Handoff Record

Handoff Record

September 10–13

New analytical exploration: X-027 connects the Stromquist correspondence with the recent certificate and owner results. Three cross-reviewed reports derive the full-unit fractional obstruction at $38200/9977$$38200/9977$, a precise interior-duality argument, seven-of-eight corner-mark ownership, and at most three normalized physical contact components. A floor-charge example adds an exact abstract expressiveness separation. These are analytical deductions with explicit scope, not newly registered frontier results or target measurements. BC329 remains the direct-bound continuation; small geometric charge and joint-owner tests are the next new mechanism comparisons. X-027’s ranked table states their prerequisites and what each outcome would establish. The exploration and all three reports now define their terminology locally, use KaTeX notation, and identify their imported premises and supplied results. Session126 retains the analytical work, independent reviews, and validation.

Weighted atoms now exist in production: Session127 implemented the representation and source replay from the first two stages of the weighted-atom admission. Its review addendum records the consumer corrections and the remaining validation boundary. ThresholdAtom carries an explicit positive integer token count per distinct site. Geometry uses one membership rectangle per site; the threshold and resource budget count tokens. For total token count $A$$A$, threshold $k$$k$, and nonnegative atom weight $w$$w$, the budget is $w\lfloor A/k\rfloor$$w\lfloor A/k\rfloor$. The D4 orbit key preserves each site’s count, and the inclusion–exclusion expansion runs over labelled tokens. The retained seven-token, threshold-four motif $(2,2,1,1,1)$$(2,2,1,1,1)$ expands over 64 token subsets with absolute coefficient mass 209, where the same atom read as five sites reports 9, so the int64 headroom bound now reads the token count. All four retained receipts reproduce their declared token total, budget, charge $3/2$$3/2$ and exact charged-placement lists from family geometry, on rational coordinates up to 965 characters wide. Replay digests bind the supplied inputs; no retained historical digest authenticates their pairing. Unweighted admission and publication readers refuse declared weighted records. The internal interval route supports weighted member counts within its size limits; that support does not admit certificate coverage. No hypothesis, experiment or scientific target was registered or run, and the frontier is unchanged.

Selected next entry at that cutoff: think-8c9e, the weighted-atom coverage mechanics. The agreeing direct, event and interval controls on weighted atoms remain, including the closed-boundary and undercharged-core cases and the interval route’s stall handling, which is unresolved rather than a refuted atom or a failed budget proof. Certificate coverage admission stays blocked until they pass, and the paired instrument with its exact common row and point manifests is tracked separately behind it. The parallel BC329 lane has completed its bounded fixed-core runner implementation review in PR156. Its separate calibration instrument, three fresh full-shape host runs and source-distinct readbacks remain unadmitted and unrun, so BC329 execution remains blocked. The preflight addendum records the implemented controls and the remaining admission requirements.

Current combined reader entry: the consolidated PR-series takeaways, with definitions, proof results, scoped negatives and open comparisons in one place. PR137, PR142, PR145 and PR147 landed together at 1c1db463 on September 10, 2026. PR139 then merged as 3a18a05a, incorporating that owner strand and contributing T-024–T-026. At that cutoff the global lower bound was $3.8264474\dots$$3.8264474\dots$; the upper construction is unchanged at $3.8770835\dots$$3.8770835\dots$. The review corrections preserve the fixed-family scope of conditional obstructions and the existential owner-selection requirement. Finite support, net and grid results do not close entire research directions. The review addendum and PR139 carry finalization evidence. The post-merge daytime checkpoint adds no new global bound or target measurement. It proves that the translated 88-core obstruction has exact, zero-mismatch individual unit parents from $3.82345$$3.82345$, and independently verifies the analogous A6 statement from $3.82845$$3.82845$; contact, ownership and joint feasibility remain separate conditions. It also retains the fixed-angle adjacent-wall contact normal form, the correction that an arbitrary tight SAT row need not be physical contact, and the abstract $4/3$$4/3$ weighted-atom separation. The parent-domain adapter and production runner passed target-free independent admission, including deadline, timeout, failed-readback and source-closure adversaries. Exp156 then completed its sole source-bound run. The fixed exp151 residual lies inside its necessary parent box, while the first selected owner, TR / bottom-left:m1:j7, is already incompatible under the B-only model after all 181 frames and literal replay. The parent-restricted TR set is contained in that B-only set, so parent-domain gain is impossible there without running the redundant restricted arm. The frozen protocol did not evaluate BL, BR or TL; a new prospective protocol would need to skip TR and test those three owners. This complete old-model finding leaves H-158 unresolved and changes no global bound. BC329 remains the next direct global-bound target. BC337 is a secondary parallel lane, blocked on admission of a source-bound half-plane constructor, exact clipping, bounded runner and independent reader. It keeps exp151 direction 6 and open residual-centre domain C∘$C^{\circ }$. The control uses the existing TR centre-space obstacle PTR​+(−R)$P_{TR}+(-R)$ with the same nine other closed obstacles; the candidate substitutes the exact all-owner-incompatible obstacle KTR​$K_{TR}$ directly, with no second Minkowski expansion. Thus U0 and U1 remove the respective TR obstacles and the same other nine obstacles from open C∘$C^{\circ }$. The target would accept only exact area(U1) = 0 with independent union confirmation; because U1 remains open, that establishes emptiness. The strategy review puts the conditional parent comparison first and one frozen 2880-step core/net packet next, while multiplicity admission, contact-conditioned domains and mixed angle-profile charges proceed as separate blocks. The packet’s target-free preflight verifies its exact geometric headroom but identifies two prerequisites: test the raw least charge against $M/11=685457679/687500000$$M/11=685457679/687500000$, then normalize by the frozen rule $\alpha =1/m$$\alpha =1/m$; and admit a bounded fixed-core runner because the existing refinement CLI runs a different adaptive experiment. Coverage remains unmeasured, so this is a readiness result rather than a new bound. The two-attainer target remains preparation. Historical handoffs below retain their original context.

Session113 closed Agenda032 with T-023, the five-dot exclusion of one specified four-owner branch at side $96/25=3.84$$96/25=3.84$. The composed result is V3/C3, significance S3: exact full-net coverage plus audited geometric transfer, with no change to the global bound. The sprint report explains the full result and next think-yhw2 selection. The gaps and routes analysis separates certificate assurance, exhaustive case coverage and stronger geometric restrictions, including what could improve the bound at a different target side.

Agenda033 governs the continuation after T-023. Exp145 independently confirmed all 361 exact zero deficits in 39.06 seconds. Exp146 then completed all 16 wall-aware owner classes in 25.69 seconds: 12 common footprints strictly enlarged, four were equal and none was impossible. H-144 is accepted, but that geometric gain adds no owner selection or global lower bound by itself.

Exp147 completed its bounded component-containment transfer: eight of 128 relations held, it preserved the two baseline tuple labels, and it certified no additional selection. This is a negative result for that sufficient transfer, not a physical tuple census. PR142 retains the independently tallied audit and wall-aware continuation. The owner-case design shows why proper containment cannot extend the equal-area coarse patch family; simultaneous square symmetries give only two geometric owner tuples. No shared arrangement census has been promoted from this result. Usage after Session113 is retained in separate, nonoverlapping receipts.

Math startup release checkpoint. Session 111 records the prepared geometry, parameter-first hydration, reload restoration, and the local browser and PDF evidence for PR 135. PR 135 subsequently landed on main at 171bba33; its post-merge CI, Pages deployment, live publication checks, and delayed-font smoke test passed, closing the release work under think-qcmi. The research priorities below are unchanged.

