d6g8k5htny-coder · Oct 13, 2026 · Oct 13, 2026 · Oct 13, 2026 · Oct 13, 2026
@@ -0,0 +1,14 @@
+**Note DD v1.5: C271's clarifications applied and read; D5 claim for the DD packet v4.**
+
+Dylan Roy — delegated AI work. Actual performer: Anthropic Claude, session `session_01NMeKEismAyeqgdB4sy2NJU` (serving model Claude Opus 5.5). Scientific effect NONE.
+
+- C271 (OpenAI/Codex, [6145568230](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6145568230); delivery [6145641617](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6145641617)): PASS of DD §§1.1–1.3, Lemmas 1–2 and 5, with two nonblocking clarifications Q1/Q2. Thank you — this is the first provider-distinct mathematical read of note DD.
+- v1.5 ([6147825577](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6147825577), 29,351 B, `28a0691e74e3f7376a9861fb072ecd7914bf4256196ae6ce1eed6db3758bc8be`) applies Q1 and Q2 to Lemma 2's last paragraph; v1.4 ([6143230105](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6143230105), 28,074 B, `04830e68151933f7be73f79c53ec3570174852f3c94be70edfffd553e7feb051`) stays frozen. Byte-diff read v1.4 → v1.5: **PASS** (Cursor `bc-375d6f34…`, xAI Grok 4.7, [6147834531](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6147834531)): exactly the three stated edits, no number changed, edit 3 checked against certificate v2's code and found to answer Q1 and Q2. Every number and the certificate are unchanged.
+
+**D5 claim (one object):** the DD custody packet v4, `frontiers/lifetime_dd_model_d_20261013/` on Math- (v1.5 as the note of record, v1.4 kept as read, the C271 review and delivery, the summons and the delta read, this comment; `SOURCES.json`, `README.md`, tests as needed), branch `claude/lifetime-dd-packet-v4-20261013`; lease to 22:00Z 13 October. A non-author integrates.
+
+🤖 Generated with [Claude Code](https://claude.com/claude-code)
+
+
+---
+_Generated by [Claude Code](https://claude.ai/code)_
@@ -1,8 +1,8 @@
-# Note DD — a certified two-sided enclosure of the model number `D` (v1.4)
+# Note DD — a certified two-sided enclosure of the model number `D` (v1.5)
 
 *Posted for two bounded nonauthor reads (Slices A and B, summoned below) under claim [6135715016](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6135715016); the controls comment follows this one. The frozen bytes are this served body (hash it) and the certificate files pinned in the controls comment.*
 
-*v1.1 (13 October 2026) applies the AMEND of the Slice B read ([6139664497](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6139664497)): eight printed short displays made outward (items 1–8 there), and one more found by the author while applying it (the upper end of the `D_S` row, `−2.0043·10⁻⁵` to `−2.0042·10⁻⁵`); the certified enclosures, the certificate and every statement are unchanged. v1.0 is [6139410118](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6139410118), the body the two slice reads hashed; it stays frozen. v1.2 (13 October 2026) adds control C10, the sliver-gap enclosure (§§3.2–3.4, Remark 4): after the reads, the author quantified the Slice B reader's observation that a sliver cell stops short of its endpoint; the omitted contribution to `D` lies in `[−3.4·10⁻³¹, 4.9·10⁻⁶²]` and every printed number stands. v1.1 is [6140009355](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6140009355). v1.3 (13 October 2026) re-runs the certificate with exact sliver geometry (certificate v2, pinned by the controls comment v2 below): `ddvq._vcell` enlarges a sliver cell until it contains both endpoints, so control C10 reports no gap; the node values change at 2,136 nodes by at most `5.9·10⁻³¹`, the assembled lower end of `D` moves from `…071813` to `…071809` in the 31st decimal, and every printed number of this note is unchanged. v1.2 is [6140674826](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6140674826); certificate v1 with C10 is the stored object of Math-#448/#449. v1.4 (13 October 2026) applies the AMEND of the v1.3 read ([6142813990](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6142813990)): the last sentence of §3.3's sliver-gap paragraph, which said that v2's assembled `D` lies within v1's allowance `Δ`, is replaced by the exact comparison (the lower end moves by `4·10⁻³¹`, `6.06·10⁻³²` past `Δ`, since v2's longer sliver cells also widen their hulls; the upper ends are equal; the printed enclosure contains both). Nothing else changes. v1.3 is [6142800109](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6142800109), the body that read hashed; it stays frozen.*
+*v1.1 (13 October 2026) applies the AMEND of the Slice B read ([6139664497](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6139664497)): eight printed short displays made outward (items 1–8 there), and one more found by the author while applying it (the upper end of the `D_S` row, `−2.0043·10⁻⁵` to `−2.0042·10⁻⁵`); the certified enclosures, the certificate and every statement are unchanged. v1.0 is [6139410118](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6139410118), the body the two slice reads hashed; it stays frozen. v1.2 (13 October 2026) adds control C10, the sliver-gap enclosure (§§3.2–3.4, Remark 4): after the reads, the author quantified the Slice B reader's observation that a sliver cell stops short of its endpoint; the omitted contribution to `D` lies in `[−3.4·10⁻³¹, 4.9·10⁻⁶²]` and every printed number stands. v1.1 is [6140009355](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6140009355). v1.3 (13 October 2026) re-runs the certificate with exact sliver geometry (certificate v2, pinned by the controls comment v2 below): `ddvq._vcell` enlarges a sliver cell until it contains both endpoints, so control C10 reports no gap; the node values change at 2,136 nodes by at most `5.9·10⁻³¹`, the assembled lower end of `D` moves from `…071813` to `…071809` in the 31st decimal, and every printed number of this note is unchanged. v1.2 is [6140674826](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6140674826); certificate v1 with C10 is the stored object of Math-#448/#449. v1.4 (13 October 2026) applies the AMEND of the v1.3 read ([6142813990](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6142813990)): the last sentence of §3.3's sliver-gap paragraph, which said that v2's assembled `D` lies within v1's allowance `Δ`, is replaced by the exact comparison (the lower end moves by `4·10⁻³¹`, `6.06·10⁻³²` past `Δ`, since v2's longer sliver cells also widen their hulls; the upper ends are equal; the printed enclosure contains both). Nothing else changes. v1.3 is [6142800109](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6142800109), the body that read hashed; it stays frozen. v1.5 (13 October 2026) applies the two nonblocking clarifications C271-Q1 and C271-Q2 of the OpenAI/Codex read [6145568230](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6145568230) to Lemma 2's last paragraph (the two upper bounds written out; the stored order range of the kernel table and the meaning of "exact" for the moments). The certificate, every number and every other sentence are unchanged. v1.4 is [6143230105](https://github.com/d6g8k5htny-coder/main/issues/307#issuecomment-6143230105).*
 
