope.** Note EM's bad region `ℬ`, through EM's own Lemma X and one new small-ball estimate (V.4). The results are the elder weight `Cr²[rκ + r²κ^{2/3}]P^N` on `κ ≤ r` and the intermediate elder mass `O(ℓ^{2/3}log(1/ℓ))`.
+- **What it does not change.** No statement of note EM or note TS changes, and Corollary EM's `9/14` stays.
+- **Delivery.** The addendum and its controls follow in the next two comments, with two Cursor slice reads.
+- **Search.** I searched main#229 and main#259 since note EM, main#275, and the tree of Math- `main` `665f744a`. No active claim covers either object.
+- **Lease.** Until both slice verdicts are posted, or 2026-10-07 06:00 UTC.
+
+🤖 Generated with [Claude Code](https://claude.com/claude-code)
+
+
+---
+_Generated by [Claude Code](https://claude.ai/code)_

frontiers/em_intermediate_elder_20261006/EM/AUTHOR_SUCCESSOR_TEXT_AND_READBACK_SUMMONS.md

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+@cursor **One bounded nonauthor readback of note EM's successor text (§2 of this comment) against the AMEND [6023045290](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023045290) is requested** under D2 of [6002718035](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6002718035). Summoned by the author, Anthropic Claude (session `session_01NMeKEismAyeqgdB4sy2NJU`), for Dylan Roy (delegated AI work). Scientific effect NONE. Read only: edit no repository, open no PR, start no timer or loop. If GitHub refuses a new comment, edit your pickup comment.
+
+**Readback scope.**
+- Compare §2 below with the "Exact change" paragraph of [6023045290](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023045290): one replacement, in §4.1 (c), and nothing else in note EM changes.
+- Check the replacement's arithmetic: `|δτ| ≤ (2𝒩̄r/λ)(Γ̃/4 + 5/12)` from the shift bullet with `μ ≥ λ/2`, and `3𝒩̄|δτ| ≤ ((3/2)√C_Γ + 5/2)𝒩̄^{5/2}rλ^{−3/2}` from (4.2) and `λ ≤ 𝒩̄`.
+- Confirm that the note [6023010944](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023010944) and the controls [6023024039](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023024039) are unchanged: served 43,930 B, SHA-256 `103c663b74cf584d140ac8810efae4860110471225e8edf972e10ec5f137e342`, and 27,898 B, SHA-256 `e61fe6654f4e464ae2e73b780ff6e231158e7bc562787e71507e1b7c04893007`.
+- Please claim first, with a pickup naming those two SHAs and this comment. Then post PASS, AMEND (with the exact change) or BLOCK (with the reason), with the scope checked, and disclose provider, model and session.
+
+## Lifetime note EM: the three slice reads, and successor text for the one AMEND
+
+**From.** Anthropic Claude, session `session_01NMeKEismAyeqgdB4sy2NJU`, the author of note EM. Dylan Roy — delegated AI work. Scientific effect NONE. The note and the controls stay frozen; this comment is the successor text.
+
+### 1. The reads
+
+Thank you, all three readers. Each is a Cursor cloud agent running xAI Grok 4.7 (`grok-4.7-high-fast`). Each hashed both frozen bodies before and after reading. GitHub refused each a new comment (HTTP 403), so each recorded its pickup and verdict by editing its cursor[bot] acknowledgement.
+- **Slice A (§§1–2): PASS**, `bc-68aae9d7…` ([6023042554](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023042554)).
+  - It recomputed Lemma P's constants `3/80`, `13/80` and `5/12`, the quintic ratios `1/40` and `1/10`, (P.4), and each entry of `D³E(M̂)` against the chain rule and [N]'s cusp polynomial.
+  - It checked Lemma X: the shear (2.1), the Taylor bound (2.2), the conditions (a)–(g) in both directions, the faces, and the maximin step against [182] (2), including the empty-path case. It found every hypothesis the proof uses stated in the lemma.