Parallel structural lanes at $n=11$$n=11$, first wave terminal. X-021 pursued X-019’s exploration with four Fable lanes in parallel and reports what can be proved about eleven-square packings today: seven corner and wall lemmas, exact-verified angle counts at $96/25$$96/25$ on the rational cell unions specified in H-131 (rounded degree labels are approximations, not theorem endpoints), Stromquist’s Theorem 3 transported to 0.68∘${0.68}^{\circ }$ bands at $96/25$$96/25$, the spanning and chain lemmas, a weighted ownership lemma that would make four-corner containment a theorem from one LP, and a duality lemma that prices every conditional and capture certificate — including a retained-net cap below $U$$U$ with the strict endpoint corrected in the handoff review. It also records what cannot be forced (corner penetration, blocker angles, positive-length contacts, a bound on orientation classes) and prices the three closing architectures. Agenda 030, epic think-kbci, maps eleven research lanes with disjoint deliverables under BC-292–BC-302. BC-303 selected the continuation and BC-304 has dispositioned every lane, including the unmet scopes inherited from Agenda 029. H-127–H-134 register the lanes’ claims. The lane reports and every script they ran are retained under results/agenda-030/. No bound has changed. The owner started the wave on 2026-09-08: sessions 100 to 104 run BC-294 (the $B=1$$B=1$ value and the kill tests), BC-293 (the corner-skeleton measure), BC-295 (the band replay and widening), BC-297 (the $3.82$$3.82$ plateau) and BC-302 (the eleven-mark ownership set), each in its own worktree on claude/squares-n11-constraints-wl9atd; exp-130 was the next experiment id at launch. Session-103 is the first terminal lane: the exactly-eleven plateau at $191/50$$191/50$ is not a Trump-strip artefact (45 grid-seed sites and 822 of BC-200’s retained sites lie in two or more of the scaled cores), the general site-invisible-overlap mechanism holds, adding strip sites left the value at $11.07$$11.07$ with the generator stopping on its 32-row pricing cap, and an exact census at the different mass $11.118805$$11.118805$ exceeds one million near-tight cells with no clustering on Trump’s cores. This rejects the proposed strip explanation; it does not prove an obstruction at mass eleven or decide full-dual pricing. Session-102 replayed every count in H-131 exactly and widened the robust end band far past H-130’s 3∘$3^{\circ }$: no packing at $96/25$$96/25$ has every folded angle in Theorem C’s exact end-cell union (degree boundaries approximately 10.387466∘${10.387466}^{\circ }$ and 43.0737∘${43.0737}^{\circ }$) (Theorem C, grid 119, mass $11083/1024$$11083/1024$), with [0∘,1.7139∘]∪[43.5293∘,45∘]$[0^{\circ },{1.7139}^{\circ }]\cup [{43.5293}^{\circ },{45}^{\circ }]$ the first rung on grid 79; the dual of the band toward 40.19∘${40.19}^{\circ }$ puts its weight near the axis, not at Trump’s angle, and ceiling.py decides that none of those duals is a continuum obstruction, so the band’s true value stays open from below. Session-104 met H-134 in segment form: ten horizontal segments of length $1/10$$1/10$ centred on Stromquist’s ten Figure-13 points at $96/25$$96/25$ are a robust unavoidable set at tolerance $3/500$$3/500$, certified by an interval reader over pose space with every one of its 184,756 leaves re-decided in exact arithmetic, while every point-mark set built from the atom skeleton has an exact escape; every contained unit square is therefore localised near one of ten known segments, which is the premise route (a) needed, though not exactly-one ownership. Session-101 found H-128 unsuccessful on its tested finite support at $96/25$$96/25$: the corner-bounded measure sweeps exactly at mass $11.798$$11.798$ against $11.262$$11.262$ free, and the corner atom’s position, not the bound, is the obstacle on that support. H-128 remains open over the retained net; it proved the corner-pair form instead, that every packing at $96/25$$96/25$ has four distinct squares each containing one of its corner’s two marks, so the anchor for BC-299 is a corner pair. Session-100 left H-129 undecided: the $B=1$$B=1$ family at $96/25$$96/25$ verifies exactly at $8.918$$8.918$ on a 203-direction net, with its weight diffuse in angle and mostly outside Trump’s neighbourhood. The handoff review found a stronger retained control: exp-070’s family transports by $10000/9977$$10000/9977$ to unit squares at side $38200/9977<96/25$$38200/9977<96/25$, preserving depth one and mass $21342289572/2055263195\approx 10.3842$$21342289572/2055263195\approx 10.3842$. A smaller feasible family does not certify an upper bound. The depth polisher will start from that retained control; its missing scratch state is not a runnable handoff.

Session117 completed exp147’s bounded containment screen under H-145. All 128 relations completed; the screen preserved only the two baseline labels and added none.

BC-319 then ran under think-ykd6, with exp-148 registered under H-146. It keeps the five dots fixed, builds a reusable exact witness bank, and permits one surviving tuple check. Exp148 retained two exact witnesses before its seed deadline: 49,152 labels rejected, 16,382 nonbaseline labels remaining, no candidate attempted. H-146 remains unresolved.

Session120 continues the published work from Session119. Exp-148 was partial. The separate analytic transport rejects 61,440 labels for fixed D, leaving 4,094 nonbaseline labels. Exp-149 refutes H-147 at its first required direction: owner-000 has a positive exact uncovered area and a retained rational strict escape for the selected four-patch relaxation labelled by tuple $(0,0,0,7)$$(0,0,0,7)$. This refutes fixed D as a cover of that relaxation, not the physical tuple. H-146 remains unresolved over other labels.

BC-320 then tested the saved escape and every one-site extension of fixed D on that same relaxation. Current evidence: exp-150 refuted individual-owner exclusion in the unchanged B-core model, with one frame-0 witness in each of four classes; exp-151 refuted the fixed sixth site; exp-152 accepted the necessary two-core screen; exp-153 is the completed refutation of every one-site extension of fixed D on the selected four-patch relaxation. exp-154 refuted H-157: six of its eight refined subclasses retain survivor weight ten, while two improve to $19/2$$19/2$. The two improved patches intersect their fixed target cores, so their old positive distance explanation was invalid; the six neutral children retain the reported positive distance. The corrected T1 and T2 statements concern the retained finite ray universe and the fixed patch-only residual domain. They do not rule out other angular restrictions, stronger domains, changed charges, or owner-selection routing, and they do not establish that the conditional strategy fails. Separately, the retrospective BC303 T1 literal replay rejects the named bottom-left role-C universal local surplus inequality: one admissible parent has closed labels $\{3,4,11,12\}$$\{3,4,11,12\}$ and surplus $3/800000<ϵ$$3/800000<ϵ$. It decides no continuous-domain minimum, T2 forced-type case, global routing, or new $s(11)$$s(11)$ bound. Exp150’s compatibility result does not establish continuous unit parents or simultaneous owners, and exp153 does not exclude the physical tuple.

Session121 and Session122 are terminal. Session123 is terminal. Session124 resumed at 2026-09-10 01:52:40 UTC after the elapsed interruption. Its interpretation work and the BC-324 audit were subsequently completed and merged through PR139.

Historical interpretation selection: think-rm3k, BC-324, is complete. That factual block defined the terms used in the argument, separated exact computations from analytic implications, and audited the premises still required for a global result. The key routing obligation is

The record does not prove this statement. A reviewed two-attainer instrument is source ready but unrun; any future target needs a separate prospective registration and allocation. PR145 is ready after matching fast, page and full checkpoint validation. Historical status at that checkpoint: PR142 and PR137 were ready and unmerged. Both later landed with PR145/147 at 1c1db463.

The two-hour sprint in Agenda032 is complete. Exp141 independently confirmed the retained-family negative screens; exp142 completed the one-owner numerical comparison; exp143 found the four-owner five-dot candidate; exp144 checked those unchanged dots on all 361 canonical orientations. The footprint-containment and strict-core arguments supply the physical implication recorded as T-023. BC-316 subsequently completed the independent polygon-union audit in exp-145: all 361 exact deficits were zero. The saved-escape decision tree is now a historical decision record: exp150 took its compatible-owner branch, exp151 tested the selected sixth site, and exp153 closed the broader fixed-D-plus-one-site family on the relaxation. A global exclusion does not require every raw tuple label to be excluded. It requires the existential owner-selection routing statement above for every hypothetical physical packing. Any next experiment requires a fresh hypothesis or explicitly scoped successor, prospective criteria, published source, and a separate session usage interval. The figure and T-023 registration are post-sprint documentation amendments and are not charged into the frozen session113 receipt through 2026-09-09T05:16:31Z. The separate post-sprint usage delta was initially refused for non-monotone wait timing. The repaired meter retains that tail separately through 07:05:32 UTC, followed by Session114’s separate receipt through 07:53:52 UTC. The original Session113 receipt is unchanged.

PR137, on codex/n11-ownership-continuation, is ready for review and targets main. PR142 stacks the independent audit and overnight continuation on that milestone. PRs 116, 121 and 127 have merged; PR127 merged as 6aa9e72c. Session112 retains the earlier research continuation through 03:18:37Z; main’s independent font session111 retains its own identifier and receipt. Session110 and the handoff review preserve the original stack review and its separately tallied cost.

Full-support pricing H-135 remains an unrun reserve under think-7lp3. Exp134’s exact transport control passed with depth one and unchanged mass $21342289572/2055263195$$21342289572/2055263195$ in 135.91 seconds, but the pricing target was never invoked. Neither that administrative stop nor the deferred H-125 kernel is a negative scientific result. The owner-case continuation above takes priority.

Agenda 028’s restricted-family results. Session 092 and session 098 retain the independently reviewed work published on PR 110. The accepted results include the guarded central-parent exclusion, the signed short-slide exclusions, partial full-angle exclusions, exact counterexamples to the proposed disk and octagon capacity-six shortcuts, and the ten-square residual skeleton’s exact translation-fiber reduction. They apply only under their declared wall, contact, angle, or skeleton conditions and do not change the global $n=11$$n=11$ bracket. The matched H-118 coupled-LP comparison and H-120 residual-family determination remain open, and Agenda 028 stays paused. Its dated strategy review records the evidence available before Agenda 030; the current selection above governs new work.

