# Session 2026-08-29: the Z and G objects read, measured, red-teamed and applied; the refuted registry audited; wall unchanged *(HELD staging record, written by the orchestrating session at day close. Every number below is cited to the note that carries it; nothing here is computed. What is open first, then what moved, then the debts.)* ## 0. What is still open, first - **The wall is unchanged.** G₂ exponent band (2, 4.26645], target 2. Z₂ has no band below the zone width that is not TPC-strength. 42 attacks, ~100 imports and recon angles, and today's two recon passes (`recon-0829-farfields2.md`, eight fields; `recon-0829-escapes.md`, nineteen in-print escapes for the three killers) opened zero routes; every angle died on a killer whose coordinate the corpus already held, and the base rate stated in each note's §0 held again. - **The Var/E identification step stays OPEN.** Scourfield 2008 is unreachable at the page after ten channels; her 2016 restatement (read at a rendered page image) has three gaps against the step (`lit-scourfield-2008.md`, red-teamed: two gaps independently fatal, one ambiguous, and the precision register is `O(1/log x)` where `o(1/ln y)` is needed). - **Two model-vs-truth deviations are OPEN on the tile side.** The light tail of the gap spectrum is carried by the ORDER of the gap word, not by the qualifying-gap constraint (`measure-tail-deficit-0829.md`: zero-parameter CRT thinning predicts a HEAVIER tail; first-order adjacent-gap correlation carries 28 to 62% of the deficit at the deepest resolvable abscissa, the rest to order three or higher; red team C: the 54.6% headline rests on a tail count of 2, the stage split needs rate-matching). Kourbatov's b keeps a residual 0.78 to 0.97 at 3.2 to 4.2 ensemble sd with no mechanism after the two owed nulls ran (`measure-record-null2-0829.md`). - **One rung question was raised by the refuted audit and ruled the same evening:** Lemma V's mean-square bound (attack-AB-bounded.md Theorem 1) is PROVEN, scoped to the bound on B (`redteam-0829-theorem1.md`: the three steps re-derived for every z ≥ 3 and s > 0, constants and the p = 2 case checked by brute force); its record's INFERRED was one rung low, README and G2-STATE were right, and REFUTED's "published as Opera de Cribro 6.18" was wrong (that lemma needs s ≥ 9 and its inner sum is signed). Applied. ## 1. The four object reads (morning) `object-g2-read-0829.md`, `z2-state-draft-0829.md` (the missing Z2-STATE, 1,235 lines), `object-bridge-read-0829.md`, `object-models-read-0829.md`; red teams `redteam-0829-objects-gb.md`, `redteam-0829-objects-zm.md` (156 claims: 131 CONFIRMED, 19 WEAKENED, 2 REFUTED; zero TPC-strength labels wrong in the expensive direction). The lines that matter, all at their rungs in the notes: - The Gap Reformulation discards the origin; the discarded information is PROVABLY NOT NEEDED for the implication (a rotation-invariant statement reaches ZP), MEASURED worth about one unit of exponent against a deficit of 2.2665, and the anchored gap's only proven bound is the IDENTICAL DHR theorem, so the reduction gives up an advantage the proof never used (bridge §3, §5; `Q-anchored-vs-global-gap`). No separation theorem exists on either side; a proof of one would have to quantify over method classes. - Each object now carries a legal open set with (i)/(ii)/(iii) labels (G₂ note §4b: L1 to L10, U1 to U3; Z₂ draft §4b: twelve items) and the (ii) list beside it. One TPC-strength target had sat unlabelled in two live documents for weeks ("prove window/G₂ is unbounded"): labelled and folded into ZONE-POSTULATE §8 item 3. - Nine model-vs-truth deviations classified: seven residue-level (free, classical), Kourbatov's b interval-level in form but blocked by the log-sparse quantifier, one open for want of a null (now run, §2). ## 2. The measurement wave (afternoon), each red-teamed - `measure-g2z2-0829.md`: G₂/Z₂ at 22 levels, 8.14 at x = 79 (max 8.32 at x = 71), Z₂/G₂ → 0.12; no gap of length G₂(x#) lies wholly in the zone for x = 11..79 (PROVEN at named levels); zones with exactly two pairs: 0 of 27,292 above p = 2. Prereg 3 of 5; one label inside a bound block corrected by producer fix and forced re-embed. - `measure-g2-generic-0829.md`: the free-pairs and constant-shift ensembles are the same ensemble up to translation (PROVEN before the run), exhaustive at x ≤ 19; G₂ sits at the 14th to 26th percentile, about one sd low at all five levels (nested, no p-value); the falsifier does not fire; the exhaustive maximum reproduces h₂ = A288815 at seven levels. - `measure-g2-provenance-0829.md`: the exponent does not depend on the eight unreproduced terms (block moves ≤ 0.035 against a control range sensitivity 0.93 to 1.23); x = 37's three instruments share G₂(37#); nine G₂-free instruments read nothing high; the blind seven-term forecast overshoot z = +6.58 is the one surviving fact and is unexplained. - `measure-roughpair-null-0829.md`: the independent-thinning null is binomial, χ²/df = 1 − p (0.82 to 0.98), so "sub-Poisson everywhere" in `attack-roughpair-error.md` is WEAKENED (reference 1 was wrong); the measured dispersion is still below the mean-matched