# Changelog entries from wave-2 partition B *(Staging file. Merge into `research/history/CHANGELOG.md` under a wave-2 heading, keeping the per-document grouping below. Partition B owns `research/U-FRAME.md`, `research/ATTACKS3.md`, `research/gate-multiplies.md`.)* --- ## 2026-08-17, wave 2: the consistency campaign applied (partition B) ### research/U-FRAME.md **§§10-15 were titled by which attack produced the result** — "Attack A4's corrections to this note", "Attacks A5 and A9", "Attack A10", "Attack A3", "Attack A8", "A8's extension" — so the status of L was spread over six attack sections and had to be synthesised by any reader who asked for it. RESTRUCTURED by claim: the mathematics went into the sections that own each object (§5a, §6a, §8) and the residue became three claim-named sections, §10 L and κ(m), §11 the transfer operator and the pair count, §12 f and the staircase. §§1-9 keep their numbers, because 128 inbound section pointers land on them and 15 of the citing artifacts are scripts whose pointers sit in pasted output. Forced by `qc-arch.md` §2. Nothing went to `history/`: the attack chronology already has a home in `ATTACKS3.md`. **§5a Step 3 and old §10 disagreed on strategy while agreeing on the facts.** Step 3 stated maxsum₂ ≤ G₂(new) ≤ maxsum_{L+1} and read as an invitation to bound L; §10, four hundred lines later, recorded that the sharp shift measures strictly below L at three of five folds and that "a proof aimed at L is aiming past the target". A reader who stopped at §5a took away the wrong strategy. RESOLVED: the looseness verdict and the strategic verdict now sit in Step 3, where L is defined, in the form **aim at κ(m), not at L**. **The sharp shift j\*(1) and the effective run length were the same object under two names**, measured over five folds in old §10 (j\*(1) = 1, 2, 1, 2, 2 against L = 2, 2, 2, 3, 2) and over nine folds in §5a's EXTENDED block and old §12 (m_eff = 3, 2, 2, 3, 2, 3, 3, 3, 4 against L+1 = 3, 2, 3, 3, 3, 4, 3, 5, 5). 1 + j\*(1) = m_eff by definition and the five overlapping values agree. MERGED into one statement in Step 3, with j\*(m) defined once. **§5a Step 3's inline dated block, "EXTENDED to folds 31 and 37, and A10 answered NEGATIVELY (2026-08-16)", was a correction sitting beside the claim it corrected.** FOLDED into the statement of the bound as present-tense fact: the bound is verified at 329 (tile, prime) cells over folds 7 to 37, and the two mechanisms that stop the lower half becoming exact live in §10 with the rest of the A10 result. **§5a Step 4 was stated twice, 90 lines apart**, once with the reason and once with the table. MERGED into one statement carrying both. The Step 2 kill law's copy theorem now also carries its family form, which lived in old §10 and which `TODO.md` item 0c and `gate-multiplies.md` §9 both cite. **One qualifying-gap closed form was stated three times** (old §§11, 13, 14), one Alternation Lemma twice (old §§11, 14), and one fold-11 explanation twice. COLLAPSED to one statement of each in §10, keeping every distinguishing detail: the weights 1, 1, 2, the 3p window threshold, the check at all 302 primes from 5 to 1999, and the two-state walk as the proof sketch. **The L(T₂₃, 29) = 2 custody note was stated three times, each claiming a different ordinal** — "established independently five times" in §5, "the fourth of five independent confirmations" in old §12, "confirmed here for the fifth time" in old §14. The ordinals were per-attack bookkeeping and disagreed. SETTLED as one custody statement in §8 naming all five confirmations (A4, A5, A8, A9, A10) and dropping the ordinals. `Lgrowth.js`'s hazard warning and the streaming custody moved into §8 with it. **Old §11 held a prior-art finding.** The Holt and Rudd arXiv:1408.6002 §5 attribution and the instruction that nothing below may be presented as new structure MOVED to §6a, the file's own prior-art section, which is why `PRIOR-ART.md`:117 had to point into an attack section to find it. **§9's "the same ratio ρ is measured rising with level, 1.58, 1.78, 1.83, 1.41, 1.84, 2.39" and old §10's "about 1.3 at T₁₁ and about 1.7 at T₂₃, rising with level" both named no statistic and both asserted a trend.