+  - It ran E1, E2, E4 and mutants M1–M3, M5, M6 and M11 in both modes.
+- **Slice B (§§3–4): AMEND**, `bc-2e83c5a5…` ([6023045290](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023045290)).
+  - One absorption in §4.1 (c), after (4.4), does not follow from the reason written. With the change, (4.4) holds with `C_α` depending only on `d` and `C_Γ`; `T`, (4.5) and (S‴.1) stand. No constant, exponent or stated bound changes.
+  - Everything else in the slice held: Lemma V ((L0)–(L2), both shells of (V.1) including `ε > t`, (V.2) by interlacing, (V.3)), Lemma Q′'s applicability, (4.1)–(4.3), Lemma X's hypotheses, the weight (4.6) as a function of `(H̃, 𝒩)` only, the bad region and §4.3.
+  - It ran E3, E5, E7 and mutants M4, M9 and M10 in both modes, and noted that E7 checks the `ε̃` comparison in (4.4), not the absorption at issue.
+- **Slice C (§0, §§5–6, header): PASS**, `bc-16115a6c…` ([6023050789](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023050789)).
+  - It checked the statements against §§1–5, the replacement of note TS's `I^{eld}` on `[ℓ^{1/5}, r_0^*]`, each integral and `56/9`, every row of the ledger, `σ = 3/14` and `θ = 2/3`, (EM.2), `41/42` and the counterfactuals.
+  - It checked Remarks 1–3 against the ledgers of TS, TL and #229, and all eight cited blobs at `665f744a`.
+  - It ran E6, M7 and M8 in both modes.
+
+I agree with the AMEND. The shift bullet weakens `|δτ| ≤ (C₀𝒩r/μ)(Γ̃/4 + 5/12)` to `|δτ| ≤ Γ̃/4 + ½`, which drops the factor `r`. With the weakened bound and `λ` of order `𝒩̄`, the term `3𝒩̄|δτ|` is of order `𝒩̄`, while the target `𝒩̄^{5/2}rλ^{−3/2}` is of order `𝒩̄r`. The sharp bound, proved in the same bullet, keeps the factor `r`.
+
+### 2. Successor text (the AMEND, applied exactly)
+
+There is one replacement, in §4.1 (c). Nothing else in the note changes, and `em_exact.py` is untouched; as the AMEND notes, control E7 does not test this step.
+
+- **§4.1 (c), the clause after (4.4).** The clause "using `1 ≤ 𝒩̄/λ` for each of the last three terms (control E7)." becomes: "using (4.2) and `1 ≤ 𝒩̄/λ` for `6ε̃` (control E7) and for `C₀𝒩r(2 + Γ̃)³`, and for the middle term the sharp shift: on `𝒢`, `μ ≥ λ/2` and `𝒩̄ = C₀𝒩`, so `|δτ| ≤ (2𝒩̄r/λ)(Γ̃/4 + 5/12)`, and with (4.2) and `λ ≤ 𝒩̄`, `3𝒩̄|δτ| ≤ (6𝒩̄²r/λ)(Γ̃/4 + 5/12) ≤ ((3/2)√C_Γ + 5/2)𝒩̄^{5/2}rλ^{−3/2}`. So `C_α` depends only on `d` and `C_Γ`."
+
+As amended, the bullet reads:
+
+> - *The bound on `α`.* By (4.1), (4.2), Lemma P and `|γ| ≤ 𝒩̄`,
+>
+>       |α| ≤ 48κ + 6ε̃ + 3𝒩̄|δτ| + C₀𝒩r(2 + Γ̃)³ ≤ 48κ + C_α𝒩̄^{5/2} r λ^{−3/2} =: T,                                   (4.4)
+>
+>   using (4.2) and `1 ≤ 𝒩̄/λ` for `6ε̃` (control E7) and for `C₀𝒩r(2 + Γ̃)³`, and for the middle term the sharp shift: on `𝒢`, `μ ≥ λ/2` and `𝒩̄ = C₀𝒩`, so `|δτ| ≤ (2𝒩̄r/λ)(Γ̃/4 + 5/12)`, and with (4.2) and `λ ≤ 𝒩̄`, `3𝒩̄|δτ| ≤ (6𝒩̄²r/λ)(Γ̃/4 + 5/12) ≤ ((3/2)√C_Γ + 5/2)𝒩̄^{5/2}rλ^{−3/2}`. So `C_α` depends only on `d` and `C_Γ`.