Agenda 030’s selection, made. Session-107 replayed the first wave’s three strongest claims with readers written from their statements, and all three agree: the segment cover at $96/25$$96/25$, the corner-pair containment theorem, and the band exclusion at grid 119. Two corrections came with it: the segment length threshold is in $(7/100,8/100]$$(7/100,8/100]$, and the cover’s certified domain now closes a far-wall sliver. BC-303 funds the segment cover toward an ownership argument as the next sustained block, with the $B=1$$B=1$ depth polisher as the efficiency block and the plateau’s full-dual pricing as its first task; it retains the band ladder as filler and defers the corner-pair anchored certificate until the restricted fractional packing value is measured, since X-021’s duality lemma bounds any conditional certificate by it. Two more lanes ran and were halted by an external usage limit with their mathematics written and their validation unreached at that handoff: session-108 proves the grazing localisation of the escape class and records where exactly-one ownership fails (a segment can be shared, even by separated squares), and session-109 bounds the corner class’s surplus exactly at 1.6 to 1.8 per cent of the gap to the certificate line on its tested support. Its ratio optimum equals one on site set A; mark banking only proves an upper bound of one on other supports. Ratio and slice forms have the same exclusion power. Run 4 remained partial and run 5 never ran. The review also retracts lane E’s rounded-cover and enlargement helper claims while independently confirming E.4. BC-304 now closes the handoff before the funded continuation, as the owner requested. The same block repaired the deferred checkpoint (a third label-gated job for the slow behavioural lane and a declared budget for the escape screen) and amended OR-2, OR-3 and OR-6.

Atlas expansion to $n=324$$n=324$, owner-directed, beside the research line. The plan under epic think-0juv and session-099 widened the frontier register and the known-best atlas from $n=1\dots 100$$n=1\dots 100$ to $1\dots 324$$1\dots 324$, the end of the catalogue’s audited range, on PR 111. The unseen-corpus baseline is commit 6e21c4ca; the calibration-only layers stay pinned to the first hundred. The known-best-1-324 poster ships beside the untouched 1-100 figure, the prospective seed is retired to a pointer, and the sweeps tier is re-priced from measurement with two deferred steps. PR 111 landed on main at 28696526. The exact grid replay is also priced and deferred, with sampled replay retained on every pull request. The plan still records owner questions about the derived-facts retention route (D2) for the 123 catalogue cases, a caveated $325\dots 400$$325\dots 400$ extension, and a 2x poster raster; merging this research line does not answer those questions or authorize an extension. PR 116 must obtain its own matching fast and deferred coverage after integration. This line does not preempt the research selection below.

Focused parallel strategy prepared. X-018 reviews PR108 and ranks the overnight opportunities: direct compatibility and complete restricted-family domains first, a bounded contact-release investigation alongside them, and shared-anchor correlation only on a diagnosed residual. Agenda 028 owns H-118–121 and BC-269–275 under epic think-pxv5; it preserves the X-017 allocation below and consumes its single BC-261 geometry interface. Both proposed agendas are paused, with no new target run launched by this planning. The live task Squares plan X-016 continues the source H-110 and conditional compatibility allocation independently; session-091 is already occupied there.

Independent alternative prepared. X-017 reconciles the contributed research packet with PR105’s committed state at 46f38ab4. Agenda 027 proposes resource-and-anchor and six-plus-five restricted-family pilots, with a separate pair-kernel discriminator. It is paused, with no target experiments launched. Its X-017, H-111–117 and BC-258–268 records and epic think-sz5t keep its ownership and numbering separate from the continuing agenda below. None of its dependencies requires that run to finish; the original handoff remains the entry for that run.

The next research phases run in PR101 on codex/post-381-next-phases, with the landed PR100 depth fixes and PR98 validation improvements integrated. Session 089 records live assignments and checkpoints; it was renamed from the branch-local session-088 to preserve the separate landed efficiency session below. Coordinator think-jgnv owns the integrated research line and its first two-hour checkpoint. Source controls have passed; independent review and bounded end-to-end target work remain distinct. Supporting fixes stay on this PR.

Efficiency implementation checkpoint. Session 088 records the bounded W5 slice: detailed timing artifacts, two independently guarded component optimizations, configuration-selection repairs, and integrated fast validation on main edccf294 plus the reviewed changes. Its 62 selected steps passed in 232.89 seconds on the recorded ten-CPU local host with two outer/two inner workers; this is a dated local measurement. PR98 retains the later hosted results and the checkpoint status as upstream work is integrated. The W5 plan links the measured results, retained profile, complete project documentation matrix, and upstream tbd proposal. Automatic exhaustive selection and evidence reuse remain planned.

Research continuation. The T+2-to-T+10 continuation addendum is the cold-review entry point for the partially completed post-T+2 continuation. The Agenda 024 allocation owns prospective priorities. Its planning block BC-250 links the tbd assessment of both prior reviews, and distills their directions into H-093–103 and the existing agendas. Coordinator think-jgnv next dispatches scalar BC-251, adaptive controls BC-231, density support BC-254, and restricted assessment BC-255 as capacity and their readiness conditions permit. The addendum owns command custody and recovery; no successor experiment started during the planning block. The user’s credit-interruption amendment excludes unavailable time from the wall allowance. The addendum records the accounting boundaries, revised deadlines, and conservative active-minute position 124:14, the inherited reference position for this continuation. Session089 is closed; no current active-time total is inferred from elapsed wall time. BC-232’s completed recovery produced no row-converged covering; BC-241’s independent local-scope review was published in ad600896. H-092’s fixed-weight refined-core negative passed independent review and awaits integration under think-xsma. The eventual handoff records the active minute actually reached. The addendum preserves the first block’s frozen packets and binds the active-time, role, safety, BC-241, BC-232, BC-243, and gate contracts. Agenda 024 remains its control plane. It coordinates two disjoint programs: the exact fractional frontier in agenda 025 and density, typed stationarity, and Trump capture in agenda 026.

Research and tooling have separate continuation work. Session 087 completed Session 086’s BC-213 rung and accepted H-062 at bracket width $0.015$$0.015$. Session 089 retains the finite-row density candidate, its complete pair exclusion, the exact-angle auxiliary result, and the next complete-method assessments.

BC-264’s entry: think-mq0d retains BC-264’s disposition after the completed H114 feature and kernel-contract pricing. Its immediate prerequisite is the stopped Session097 checkpoint’s operational certification and draft publication. Exp129 missed its launch cutoff; its expired allocation cannot authorize a scientific invocation.

Session097 completed that pricing on codex/n11-kernel-pricing, following the user’s request to continue. Independent reviews accept an exact obstruction to cubic center features and the design of a finite test for one richer family. Independent source-free code reviews admit its LP proposer and exact reader; all 75 controls passed. Exp129 closed as blocked when protocol admission was incomplete at the September 7, 22:20 UTC launch cutoff. The engine push passed, but the protocol records and push checks failed on a stale round-count control anchor. No scientific source or packet was constructed, no target solver ran, and no result directory was created; scientific execution time is zero. The dependency guard gives no mathematical verdict on H125 or continuum certificate. Its new checkpoint is separate from the completed eight-active-hour block.

Session096 reviewed Stromquist’s three memos, corrected the paper’s chronology and five case-proof descriptions, and independently checked a five-dot obstruction and the local segment helper. Its source brief retains the remaining geometric replay under think-0krc; the selected target-research entry remains BC-264. All 66 full-checkpoint steps passed at dd92b2a0.

Session105 follows the author’s clarification about $n=26$$n=26$. Its verification report checks Stromquist’s historical packing exactly and confirms that Friedman’s current upper bound is smaller. A scoped support argument closes rigid central-block rotation with two fixed corner separations. Green’s stronger source-reported lower bound is now recorded separately from the verified one at $n=26\text{–}27$$n=26\text{–}27$; proof recovery is think-0x08, the remaining source-table audit is think-4g6w, and think-z0fi implements and controls the specified contact-release family. The MacIver review adds three previously unindexed manuscripts. His reported lower bound at $4.450208382\dots$$4.450208382\dots$ is below the verified bound at both n17 and n18. The missing computational artifacts remain a source gap; think-sske owns local replay of the center-area and capacity lemmas before adoption. Exact design controls show potential local cuts, not a new global bound. This source review does not authorize further kernel research.

Session106 extends the source-table audit through n324 and corrects 56 additional reported lower bounds, preserving every verified bound and every upper bound. The dated n26 search finds no smaller packing among the checked public sources; exact normalization shows that two recent numerical submissions are slightly worse than Friedman. This is a best-known conclusion with recorded search limits, not a proof of optimality.