** The two are different statistics of one quantity, ρ = (maxsum_m − G₂)/((m−1)·m̄): §9 quotes the per-level maximum over m ≤ 8, old §10 the per-level median. Both are arithmetically right. **"Rising with level" is REFUTED for all three natural statistics**: the median runs 1.33, 1.26, 1.15, 1.27, 1.71 at T₁₁ to T₂₃, the mean the same shape, and the max dips 1.83 → 1.41 at T₁₉. Both sites now name their statistic and neither claims a trend. Forced by `qc-numbers.md` Task 0, which sieved T₁₁ to T₂₃ from scratch and reproduced both recorded maxsum tables digit for digit. **§9 said "we have seven integers" and listed eight**, omitting fold 37's value that §5 carries. CORRECTED to nine, 2, 1, 2, 2, 2, 3, 2, 4, 4 at folds 7 to 37. **"The gap is a factor 0.58 ln p, and it is the only gap" was the optimistic end of a range.** 0.58 is 0.18/0.31; the other end of the corpus's own range, 0.18/0.19, is 0.95. CORRECTED at §7 and §9 to **0.58 to 0.95 ln p**, with the note that the two ends are ρ = 1.5 and ρ = 2.4 and that ρ is not monotone in the level, so neither end may be presented as the one a trend favours. Forced by `qc-numbers.md` Q5.1 as amended in `qc-CAMPAIGN.md`. **§7 item 3 priced G₂(41#) at about 37 hours with no alternative given.** The lattice-walk figure stands as the lattice-walk cost; the streaming leg of §8, which scales in slots rather than positions, prices the same term at about 6 hours. Forced by `qc-CAMPAIGN.md` Decision U1. ### research/ATTACKS3.md **Five Landed verdicts pointed at U-FRAME sections that the restructure retired** (§§10, 11, 12, 13, 14-15). REPOINTED to the sections that now hold the mathematics, in the same edit as the restructure, which is why the restructure did not move the chronology to `history/`. **"min(N_P, N_M) still decays, so A5's hole remains" (A8's verdict) said the opposite of what it meant** and of what U-FRAME's honest limit states. CORRECTED to "nothing shows min(N_P, N_M) decays". The two halves of the sentence contradicted each other: a decaying min would close the hole, not leave it open. **The organising principle presented the additive chain G₂(new) ≤ G₂(old) + L·m̄ as the live route.** That chain is §5a step 4 and is REFUTED. The paragraph now states the interval difficulty on its own terms and records that the chain the wave was framed around is dead, so the R/I marks read as a statement about the attacks rather than about a live route. ### research/gate-multiplies.md **§7 attributed to `U-FRAME.md` §§4 and 6a a claim those sections no longer make** — "the multiplier uses only 15 to 45 percent of its budget and the fraction is TRENDING DOWN" — while the numbers in the two files agreed. The quotation was dead: a reader following the pointer found agreement rather than the error being described. REWRITTEN to make the point against the softer `2 ln² p/p` budget without attributing a retired claim to a document that no longer holds it. Forced by `qc-history.md` O1. **§8's "ρ MEASURED at 1.0 to 1.9 across T_11 to T_23 and rising with level" named no statistic and asserted a trend the same file refutes sixty lines later** at :424, which prints the dip 1.83 → 1.41 at T₁₉. The range is the min/max over every (tile, m ≤ 8) cell, 1.015 at (T₁₉, m=4) to 1.839 at (T₂₃, m=6). CORRECTED to name the statistic, give the per-level medians, and drop the trend. §10's honest-limits note lost its "and it is rising" for the same reason. **§7 and §9 were written as a verdict on TODO item 0b as that item used to be written**, and TODO.md has since been rewritten to the corrected form, so the quoted premise is absent from the file cited. MIGRATED: §7's heading and opening state the required rate as the fact it is, §8's heading and threshold box speak of the surviving form, and §9 item 3 states the per-fold multiplier bound without quoting the retired item or its retired win condition. Every number, the VERIFIED table and the `ln x / 2` mechanism are unchanged. **§10, "Where the corrections went", was pure process record** duplicating both the standing footer and the CHANGELOG's own index by document. DELETED; §§11 and 12 renumber to 10 and 11. No working document pointed at either. **§6's recursion table and §9 labelled their rows by the U-FRAME section that held each object**, four of which moved. RELABELLED: A4's three recursions now name §5a steps 2, 3 and 3a; A5's theorems and A10's effective run length name §10; A9's operator stays at §11.