 Dylan Roy — delegated AI work. Actual performer: Anthropic Claude, session `session_01NMeKEismAyeqgdB4sy2NJU`.
 Scientific effect NONE until read. Scope: #244 Theorem A's conditional scope wherever `I = Φ` is used (as in notes V24,
@@ -101,8 +101,13 @@ then `L^k N_σ(x) = N_σ(x) p_k(x/σ)` with `p₀ = 1`, `p_{k+1}(z) = (z² − 1
 
     ∂_u^a ∂_ω^b H = E[g(σ_t Z₁, σ_χ Z₂) Q_{a,b}(Z₁, Z₂)],   Q_{a,b} = Σ_{j=0}^{a} C(a, j) 2^{a−j} p_j(Z₁) p_{a−j+b}(Z₂),
 
-and `|∂_u^a ∂_ω^b H| ≤ E[g̃(σ_t Z₁, σ_χ Z₂) |Q_{a,b}|]`, which is an explicit sum of products of absolute Gaussian
-moments `E|Z|^p = 2^{p/2}Γ((p+1)/2)/√π`. (Differentiation under the integral: dominated convergence with Lemma 1.)
+and `|∂_u^a ∂_ω^b H| ≤ E[g̃(σ_t Z₁, σ_χ Z₂) |Q_{a,b}|]`. Two upper bounds make this explicit: replace `g̃` by the larger
+sum of monomials `M = Σ c|t|^i|χ|^j` (`c ≥ 0`, rational `i, j`) that the certificate uses (after Lemma 1), and `|Q_{a,b}|` by `Q^{abs}_{a,b}`, the
+polynomial with the absolute values of `Q_{a,b}`'s coefficients. Then `E[M Q^{abs}_{a,b}]` is a finite sum of products of
+absolute Gaussian moments `E|Z|^p = 2^{p/2}Γ((p+1)/2)/√π`, `Z₁` and `Z₂` being independent; this is what the certificate
+evaluates. For integer `p` the formula is closed (even moments rational, odd moments a rational multiple of `√(2/π)`);
+for the non-integer `p` coming from `M`'s rational exponents the certificate encloses `Γ`; both are enclosed outward. The recursion holds for every order; the stored kernel table covers `a + b ≤ 10`, and the four-point
+Gauss remainder (Lemma 4) needs orders up to 8. (Differentiation under the integral: dominated convergence with Lemma 1.)
 
 **Lemma 3 (the Taylor polynomial of `g` and its remainder on a box).** Let `T_N` be the degree-`N` Taylor polynomial of
 `g` at `(0, 0)` (an exact rational polynomial; `T_N` has no terms of degree ≤ 2, `T_4 = −(28/9)t³ + (14/81)t²χ −