The Session094 handoff was updated after the first result in Session095. Exp125 independently certified the entire diagonal compatibility branch, but its axis representation returned no_chain. Exp127’s fixed collision-augmented axis cover also returned no_chain, in 0.25 seconds, without an independent reader. H124 and restricted H036 remain unresolved; that representation receives no retry or parameter sweep. BC-259 is complete: exp128 independently bound all 88 source images, 60 placements and eight orbits, verified 41 strict inclusions on seven fixed boxes, and established the attained support optimum eleven in 1.12 seconds. H099 is refuted only on that support. BC-265’s independent designs derive an explicit mass-eleven calibration on the old support, but a new undercovered pose would reject only that density. Session097 completed the selected BC-264 pricing and kernel-specific BC-260 review. Its reviewed source-free instrument targets the fixed family in H125: an exact finite obstruction would reject that family, while feasibility of the outer LP proves nothing about a complete kernel. Exact PSD evidence and complete pair-domain verification remain prerequisites for a positive continuum certificate at side $96/25$$96/25$. H101’s stronger common-support obstruction is a conditional fallback, with no candidate asserted. Exp129’s blocked, never-invoked outcome is retained in Session097. Any future scientific attempt needs a fresh bounded allocation and admission; repairing the publication control does not reopen exp129. Session 090, under think-9qrx, completed the user-approved research block after PR 101 merged. BC-251/exp-116 finished unresolved: no row convergence, and an independently replayed dual mass of about 10.080180 at depth one, below the obstruction threshold. No bridge or unchanged retry is selected. At that earlier checkpoint, BC-243’s uniform control had timed out on three separately reviewed algorithms. Session094 later completed all five repaired graph controls and ran exp126 once. Its graph-only obstruction left H099 unresolved; no retry is open. BC-255 accepted H-106’s full continuous near-axis ten-point clause through an independent exact rectangle reader. H-108 and H-109 also accepted canonical near-45 A3 and A1/A2 forcing through independent exact replay and a reviewed reflection. These are restricted-theorem auxiliaries, not a packing bound. H-110 is accepted through exp-121: the fixed unit square is independently verified to fit in the actual domain and strictly avoid all twelve marks. This refutes the unchanged unconditional P12 auxiliary, not H-036. Exp-122 refutes H-122’s small-diamond conditional cover through an independently checked square. Exp-123 accepts complete near45 localization through four exact continuous guards and the reviewed geometric reduction. The fixed-S H-124 screen found no witness without certifying continuous coverage; the broader bound is unchanged. At Session090’s earlier allocation, H-107’s reviewed fixed-site scalar protocol was held out of that two-hour block under paused think-7fec; later-session reconsideration preserves its unlaunched history. The freed attention went to a bounded conditional-compatibility assessment from the accepted A-point lemmas, not an automatic P12 repair. Full validation of research checkpoint 99a3ad42 passed; Session 089 retains that verdict and the completed experiments, which must not be repeated. Agenda 024’s Current Allocation owns the scalar, complete-density and continuous-angle packages, including independent-review assignments. Keep these on one integrated successor PR from codex/structural-compatibility-continuation, based on merged PRs 105 and 106. The earlier BC-215 efficiency work remains available in Agenda 023; this handoff does not mark it complete or erase its evidence. BC-219 was the preflight for Agenda 024’s original launch inputs. Its completion does not replace the continuation addendum’s current gate contract.

The completed commissioning slice consumed the first two active portfolio hours of the same roughly 24-active-hour agenda. It exercised the coordinator, both managers, one floating worker, retained-state resume and checkpoint seams, the local Trump theorem packet, central integration, and interruption recovery. The T+2 integration checkpoint left 22 active portfolio hours; the continuation resumes those cells without resetting their clocks or budgets.

At the historical T+0 launch, the only takeable research cells were BC-230, BC-232, BC-233, BC-240, BC-242, and BC-245. Agenda 024’s current allocation now governs which cells may run. The coordinator alone allocates experiment IDs, edits shared or generated records, integrates manager packets, and moves a gate. Codex uses max reasoning for theorem scope, proof boundaries, mathematical disposition, and strategic routing; bounded implementation and independent reviews use xhigh, while replay, manifest, formatting, and value checks may use high when they require no mathematical choice.

Agenda 021 supplied the retained T-021 result and the 3.82 fractional state used here. Agenda 022’s Session 087 closed after PR 83 merged and the full gate passed on main. Agenda 024 is a separate portfolio; its active-hour clocks and T+2 disposition do not resume the completed efficiency block.

PR 93 subsequently landed two operational guards on main without changing this research entry point. The on-demand deep-gate.yml runs the 11 deferred steps in four jobs against a pull request before merge; because it is advisory, the post-merge full gate remains the backstop for a pull request that does not request it. The push-triggered branch-mergeability.yml now reports a branch that cannot be merge-built even when GitHub cannot create its pull-request merge ref. Its remaining blind spot is an idle branch after main moves and before the next push. Session 087 retains the full-gate evidence from run 34010683180 at c743d7bb.

The later upstream efficiency corrections preserve that historical accounting. Session 087 reduced the then-required CI surface from 1369.60 s to about 221.70 s without removing checks. Exact-tree reuse is now fail-closed. A matching successful packing-required proof lets the post-merge integration job omit only explicitly allowlisted tree-pure fast steps; deferred and unclassified steps still run, and any lookup or proof failure repeats the complete surface. The work was motivated by the earlier measurement that 20.2 percent of deep-run work repeated and 92 percent of that repetition came from unchanged trees. Per-test CPU readings are diagnostic because child costs cannot yet be attributed reliably; the 12 s call-wall backstop remains enforced. D-472 records why one hosted timing sample cannot establish a speedup. Development’s validation tiers own the current configuration and measurements; none of these historical selections supersedes Agenda 024’s allocation.

Earlier Handoffs

Open the house rendering of the retained 100-square witness.

The renderer’s standing exact-motion control remains independently replayable:

As of 2026-08-30. agenda-008 is closed with all four commitments terminal; session-045 then ran nine unplanned phases on BC-049 at $n=40$$n=40$ and carries a handoff at its end that is the authoritative summary, and session-046 took the cheapest thing that handoff named. session-047 then left the mathematics alone and worked on the record itself: it promoted the three sizes whose exact certificates were already running in this gate while their records denied one existed, and filled in the two facts the register could not previously state — whether anyone here has read an external argument, and what a novelty claim was searched against. session-048 closed the same gap one level up, joining every session to what it cost and finding that both obvious ways of totalling that were wrong in the flattering direction — see Sessions Conducted. session-049 then did three things in one morning: reconciled the queue against the tree (BC-085 and BC-087 had landed while the agenda still advertised both as ready), built the pre-push floor BC-086 asked for (packing-validate --push, 58s against --fast’s 646s), and ran the BC-088 reassessment whose sequenced plan is X-009 — then executed that plan’s first block: twelve verified ceilings moved off the integer grid onto exact sides at $n=18,19,26,27,38,52,66,67,82,84,85,86$$n=18,19,26,27,38,52,66,67,82,84,85,86$, every one decided by exact sign — ten over Q(2​)$Q(\sqrt{2})$ and the last two over Q(7​)$Q(\sqrt{7})$, the first exact verification outside Q(2​)$Q(\sqrt{2})$ — from a published rule or a coordinate lift, about $3.2$$3.2$ of aggregate gap. The widest trailing ceiling is now $n=50$$n=50$’s $3/7$$3/7$.

session-050 then performed the independent audit exp-045 had waited on since registration, built the -W bridge that makes the accepted helpers corroborate the certificate, and recorded the owner’s acceptance — clearing the gate that held BC-010 and BC-029.