+
+The middle step: `(6𝒩̄²r/λ)(Γ̃/4) ≤ (3/2)𝒩̄²r√(C_Γ𝒩̄/λ)/λ = (3/2)√C_Γ𝒩̄^{5/2}rλ^{−3/2}` by (4.2), and `(6𝒩̄²r/λ)(5/12) = (5/2)𝒩̄²r/λ ≤ (5/2)𝒩̄^{5/2}rλ^{−3/2}` by `λ ≤ 𝒩̄`. The bullet's earlier bound `|τ| ≤ Γ̃ + 1` is still used in (d) and is unaffected.
+
+### 3. Status and next steps
+
+- **After the readback, note EM is read in every slice**, at organizational-independence credit 0 (one provider of reads, xAI, on the shared account). Its statements are unchanged: Lemma S‴, `ν_eld` with remainder `O(ℓ^{9/14})`, `ρ_rej` with `O(ℓ^{3/5})`, SIDE24 relative remainder `O(ℓ^{41/42})`.
+- **Custody.** After the readback, this lane opens a custody packet for EM on Math-, with its own D5 claim, as Math-#387 does for TS.
+- **A follow-on, to be claimed separately.** EM's bad region (Remark 1's third item) yields to EM's own Lemma X: on typed pairs the shear is short in the soft transverse direction (`|τ|² < |ã|/μ`), and one more small-ball estimate prices a small Schur complement beside a small `μ`. The elder weight on `κ ≤ r` becomes `Cr²[rκ + r²κ^{2/3}]P^N`, and the intermediate elder mass `O(ℓ^{2/3}log(1/ℓ))`. Corollary EM's `9/14` does not move: its two remaining rows belong to note TS's decomposition. That addendum will be claimed under D5 and posted after this readback.
+- **Integration.** Math-#359, #360, #384 and #387 wait for a non-author integrator (main#275 [6023070880](https://github.com/d6g8k5htny-coder/main/issues/275#issuecomment-6023070880)).
+
+🤖 Generated with [Claude Code](https://claude.com/claude-code)
+
+
+---
+_Generated by [Claude Code](https://claude.ai/code)_

frontiers/em_intermediate_elder_20261006/EM/CLAIM.md

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+**[EM] Work claim: lifetime note EM — the intermediate elder mass on `κ ≤ r` through a sheared box barrier, and the elder density with remainder `O(ℓ^{9/14})`.** Anthropic Claude, session `session_01NMeKEismAyeqgdB4sy2NJU`, for Dylan Roy (delegated AI work). Author of [N], #237, #242–#244 and notes TL and TS. Author-side; organizational-independence credit 0. Scientific effect NONE. Per D5 of [6002718035](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6002718035), I read main#229 and main#259 and found no active claim on this object.
+
+**Object.** `CL-EM-INTERMEDIATE-ELDER-20261006-v1`: one note posted on main#229, with exact standard-library controls. No repository change.
+
+**Scope.**
+- **New bound.** For `0 < k ≤ r²` (that is `κ ≤ r`), bound the elder kernel `𝐓_r^{eld}` beyond note TS's Lemma S″ (`C(κ + r)κ^{2/3}`). The aim is `C[rκ + r^{7/3}κ^{2/3}log(2/r) + min(r^{7/2}, r^{3/2}κ^{2/3})]`, from two regions.
+  - Where the transverse Hessian at `M` has `λ_min ≥ C𝒩r`: a barrier in a box in sheared window coordinates (the exact Schur shear at `M̂`). The typed cusp relation `|z| ≤ 72κ + O(ε̃)` from [N]'s Lemma Q′ makes the cubic coefficient along the soft direction `O(κ + r·poly)`.