null at pooled z −5.9 to −11.4, and an exact-kill-count null brackets it from below: D8 is interval-level in form, elementary in content. - `measure-record-null2-0829.md`: b's 15% estimator disagreement is the exact identity cov(−z, 1/L)/mean(1/L); the inhomogeneous null carries none of b; the 6ℤ lattice carries 8.6% (the argued 1.7e-4 was one order low as a share of the deficit); residual as in §0. First of that family in output custody. - `zone-tail-02-0829.md`: 27,292 zones to 1e11; t/R 1.0619 → 1.0298 [1.0156, 1.0443] height-matched, 1.0157 [1.0013, 1.0308] class-matched; corr(head, tail) = −0.0009 (p = 0.89); c_local 0.7522 [0.7410, 0.7630] containing HL's 0.7574; its own head interval was priced over draws the field lacks (1,910 distinct openers among 17,700 zones; cluster inflation 4.10, interval still inside the registered band; no other head bootstrap in the corpus affected). - `zonegap-03-score.md`: the sealed 1e12 prereg scored on the laptop, then completed in the wrap-up pass with the band edge added: ten sealed rows, ten HIT, zero MISS (T5's decade band 4.182 ± 0.132 exact, S1 at −0.29σ); Z₂ = env at all 78,497 zones; the run needed a derived engine because `zonegap-01.js` inlines 41 records and exits at record 49 (guards printed). - `measure-tail-deficit-0829.md`: §0 above; the U-FRAME §11 operator reproduces the sieve bin for bin at five folds. Red teams `redteam-0829-measure-a/b/c.md` (216 claims: 170 CONFIRMED, 34 WEAKENED, 9 REFUTED, 3 UNVERIFIED; no verdict overturned; all producers `--check` bit-honest; prereg integrity clean where file evidence exists, one producer inode uncorroborated). Applied passes `applied-0829-measure-a/b/c.md`. ## 3. The refuted-claims audit (Chris: "see if we were wrong") `refuted-audit-0829-1/2/3/4.md` re-derived every closure in `REFUTED.md` at its record: **67 rows, 40 SOUND, 27 SOUND-NARROWER, 0 WEAKENED, 0 UNSOUND. No route reopens.** The closures were right; about a third of the one-line clauses claimed more than their records carry (a transposed quantity, a "search is finished" where the record says the owning-convention row does not exist, a post-hoc reading quoted as registered, a stale "published as" for a lemma whose published form needs s ≥ 9). 25 clauses rewritten (`applied-0829-refuted.md`), row 16 deferred to §5, 7 HOLD for Chris. ## 4. Applied to the live layer today (CHANGELOG 2026-08-29, three entries) TODO.md (the tail's unit, Z4, Z5, Z7, the Z₂ line), ZONE-POSTULATE.md (§3 count, §8 label and fold), G2-STATE.md (§2 x = 37, §6.1 provenance, §9 label), SEARCH-CONVENTIONS.md (the smooth-divisor row), REFUTED.md (25 clauses), plus the HELD notes named in the CHANGELOG. Gate green after each batch. ## 5. Debts and HOLD items, for Chris - README §Status's Lemma V clause could name the constant (`redteam-0829-theorem1.md` §7.4); the attack-AB-bounded L1-L5 mean-square chain was not re-derived, only the bound on B. - README §Status's constant-shift sentence (form versus value d = 2); `paper/anchored-note.md`'s bare "factor 81"; `zonegap-02-reduction.md`:122 (Euclid anchor for head where only F is unconditional); ZONE-POSTULATE.md:325's rung; the 3.5/3.9/4.2 margin constants; IMPORT-MAP rows 20/21 and the PRIOR-ART eigenvalue line; Z₂'s absence from ZONE-POSTULATE.md and the router (the Z2-STATE draft's promotion is his call; red team ZM's §5 lists twelve non-fit lines). - Custody: closed in the wrap-up pass (§5a); the tail-deficit note's figures are the last, in the same pass. - Compute owed: closed in the wrap-up pass (§5a), the 1e12 band score being the last. - Box-class, not run: β(37) ~20 h (his go), 47# (35.8 h ×2), Var(41) (days). ## 5a. The wrap-up pass (late night) Everything the notes had recorded as owed was taken to its end, per Chris's instruction, and the CHANGELOG entry of the same hour lists it: Lemma V's whole L1 to L5 chain ruled PROVEN with no hypothesis (a period mean, not a supremum); every scratchpad-grade figure of the day moved into a producer's OUTPUT block; Kourbatov's b weakened its own headline under the second lattice law (the lattice share is a bracket, −0.006 to +0.111, null side 16 to 25% of b, shape assumption open at 1.6 sigma); IMPORT-MAP rows 20 and 21, the PRIOR-ART spectrum line, the sixteen escape labels, three REFUTED HOLD rewrites, the covering-economy root (7.182) and the underived "≳ 0.4" replaced; nine notes linked into the ledger's TODO guard; the margin band (2.9 to 4.2, worst case 4.2) landed in five files after nine days; Z₂ routed from ZONE-POSTULATE and the router. What remains for Chris is §5's first two bullets (the draft's promotion and the box runs) and the items the registries note lists as his. ## 6. Method notes Three of four object-readers converged on the same live defects; a brief of the orchestrator's conflated the h control with h₂'s exponent and an agent refused it; one measurement question was half on disk (`exact-g2-ladder.js` carries argmax and multiplicity) and was caught by grep before briefing; two agent preregs were wrong in direction (the binomial null, the mirror-partner formula) and both were reported misses-first as the rules require.