Queued for the next run: agenda-010 — the two-lane overnight program from X-010: nine hours in blocks of two to three hours, instruments before research in both lanes, a checkpoint (BC-098) resequencing the tentative half mid-run, and the standard unattended rules stated in the agenda’s own objective. The run is live: blocks 1 and 2 are complete — session-054 landed the certifier core and the falsifier (BC-093, BC-094; the session ran as 050 and was renumbered at the merge — the audit session above holds that number), and session-051 landed the stage-1 price and the exact-LP measurement (BC-095, BC-096) — and the checkpoint (session-052) has resequenced the tentative half; session-053 closed block 3 on BC-099 under think-1o1f with the run’s first research result: Bentz 2010, Theorem 8 ($s(46)=7$$s(46)=7$) machine-certifies as printed — 92 exact cells over Q(2​,3​)$Q(\sqrt{2},\sqrt{3})$, the Lemma 5 threshold by a rigorous rational subdivision bound of $0.955390$$0.955390$, all 45 points charged — held unresolved with needs_review under the unattended rules that night (resolved by the review below), with the $m=4$$m=4$ remainder typed on think-1o1f and one candidate printed gap flagged for replay. The same session absorbed a mid-run merge from main (the parallel audit session had taken session-050 and D-404, so block 1’s record is session-054 and the reassessment defects are D-405/D-406) and root-caused the base branch’s red full surface to two stacked control defects, D-407 and D-408, both fixed on this branch. Block 4 is complete too (session-055, BC-100): the H-044 chunk-expressibility verdict exists as exp-046, exploratory by the hypothesis’s own calibration-only amendment, held unresolved with needs_review that night (resolved below) — the criterion is missed under both denominator readings the registered text supports (23/30 = 0.7667 over all records at $n\le 30$$n\le 30$; 3/10 = 0.30 over the non-grid sweep records), identically in both bands, every miss typed and determinate. The measured mechanism: the lattice grammar expresses the grid stratum completely and the tilted stratum not at all (flush groups are tangentially slid off the integer lattice step), so stage-1 over this grammar is a restricted-class instrument — converging with BC-095’s repricing from the price side. Block 5 closed (session-056): BC-099’s own question continued under think-1o1f — the m = 4 foundation layer. Two results landed on first complete runs, both held that night for review (resolved below): Figure 2’s sixteen-point base configuration is machine-certified (30 exact rational cells: 4 Lemma 1 corner pentagons, 8 Lemma 4 wall rectangles, 18 Lemma 2 triangles; 16/16 charged), and Lemma 10 is machine-settled both ways — the printed replacement point $(1,1.74)$$(1,1.74)$ is refuted by an exact escape certificate, and all three corrected replacement sets ($(1.12,1)$$(1.12,1)$, $(1.74,1)$$(1.74,1)$, (1.87, 0.76)) certify exactly, their Lemma 5 quadrilaterals landing inside the very parameter families the paper’s Section 1 lists. The certifier gained subset semantics, margin and near cells, and the rational-a threshold bound along the way. Block 6 (session-057, BC-101) then moved the verified lower lane for the first time since 2005: $s(17)\ge 17/4=4.25$$s(17)\ge 17/4=4.25$ and $s(18)\ge 17/4$$s(18)\ge 17/4$, certified exactly by a sixteen-point unavoidable set in [0,17/4]2$[0,17/4{]}^2$ (cases/green17) — above Nagamochi’s $\approx 4.1623$$\approx 4.1623$, below Green’s unadoptable $\approx 4.4452$$\approx 4.4452$ — the cell plan pinned to $17/4$$17/4$ by an $11/1000000$$11/1000000$ slack, the falsifier corroborating by saturation, and the verdict held that night for review; the review’s independent audit then showed $17/4$$17/4$ was the plan’s ceiling rather than the set’s, and the upgrade below carries the adopted bound. The run then discharged the checkpoint’s two authorized fillers and closed early. Session-058 (BC-103) sized the $m=8$$m=8$ attempt exactly and parked it: the m = 7 pattern’s ceiling 73​/2+22​−1≈7.8906$7\sqrt{3}/2+2\sqrt{2}-1\approx 7.8906$ sits below both side 8 and the standing $7.9282$$7.9282$ at $n=61$$n=61$, with the lattice dilemma exact (8 rows overrun the Lemma 2 pitch cap by $0.0157$$0.0157$; 9 rows overrun the 60-point budget by 7). Session-059 (BC-102) built the τ* pilot and read the method diagnostic: the eleven-crossing sits near side $3.83$$3.83$ (uncertified, typed), so a pure eleven-point set has at most a $\sim 0.04$$~0.04$-wide window above 2+4/5​$2+4/\sqrt{5}$ and any ambitious bespoke $s(12)$$s(12)$ bound forces the threshold/segment/moving-resource machinery. Everything mathematical from the run was held unresolved with needs_review overnight per the unattended rules; the verification review below resolved every hold the same day.

As of 2026-08-31, evening. The owner moved the review from their queue to the repository’s own rubric — determinations, not deferrals — and session-060 is running it as BC-106 under think-ngf0 in agenda-011. The determinations, each grounded in conventions.md §4 and the frontier evidence contract: Theorem 8’s audit is verified and fully machine-checked (E-bentz46-theorem8-audit); the Lemma 10 settlement is verified and now source-settled — the published page image itself prints the transposed $(1,1.74)$$(1,1.74)$, so the defect is the journal’s, recorded as defect-found on E-bentz-2010-proof with the partial Theorem 9 audit in E-bentz13-figure2-audit; exp-046’s hold is cleared with H-044 undisposed by its own registered amendment (the miss is determinate under both readings); the m = 8 parking statement stands as exact arithmetic; the τ diagnostic stays uncertified by construction* — final typed status, nothing pending. The green17 determination became an upgrade: the independent interval certifier built for the review (cases/green17/interval_audit.py — exhaustive exact integer branch-and-bound over the full pose space, pair-handoff and wall-tightened discharge rules, negative controls refuting tampered sets and oversized sides with exact witnesses) proved the run’s $17/4$$17/4$ was the cell plan’s ceiling, not the set’s: the same sixteen points certify at $4426213/1000000=4.426213$$4426213/1000000=4.426213$, the cell certificate was rebuilt there (right-wall Lemma 4 rectangles replacing the near-slabs), and verified_lower_bound at $n=17$$n=17$ and $n=18$$n=18$ moved to $4.426213$$4.426213$ on two independent formal methods (E-green17-sixteen-point-lower, E-green17-interval-audit), the set’s exact ceiling 753/250+2​≈4.42621356$753/250+\sqrt{2}\approx 4.42621356$ bracketed by certification at $4.426213$$4.426213$ and refutation at $4.427$$4.427$ and typed as follow-on. The assembled case is the 2026-08-31 verification review under docs/project/reviews/; the owner reviews the PR as a whole. Follow-ons stay on their beads (think-1o1f, think-q6vy, think-07t7 paused, think-0z9b); BC-097 and BC-089’s remainder remain the sanctioned gate filler.

Session 061 summary. The review’s epistemics became infrastructure: verification is the highest rung supported by the evidence a result cites, regardless of who performed it; confirmation records what this repository has read, replayed, or established. Session 061 codified that distinction as BC-107 under think-n8vl in agenda-011, a pipeline-improvement slice. epistemics.md at the repository root now owns the four axes — V0–V5, C0–C5 with structural promotion checks, anchored significance that never gates, and a scoped novelty classification — and the results register (packing/frontier/results.yaml, rendered as RESULTS.md) declares the whole results T-001–T-016, whose declared rungs devtools/check_results.py checks against cited evidence, required notes, and review metadata on every validation run. Unsupported promotion and unexplained understatement fail the build. The register subsumes the review’s determinations (the $s(17)$$s(17)$/s(18) upgrade is T-001/T-002 at V4/C4) and the legacy first-party theorems (the Stromquist repair is T-010; this document’s own T-1–T-4 below remain declared shorthand). softschema is upgraded to 0.8.0 across the schema toolchain in the same slice. The one-shot post-merge check found main’s full surface still red on one negative control, behind the same mask D-407 named: the worker-snapshot link copy covered the pruned archive but not the pruned renderings, and the control’s expected message lagged the ledger’s round count — fixed as D-409 and D-410 on this branch, with epistemics.md added to the snapshot’s root documents before the same gap could ship again. Research follow-ons are unchanged on their beads.

As of 2026-08-31, late evening — historical agenda-012/013 launch record. X-011 reconciles the new $n=17$$n=17$ weighted certificates, the $n=68/69$$n=68/69$ precision gap, the medium-case construction ladder, and the opportunity cost of a thirteenth open-ended $n=5$$n=5$ round. Agenda-012 turns that synthesis into three disjoint first-wave blocks with real beads and 15--30 minute check-in cells: BC-108 runs an independent-implementation agreement check on the proposed $4.5058$$4.5058$ certificate while naming shared assumptions; BC-109 builds the hash-verified parent-child serialization bridge at $n=68/69$$n=68/69$; and BC-110 decides whether $n=50$$n=50$ can become the rational exact-promotion control. They were scheduled to run in parallel, followed by BC-111’s bounded checkpoint. The dependency-linked successors are already filed. Agenda-013 is the owner-authorized nine-hour execution graph on one pull request: 150 minutes for those three first-wave blocks, a 15-minute W5 efficiency checkpoint, 30 minutes for BC-111, 180 minutes for one positive or refusal-path continuation per lane, 30 minutes to measure throughput again and freeze review packets, 90 minutes for three independent reviewers, and 45 minutes for synthesis and final validation. Every wave boundary requires a commit, tbd and generated-view reconciliation, validation receipt, push, and PR update. Existing BC-010 gets one final 90-minute discriminator with a matched $n=10$$n=10$ transfer under dedicated bead think-iivb. Its first cell freezes both fixtures, the observable, threshold, and refusal conditions before measurement. Only a passing transfer may remove BC-011’s blocked hold; a refusal stops the dedicated BC-011 through BC-014 chain and parks H-023. Legacy owner think-1s0h is not the queue gate. Those launch instructions are retained as chronology; use the Current Handoff for the live entry point.

The parallel recognition slice remains BC-089 on think-d0j1 in agenda-009: agenda-012 transfers $n=50$$n=50$ to BC-110, leaving thirteen disjoint cases on BC-089; $n=54$$n=54$ follows only if that result shows nested-radical representation is the next missing seam. The robust-rational sweep and typed $n=53$$n=53$ refusal remain on the parent bead. BC-049 on think-xdly is the research cell all of the mathematics below sits under, and it stays open.