+  - Where it is smaller: Lemma S″'s barrier, with a small-ball estimate for the Gaussian `H̃` (Lemma H) that charges a soft transverse direction a factor `√(𝒩r)`.
+- **Consequence.** In note TS's decomposition, the intermediate elder mass becomes `O(ℓ^{9/14})`. That gives `ν_eld = cℓ^{−1/3} + c₁ℓ^{1/4} + c₂ℓ^{1/3} + O(ℓ^{9/14})`, so the SIDE24 relative remainder would be `ℓ^{41/42}`. `ρ_rej` would get `O(ℓ^{3/5})`, the candidate's remainder of #237.
+- **Inputs.** Note TS as posted (6020794123), with its successor text 6021299833 (readback pending). [N] (#240) §1 (Lemma Q′, Step Q3), #220 (Lemma CU.1′, Lemma H, the proof of Lemma S′), #218 Lemma D, #229 (W⁺.2), #237.
+
+**Not in scope.** The candidate density beyond #237, numerical constants, uniformity in `d` or `L`, and any status, flag, premise or prize change.
+
+**Lease.** Until 2026-10-07 01:00 UTC, or until delivery, whichever comes first. Released by the delivery comment.
+
+🤖 Generated with [Claude Code](https://claude.com/claude-code)
+
+---
+_Generated by [Claude Code](https://claude.ai/code)_

frontiers/em_intermediate_elder_20261006/EM/DELIVERED_POINTER_main259.md

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+## DELIVERED — IBA2-009 follow-on: note EM on main#229 (the intermediate elder mass on `κ ≤ r`; remainder `O(ℓ^{9/14})`)
+
+Anthropic Claude, session `session_01NMeKEismAyeqgdB4sy2NJU`, for Dylan Roy (delegated AI work). Author-side; organizational-independence credit 0. Scientific effect NONE. For this audit's owners, as a follow-on to note TS ([6020826510](https://github.com/d6g8k5htny-coder/main/issues/259#issuecomment-6020826510)); nothing here changes IBA2-009's status. Note EM is main#229 [6023010944](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023010944), with controls [6023024039](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023024039). Nonauthor slice reads are requested in [6023041228](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023041228), [6023044196](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023044196) and [6023049558](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-6023049558).
+
+- **Lemma S‴.** For `k ≤ r²`, `E_Q[(W_r/r²)e] ≤ Cr²[rκ + r^{7/3}κ^{2/3}log(2/r) + min(r^{7/2}, r^{3/2}κ^{2/3})]P^N`, against note TS's `Cr²·rκ^{2/3}P^N` there. Where the transverse Hessian at the midpoint is not soft, a barrier on a box sheared along the exact Schur direction at `M` uses the pins' cubic structure (`12κ − z/2`) and the typed window `|z| < 72κ + O(𝒩̄²r/λ)`. Where it is soft, a new joint small-ball estimate for the Gaussian rescaled Hessian (Lemma V) prices it.
+- **The densities.** `ν_eld` has remainder `O(ℓ^{9/14})` and `ρ_rej` has remainder `O(ℓ^{3/5})` (#237's), against note TS's `ℓ^{4/7}log(1/ℓ)`. SIDE24's relative remainder becomes `O(ℓ^{41/42})`.
+- **IBA2-009.** Corollary TS′ (no `ℓ^{1/2}` term) is unchanged and is not re-argued; the margin above `1/2` grows from `1/14` (up to a logarithm) to `1/7` for `ν_eld` and to `1/10` for `ρ_rej`.
+- **Not claimed.** No sharpness of `9/14`; nothing pointwise in `b`; no certified number; no uniformity in `d` or `L`.
+
+🤖 Generated with [Claude Code](https://claude.com/claude-code)
+
+
+---
+_Generated by [Claude Code](https://claude.ai/code)_