$n=40$$n=40$ is infinitesimally flexible, exactly, over Q(2​)$Q(\sqrt{2})$: seven retained directions turn the sixteen squares of its tilted block and leave the frame fixed, and every one is refused at second order by a verified self-stress. The property stays undetermined because an infinitesimal flex is not a motion — the gaps curve shut at order t2$t^2$ — so what is settled is that no first-order argument can establish rigidity there. Getting further needs an instrument this repository does not have: the cone is bounded to dimension 45 against six dimensions of anything found admissible, and closing that gap means reasoning about 242$2^{42}$ corner disjunctions without enumerating them.

The correction underneath it generalized. Göbel’s published family is exactly the best known at $n=5$$n=5$, $40$$40$, $65$$65$ and $89$$89$; all four now have exact constructions here, and the last two turn out to be what their retained decimal witnesses were all along — agreement to 5×10−33$5\times {10}^{-33}$ identifies rather than merely permits. $n=28$$n=28$ is the near miss that stops the obvious guess: the family gives it a valid packing $0.004$$0.004$ worse than the best known, whose optimum is at algebraic degree 6 and is not in the family at all. Take the next slice from agenda-map.md.

BC-017 delivered its readiness input and stopped there. The $n=3$$n=3$ full-cell control already retained the target-free execution-plan receipt the commitment asked for, so the slice produced what that receipt authorizes instead: on the same three-square subject the structural plan reports 4 seated-wall equalities and 8 open-wall inequalities against 2 contact equalities and 1 non-edge inequality, while solve_cell builds 12 containment rows and 3 pair rows — the same twelve and the same three. Every total agrees and every composition does not, so the LP-solve half of the exit is reachable and pair_tests does not transfer between instruments that both report it.

BC-019 is closed. The contact-assembly contract is at contact-assembly-v2-draft and carries the clause it never had — 17 certificates and 13 typed limitations over $n\le 30$$n\le 30$ — with the missing grammar move named rather than guessed: a primitive for axis-aligned polyominoes that are not a bar, rectangle or corner L. BC-024 is what made that safe to say: X-008 measures that every component the grammar cannot express is axis-aligned — every other-polyomino in the corpus has angle exactly zero — so all 295 tilted components are already covered. Wall seating splits the residue into two populations with nothing between them: 44 whole-record grid subsets on four walls, 65 corner-seated blocks on two. BC-038 is closed and rejected on measured arithmetic — 35 evaluate_stress calls arrive with eleven distinct number fields, and RowJetInventory refuses a foreign field by identity, so the floor is a 1.54x ceiling against an exit wanting five-fold. BC-010 and BC-029 were gated for four days on independent acceptance of exp-045’s preregistered criterion, which an unattended runner may not grant to itself; on 2026-08-31 the owner accepted the round after session-050’s independent audit (findings and the corroborating -W bridge are the experiment record’s Amendment and D-404), so exp-045 now records decision: accepted, BC-029 is complete, and BC-010’s readiness on the map is genuine.

$n=5$$n=5$ is second-order rigid, and that is a first-party result. X-007 settles the question BC-049 asked, exactly, over Q(2​)$Q(\sqrt{2})$ at Göbel’s construction rather than at the retained decimal witness — which is 2.4×10−30$2.4\times {10}^{-30}$ off the diagonal and so infeasible at the scale a certificate works at. The cone of infinitesimal motions is exactly the line spanned by rotation of the middle square; the other fourteen coordinates are pinned by Farkas certificates verified in the field; and that one direction is refused at second order by a verified self-stress. This confirms and strengthens the numerical account BC-069 reached from the promotion side, including its observation that the contacting corner sits at the midpoint of the contacted edge — which turns out to be the reason for both the first-order blindness and the second-order obstruction.

The frontier property stayed undetermined then, and the reason is worth carrying forward: second-order rigidity is not local rigidity, the step that would close the gap is a curve-selection argument that X-007 writes out as prose and no replay checks, and the property enum has no word for what was actually established. What did change is everything saying why — verified rather than numerically-checked, exact-algebraic rather than numerical-multiprecision, and a first-party evidence id in place of the screen’s — which takes $n=5$$n=5$ out of the assessment tool’s ownership, so it joins $n=11$$n=11$ as left to a stronger argument. Both D-354 guards stayed green without being edited, which was the test the change was held to.

For $n=5$$n=5$ that stronger argument arrived on 2026-09-03. BC-152 wrote the curve-selection step out in full and checked it against an exact accounting of all 400 local inequalities, BC-153 reviewed it independently, and the property now reads locally-rigid at fixed side on a second first-party evidence record — see T-014.

Read OR-4 before trusting any older queue. BC-081 found that agenda-005 was advertising four commitments as takeable which agenda-006 had already discharged, and four more blocked on conditions no reader could observe. That is D-374, and the repair is agenda-map.md, generated from every agenda and drift-checked in --records at 0.14s. It is the queue now; BC-010 maps to its dedicated think-iivb gate, while think-1s0h remains the broader H-023 research owner.

The identity question moved twice, and both moves were corrections. X-005 still declares contact + closure the relation the atlas should count, but D-375 records that it had scored the atlas’s own relation at the wrong level — both of that relation’s inputs are canonical under relabelling and D4 by construction, so it is a quotient statement, and the $n=4$$n=4$ labelled control it was refuted on can refute no relabelling-invariant relation at all.

X-006 then answers the question this handoff previously posed. $n=5$$n=5$ does admit a discriminating control, and it is the pair D-034 has been quoting since 2026-08-23 without ever retaining: two endpoints sharing a contact certificate, differing in geometric key, at a side difference of 8.9×10−16$8.9\times {10}^{-16}$. It is retained now, and it discriminates whichever way its component count resolves — the branch where the count is two refutes contact + closure itself. What it waits on is that count, and exp-042 already names the missing claim: A_to_B_stationary_connection, first of its eleven declared scope refusals. D-034 stays outstanding, and no proof obligation shrank.

Everything below this paragraph is the accumulated record of how the program got here, not the next action; agenda-005 is closed and appears in it as history. Block A is closed: BC-047 under think-y85e and BC-042 under think-zmh8 both met their declared exits in session 035, which is terminal. Precision is now manufactured in-repository rather than read off a source — the published $n=29$$n=29$ system refines to 1000 declared digits with a reported residual bound of 1.09829×10−1039$1.09829\times {10}^{-1039}$ — and the $n=29$$n=29$ contact structure is frozen with 89 incidences, six orientation classes, an empty ambiguity report and $97.5013$$97.5013$ decades of separation, with the same extractor reproducing the known $n=11$$n=11$ structure exactly under exact arithmetic. BC-045 is now closed at all four phases, in session 036 and session 037, under agenda-006. The interval route is built, calibrated against $n=5$$n=5$, $n=10$$n=10$ and $n=11$$n=11$, and run at $n=29$$n=29$, where it certifies $s(29)\le 5.93383346267692918974379895098$$s(29)\le 5.93383346267692918974379895098$ at a declared relaxation of 10−20${10}^{-20}$. That certificate is retained unresolved with needs_review: true and promotes nothing: it sits 5.23371×10−5$5.23371\times {10}^{-5}$ below the standing verified ceiling, and whether it moves verified_upper_bound is a reviewed human decision through the evidence contract. BC-054 is closed in session 038: contacts now identify which features meet, and assembly turns a structure into equations that vanish at the packing they came from. Three findings there went against the promotion spec — counting rows cannot say whether a system determines the pose, an angle class does not license an angle identity, and seven of the $n=29$$n=29$ squares are reflected and refused by name. The rank half of the first was later found to be measuring a bug rather than the packings: see the BC-059 paragraph below and D-361. BC-056 closed that first stretch, and the run then resumed rather than ending: a review of the commit timestamps showed it had misread its own clock and stopped with most of its budget unspent (D-358). BC-057 is closed in session 039, which built the interval checker and recorded the $n=29$$n=29$ certificate as evidence without promoting it. BC-058 is closed in session 040: a pose is now a centre, an angle and a chirality, so the reflected squares are assembled rather than refused and the $n=29$$n=29$ residual falls from $2.0$$2.0$ to 1.3×10−15$1.3\times {10}^{-15}$ with the $n=11$$n=11$ calibration unmoved. The feature-renaming cost that commitment was written to weigh was not paid — reflecting the local axis leaves the corner indices alone. BC-059 is closed in session 041, and the answer was that there were no stationarity conditions to derive. The shortfall close had been reporting — four at $n=11$$n=11$, seven at $n=29$$n=29$ — was a bug in assembly rather than a property of the packings: an edge-edge contact was written as one equation where collinearity in the plane is two, which left one square free to pivot about the shared point and drive its neighbour open at first order. With both endpoints of the edge on the line the contact Jacobian reaches full rank at both sizes — $34$$34$ of $34$$34$ at $n=11$$n=11$ and $88$$88$ of $88$$88$ at $n=29$$n=29$ — residuals unmoved at 8.9×10−16$8.9\times {10}^{-16}$ and 1.3×10−15$1.3\times {10}^{-15}$, and close now refuses at both. It is D-361, class soundness, direction conservative: it made the pipeline look further from a solvable system than it was. Göbel’s $n=5$$n=5$ has no edge-edge contact, is untouched by the repair, and kept a genuine shortfall of one. BC-069 closes it, and the answer corrects the form the pipeline had been promising. The condition is not first-order: side_leak reads 1.00×10−16$1.00\times {10}^{-16}$ there, so “no admissible motion decreases the side” is already true and adds a dependent row. The single free direction is a rotation of the centre square about its own centre, and the contacts fail along it at −0.25t2$-0.25t^2$ in both signs — an ordinary second-order obstruction, so the pose is infinitesimally flexible and second-order rigid, and the shortfall is a degenerate root rather than an unpinned optimum. Differentiating the contact map along that direction takes the rank to 16 of 16 with the residual unmoved at 1.11×10−16$1.11\times {10}^{-16}$, and each emitted condition expands to exactly the statement that the contacting corner sits at the midpoint of the contacted edge — an identity of the corner-edge contact type, checked against a midpoint expression written independently of the derivative. Both determined sizes are unmoved. The misnaming is D-363. BC-060 is closed in session 042, with one answer and one refusal. At $n=11$$n=11$ the promotion spec’s frozen margin rule recovers Trump’s published degree-eight minimal polynomial from digits alone — $C=12420$$C=12420$, $B=36.85$$B=36.85$, $M=200$$M=200$, a relative residual of 4.99×10−338$4.99\times {10}^{-338}$ at $B+M$$B+M$ still falling to 3.38×10−412$3.38\times {10}^{-412}$ at $2B+2M$$2B+2M$ — and discharges it as irreducible over $Q$$Q$ with an isolating interval containing the refined value. At $n=29$$n=29$, on a thousand digits with a reported residual bound of 1.09829×10−1039$1.09829\times {10}^{-1039}$, pslq returns nothing at any degree from 2 through 20 below a coefficient bound of 1022${10}^{22}$: not one degree reached a clause. The contrast is the finding, because the planning probe on the ~98 serialized digits got relations at almost every degree from 8 to 21. A search that answers when under-fed and falls silent when fed properly is evidence about the number, and what it bounds is concrete: if the Kingbird solution has degree twenty or less, some coefficient of its minimal polynomial is at least 1022${10}^{22}$. That is the measured reason the interval route carries the $n=29$$n=29$ bound. BC-065 is closed in session 043, and it says how to read that refusal. Under $u=\tan (\theta /2)$$u=\tan (\theta /2)$ the published system rationalises over $Q$$Q$ into six polynomials with total degrees $[11,15,10,15,7,6]$$[11,15,10,15,7,6]$, so the Bézout bound on the solution variety is $1,039,500$$1,039,500$: degree twenty surveyed a corner of the space, not the space. Every equation is degree one in $s$$s$, and solving the smallest for it gives $s$$s$ as a rational function of two half-angles alone, leaving five equations in five unknowns. Eliminating those is where the exact-algebraic route either succeeds or is shown to be out of reach at $n=29$$n=29$, and it is left to its own budget on think-obgk. The bound reads as “not small” rather than “this large” — Bézout is loose for a structured system. The next slice is BC-066 under think-obgk — eliminate the five equations in five half-angles that BC-065 left, inside a declared cap, because it is the only remaining block that can change what this run concludes about $n=29$$n=29$. BC-061, BC-069, BC-067, BC-068, BC-062 and BC-063 follow, with BC-064 reserved and last; the ordering and its reasons are the continuation schedule, and run-002 carries what a fresh agent needs that the diff does not show. Session 044 is terminal, and closed eleven commitments.

The next slice is BC-074 under think-eb29, and it is a documentation-pass. That workflow — W8 — is new, added because this run demonstrated the gap it fills: the record moved a long way in a day while the front door did not move at all, and nothing in the gate noticed. check_synopsis binds this document to the artifacts; there is no equivalent for README.md or TUTORIAL.md, so they drift silently. Its checklist is the documentation-pass runbook, and its one hard rule is that it reconciles rather than authors: a claim the record does not already carry is not a documentation change, and a disagreement the artifacts cannot settle is a defect rather than a rewrite. D-367 is what the alternative looks like.

BC-066 attempted the elimination and reached a measured wall rather than an eliminant, which is the exit that commitment names. Three msolve runs on the six-equation system: over $Q$$Q$ in an elimination order, F4 was OOM-killed at degree 32 after 25m09s with 13.8 GB resident, having completed degree 31 on a $656126\times 1670545$$656126\times 1670545$ matrix; mod $1073741827$$1073741827$ in the same order the matrix dimensions were identical degree for degree; and mod the same prime in plain grevlex — an order of magnitude cheaper per matrix — the pair list still grew monotonically to 21,661 with no basis inside a declared 25-minute cap. Neither predicted failure mode is what stopped it. Coefficients cannot swell over Fp​$F_p$, and the cheapest monomial order did not terminate either, so what the runs measure is the size of the ideal rather than the arithmetic carried through it. The claim is narrower than “out of reach”: two threads and 15 GB is not a proof of intractability. What it establishes is that the interval route carries the $n=29$$n=29$ bound for a measured reason, and that the next thing to try is a smaller question rather than a bigger computer.

That is BC-070, and its first half has landed. Homotopy continuation needs no basis at all, and the mixed volume of the Newton polytopes bounds the isolated solutions at $15,744$$15,744$ — sixty-six times tighter than the Bézout bound of $1,039,500$$1,039,500$, computed in nine seconds. The stable mixed volume is equal to it, so the bound covers every isolated solution rather than only those in the torus. So the Kingbird solution has algebraic degree at most $15,744$$15,744$. Kingbird’s, not $s(29)$$s(29)$'s: $s(29)$$s(29)$ is the optimum, Kingbird’s packing is the best known and is not proved optimal, and the bound gap there is about $0.46$$0.46$. That is still far beyond what an integer-relation search can reach, and saying otherwise would overstate it: what it replaces is an unusable bound with a merely large one, computed from the system rather than guessed.

BC-067 closed the exact route’s loop at $n=11$$n=11$, where the answer is published. discharge stops at the side, which is a claim about a number; the round trip carries it back to a claim about a packing — eleven squares, fourteen touching pairs, valid under exact_sign, and the reconstructed side equal to the field generator exactly. The obstacle is real and $n=11$$n=11$ is where it is avoidable: a pose unknown ti​$t_i$ is an angle and has no representation in $Q(s)$$Q(s)$ at all, but Trump’s construction is already over $Q(u)$$Q(u)$ with $u=\tan (a/2)$$u=\tan (a/2)$, so the question reduces to recovering $u$$u$ from $s$$s$. That recovery is a derivation rather than a search — $Q(s)=Q(u)$$Q(s)=Q(u)$, both degree eight, so writing each si$s^i$ in the power basis of $Q(u)$$Q(u)$ gives a square rational system with one solution, and a singular one is refused rather than fitted. The continuation runs the missing middle layers first, with the efficiency and research cells deliberately last. The full ordering for the sessions after it — including which of the two priority: 0 commitments goes first and why — is the session queue, which is the one place that ordering is written down. The narrative below is historical and its earlier “next bounded slice” pointers are superseded by this paragraph.

The replan followed a correction recorded in X-004. The retained $n=29$$n=29$ SVG does not merely serialize a FindRoot result: it publishes the complete closed system — nine slide scalars in closed form and six equations f1​…f6​$f_1\dots f_6$ in $\{s,a,b,c,d,i\}$$\{s,a,b,c,d,i\}$ — and the layout map, whose <use> transforms are written symbolically in those same names. cases.kingbird29.verify_svg had already transcribed all of it and used it only to evaluate residuals, never to solve. Solving that same transcription reproduces the record to all fifteen published digits and reaches a maximum equation residual of 1.11×10−1200$1.11\times {10}^{-1200}$ in about six seconds. So BC-042 and BC-043 gate nothing at $n=29$$n=29$; they generalize the route to sizes with no published system.

That moved the prize onto BC-045. Certifying the reported $n=29$$n=29$ value would move verified_upper_bound from the Schadt rational to Kingbird’s, closing 5.23×10−5$5.23\times {10}^{-5}$. Two routes reach it: BC-044 recovers a minimal polynomial and discharges it exactly, which is stronger but of uncertain feasibility — a completed sweep found no integer relation through degree twenty with coefficients below 1022${10}^{22}$ — while BC-045 needs no polynomial at all. The robust route was the one with no specification, so that specification now exists. The witness contract already named interval-certified as a method that may carry verified, and the checker is now built: scalar.kind gains interval-enclosure, exact_verify replays an interval witness instead of raising checker-not-built, and the $n=29$$n=29$ certificate is retained as kingbird-n029-2026-interval under E-n029-interval-certified-upper. Recording is not promotion: verified_upper_bound has not moved to it.

The standing rule is unchanged and applies to every block: an unattended runner may apply the accept rule only conservatively. A round that certifies $n=29$$n=29$ is recorded unresolved with needs_review: true, and a human makes the accept decision.

PR 45 is merged and session 025 is terminal. Session 026 is the terminal first-session midpoint in the two-session balanced ten-hour agenda. Session 027 stopped on an external provider usage limit after ten of eleven phases, and session 028 is the terminal successor that executed its one unexecuted phase. Session 029 closed the remaining agenda-003 commitments on measurement, and session 030 re-glossed BC as bounded commitment, retiring a collision with the linear-programming sense of cell, and made the bead / commitment / phase layering explicit in the orientation docs. Session 031 merged main and found the merged tree failing two gate steps the pre-merge tree passed, because the atlas SVG work pushed the negative-control mutation snapshot past its size cap. That is fixed and pinned, and the gate is green on the merged revision. Session 032 closed agenda-004’s first block: twelve pre-certificate mutations are now enforced on twelve distinct failure identifiers, so exp-045’s admission gap is closed. Session 033 ran exp-045 itself, and session 034 is the terminal successor: it closed BC-035 and BC-041, adding four guards that did not exist, each verified to fire rather than merely to pass and each pinned by its own negative control. Negative controls rise from 76 to 80. The next bounded slice is BC-038 under think-kdil, the row-jet inventory reuse, which exp-045’s terminal disposition unfroze. Both declared determinations report criterion_met — canonical pure -W is excluded at A, the interior, and B, and the -W coefficients equal the separately derived +W values — and record-and-replay agree. The round is recorded unresolved with needs_review, not accepted: an unattended runner may apply the accept rule only conservatively, and the sixth admission condition, an independent post-change audit, is outstanding. The next bounded slice is BC-035 under think-cja6, the pipeline guard consolidation, because exp-045’s acceptance waits on a human and the mixed and transverse successor directions have no instrument. Exactly four distinct reachable failure modes existed, with no slack: a first inventory counted seven candidates by grepping raise sites, and tracing proof_core’s call graph cut that to three reachable identifiers across four conditions. The n=29 certificate was also regenerated at the tool’s default precision, closing a gap between the documented command and the recorded artifact. Q-BC032-a is answered: the 4.94×10−11$4.94\times {10}^{-11}$ relaxation is an artifact of the promotion route, not a property of the pose, and six independently verified promotions beat the recorded baseline. BC-028’s trigger passed, so its inventory-reuse implementation is ready but sequenced behind exp-045. The outstanding work is now carried by agenda-004, which gives each remaining item its own workflow entry. BC-027 is complete. The $n=5$$n=5$ H-023 successor under BC-029, think-whwc, and think-1s0h is no longer an instrument blocker: exp-045 has run and is terminal — accepted since 2026-08-31, after the independent audit its registration required — excluding canonical pure -W at all three strata while every connectivity, component, isolation and terminality claim stays refused. CG-010 is structurally complete under BC-030; BC-016 is blocked under think-3yv8 on retained poses, an executable glued row, symbolic tie labels, and a receipt checker, while BC-017 under think-u97a remains the ready constructive W7 lane.

All $n=1\dots 324$$n=1\dots 324$ frontier entries now point to normalized witnesses and deterministic house renderings. The first hundred are calibration evidence, not an unseen holdout and not a new proof of optimality; $n=101\dots 324$$n=101\dots 324$, promoted on 2026-09-07 under the expansion plan and frozen at commit 6e21c4ca, is the unseen corpus a confirmatory run may use once its instrument and grammar are frozen, and the calibration-only layers stay pinned to the first hundred. The atlas source inventory retains attributed Kingbird-derived numerical facts but no raw Kingbird SVG because the review located no express redistribution terms; that conservative repository policy is not a legal conclusion. A broad same-angle contact census covers 1,782 of 1,860 non-grid squares, but the stricter bar/L/rectangle partition establishes 3 of 36 non-grid cases inside its narrow budget. Two cases are conclusively outside that budget, 23 have no partition in the registered candidate universe, and eight are search-capped and therefore indeterminate. Contact components also retain substantial internal sliding freedom, so component count alone is not a defensible chunk cost.

The target-free contact-scaffold layer now retains 11,013 exact size-five signed-contact orbits as an abstract, no-geometry atlas. Its local realization prefilter rejects mixed angle classes before solving and still omits walls, non-edge separation, container fit, whole-packing feasibility, and optimality. CG-010 now adds one separate literal axis-aligned three-square structural cell: all twelve wall decisions, every contact/non-edge pair and oriented axis, the 48 D4-by-relabeling images, a replayable canonical witness, and separate candidate-domain and executed-work prices. It performs zero LP solves and contains no geometry. BC-016 prerequisite instrumentation remains blocked, so the next boundary is BC-017’s target-free tagged structural execution plan and derived accounting. Actual numerical compilation remains blocked on unfrozen open-wall, nonedge, and contact-overlap semantics. This is not an H-044 verdict or an $n=11$$n=11$ run on the inspected calibration corpus.

The H-023 line shows why the distinction matters. Session 004 used W3 to turn an ambiguous terminal-family observation into the falsifiable connectivity hypothesis. Session 009 first used W4 to make basin events and exact identity controls admissible. W6 then produced exp-033’s exact fixed-angle face and exp-034’s angle-and-slide sheet. A W2 instrument review found D-194 and D-195 before the next measurement, preventing a reused contact differential and an invalid alternative-row interpretation from entering the result. W6 resumed only after the corrected criterion was frozen; exp-035 then proved exact first-order directions outside the sheet without proving nonlinear realization. W3 turned that limitation into exp-036’s registered second-order obstruction, and W6 then excluded the displayed direction from the true tangent cone. Exp-038 now certifies the complete branchwise linearization-cone inventory and leaves transverse and mixed nonlinear realization open. Exp-039 then certifies one connected five-dimensional fixed-angle cell-local LP-optimal position polytope and twelve exact paths in release classes R1, R2, R3, and R6. Its positive pathwise first-order stresses do not make the whole polytope stationary or classify a terminal component. When the post-round strict gate failed, W4 separated stale controls from an independent deep-golden solver rejection. That bounded solver repair was recorded under the owning review phase before W7 existed. Future packing-pipeline repairs whose promised output is the implementation itself enter W7; historical phases are not relabelled after the fact. The current terminal transfer line is owned by BC-010 under think-iivb; think-1s0h retains the broader unresolved H-023 question without gating the agenda. Session 015 is terminal after reaching its declared eight-phase cap, and session 016 is the completed final-hour continuation; it preserved the original deadline without extending an expired phase or relying on controller memory. Session 017 is the initial W5 efficiency record, and session 018 is its measured planning refinement. Session 019 corrects the Codex timing instrument, freezes both named task trees, and replaces estimated delay attribution with native per-turn rollups by model and thinking level. Session 020 acts on that baseline: the first hosted required surface finishes in 46 seconds, exhaustive exact work and complete macOS move to direct integration events, and two-worker controls save 58.22 seconds on the full branch. Session 021 updates that lane onto current main, restores cheap exact guards to required PR validation, preserves explicit worker caps, and targets PR 45’s measured census tail. These W5 sessions measure and improve the research and validation loops but do not supersede session 016’s scientific handoff or authorize exp-045 implementation. Session 015’s first bounded W6 slice stopped exp-040 unresolved before retained measurement after independent review found five finite proof-perimeter gaps in the draft R4/R5 checker. Exp-041 froze the exact five-blocker correction at e26fae9, then rejected its complete-zero-inventory criterion on a new endpoint-only axis without refuting path feasibility. Exp-042 corrects that endpoint inventory and meets the full frozen criterion from engine commit 2980fdc: six R4/R5 paths, both owner stresses, and twenty semantic controls pass retained generation and replay. The result is pathwise first-order only. Exp-043 then stops its pure -W test before retained measurement: the draft checker is a resume point, but it does not yet derive production rowwise second-order constants, consume a full exp-034 acceleration witness, or mechanically route the two-scale proof. The following W7 phases provide a case-free exact-jet helper, complete production row builders for all six source matrices, normalized nine-row stress evaluation with every correction column retained, and a formula-derived exp-034 sheet control across both owner inventories. Focused tests and independent review accept that substrate at checkpoint 8ee367b while refusing branch completeness, scale routing, and obstruction. Exp-044 freezes the separate case-level integration but is terminal unresolved with no target run or result JSON. The published checkpoints separate helper substrate 8ee367b, accepted memoryless design 027349b, and full-gate pre-terminal state 3629bf4. Session 016’s terminal handoff owns the branch, read order, validation, exact fifteen-record scale inventory, mutation map, and successor artifact paths, so no controller memory is required. Session 027’s active BC-017 slice under think-u97a builds the admitted target-free tagged structural plan and exact derived accounting. It retains full-cell-execution-semantics-unfrozen instead of compiling or running a numerical full-cell solver before returning to the scheduled W5 inventory. Exp-045 remains a typed instrument blocker with no pure -W target data. The -W, mixed-angle, whole-stationary-component, and unequal-side-clearance questions remain later slices; D-239 is a separate W7 line. Do not start basin-frequency work or reinterpret exp-035 through exp-040 as a connectivity proof.