Where This Stands

Where This Stands

As of 2026-09-22 the current state and execution order are the checked Research Program Status and Roadmap above. The verified external bound is $s(11)>31/8=3.875$$s(11)>31/8=3.875$; the first-party point and threshold families below remain historical method evidence, and their ceilings leave no route to that current bound by net refinement alone. The owner has selected material bound improvement or proof simplification as the governing payoff. The historical synthesis below explains how the program reached that boundary. Its weighted-resource lineage runs through Göbel, Kearney–Shiu, Nagamochi and Bentz; the recent pure-atomic rational direction-net architecture follows Burns, and the LP instance and parameter line follows Massaccesi. This project’s instances and generator moved seven registered cases in one day. $s(11)\ge 381/100$$s(11)\ge 381/100$ is T-018, improving Stromquist’s 2+4/5​$2+4/\sqrt{5}$, stated in 1984 and published in 2003; the recorded search found no intervening improvement. T-022 proves a small exact refinement to $3.810025723614703\dots$$3.810025723614703\dots$, and T-024 re-certifies the same atoms on a finer direction net and proves $s(11)\ge 3.816609502788862\dots$$s(11)\ge 3.816609502788862\dots$; both use exact dilation-limit arguments. $s(11)\ge 191/50$$s(11)\ge 191/50$ is T-025, a certificate of a new kind: threshold atoms, which charge a core holding at least $k$$k$ of a set’s points and cost only $\lfloor |S|/k\rfloor$$\lfloor \left|S\right|/k\rfloor$ of the budget, carry the side past the exact ceiling that the point-atom method provably cannot pass. T-026 then re-certifies those atoms on a 1440-step net and proves $s(11)\ge 3.826447410572939\dots$$s(11)\ge 3.826447410572939\dots$ by an exact dilation-limit argument, and T-033 repeats that on a 2880-step net for $s(11)\ge 3.826997548829543\dots$$s(11)\ge 3.826997548829543\dots$. T-033 is the strongest retained first-party rung in this family, while the current verified case bound is the stronger external strict result $s(11)>31/8$$s(11)>31/8$. “Dilation-limit” describes T-033’s proof construction, not a weaker theorem or assurance level. The result retains its historical S5 registration; its current significance is S3 as method and calibration evidence, while the external certificate supplies the current case bound. $s(12)\ge 99/25$$s(12)\ge 99/25$ is T-017, proved about twelve squares rather than inherited from eleven, and reached independently of Evan Daniel’s stronger $15680/3951$$15680/3951$, which was in his repository from 25 August; that is now the case bound, replayed here on 2026-09-27 (n-012). $s(17)\ge 459/100$$s(17)\ge 459/100$, and $n=18$$n=18$ and $n=19$$n=19$ at the same side without a monotonicity step, is T-019 and displaces Massaccesi’s published $4.5058$$4.5058$ by $0.0842$$0.0842$. $s(19)$$s(19)$, $s(20)$$s(20)$ and $s(21)\ge 24/5$$s(21)\ge 24/5$ is T-020, which carries $n=19$$n=19$ past T-019 the same evening and displaces Nagamochi’s 2005 closed form at the other two — 1+13​$1+\sqrt{13}$ and 1+14​$1+\sqrt{14}$ — by $0.194449$$0.194449$ and $0.058343$$0.058343$. Its $0.21$$0.21$ at $n=19$$n=19$ is the largest single-case movement in the register, and twenty and twenty-one had never carried a proved bound of their own. Between them T-019 and T-020 are the only values in print this project has replaced. Evan Daniel has since proved $s(21)=5$$s(21)=5$ (n-021). All four stand at V4: each was decided twice from frozen bytes by an exact event-cell sweep and by an interval branch and bound with directed rounding — two routes that share the certificate and the closed-form conditions but decide Condition 5 by different methods, which fail differently — agreeing on the least covered mass to the digit. Three of them stand at C4, and T-018 at C5 — the rung epistemics.md defines as review-ready, a mapped and non-superseded review artifact, which the adversarial review of PR 78 supplies. None of the four has been read by anyone outside the project, which that rung does not ask for; a self-contained package for third-party checking ships at packing/cases/n11_fractional_certificate/thirdparty/ so that a stranger can decide the $19/5$$19/5$ rung without trusting this repository.

That lane also has a measured edge, which is the more useful thing to carry. $n=11$$n=11$ at $3.82$$3.82$ is closed to both pre-registered routes and the closure was checked rather than assumed. The covering LP was run on two independent site sets and both converged to an objective of exactly $11.000000$$11.000000$ from above, where a certificate needs mass strictly below eleven; the rejection route was then built and decided exactly, and its maximum pointwise depth of $1925/1152$$1925/1152$ caps the feasible total at $1152/175=6.58$$1152/175=6.58$ against the eleven a ceiling needs. Where the two routes fail by an infinitesimal at the same value, neither closes. That is a limit on the method’s reach at that side, recorded as measurement and not as a claim about τ∗${\tau }^{*}$.

The method also has a ceiling that is structural rather than measured, and it forecloses one of the three cases outright. No certificate for $n$$n$ can exist at a container side above ⌈n​⌉⋅B$\lceil \sqrt{n}\rceil ·B$: a wider container holds ⌈n​⌉2$\lceil \sqrt{n}{\rceil }^2$ pairwise disjoint axis-parallel $B$$B$-squares, direction $0$$0$ is always in the net, so Condition 5 gives each of them mass at least $1$$1$ and the total passes $n$$n$, which Condition 2 forbids. With Condition 4 bounding $B$$B$ below $1/(1+D)$$1/(1+D)$, the ceiling over every shrink a net admits is ⌈n​⌉/(1+D)$\lceil \sqrt{n}\rceil /(1+D)$, and refining the net raises it only as fast as $D$$D$ falls — about $T/K$$T/K$, so twice the directions for half the gap, and twice the cost of every decision taken over them. Since the grid packing gives s(n)≤⌈n​⌉$s(n)\le \lceil \sqrt{n}\rceil$ for free, this ceiling always sits strictly below the trivial upper bound: no single certificate of this shape certifies the grid value. For $n=12$$n=12$ that bites: the ceiling is $4B=3.9908$$4B=3.9908$, the conjectured value is $4$$4$, and $99/25$$99/25$ has $0.0308$$0.0308$ of runway to the ceiling and that is all there is for one certificate. What the ceiling does not exclude is a proved family of certificates with sides tending to $4$$4$ and a limit argument on top of it; whether such a family exists is a question about the covering value, which nothing here settles. Nor does it bind a certificate of a different shape. Evan Daniel’s third-party $s(32)=6$$s(32)=6$ is a weighted cover of the closed container [0,6]2$[0,6{]}^2$ itself, decided at margin zero by an exact subdivision of pose space rather than over a direction net, and it certifies the grid value directly (n-032). $n=11$$n=11$ and $n=17$$n=17$ are not foreclosed: their runways are $0.1808$$0.1808$ and $0.3985$$0.3985$, and both truths sit below their grid bounds. At $n=19$$n=19$, $20$$20$ and $21$$21$ the ceiling is $5B=4.9885$$5B=4.9885$, so T-020 has $0.1885$$0.1885$ above it at twenty and twenty-one; at nineteen the best known packing binds first and the runway is $0.0856$$0.0856$. $s(21)=5$$s(21)=5$ was reached by a mixed cover, a certificate of a different shape, which puts mass on the grid lines as well as on points.

Joining that ceiling against the register says the lane has been looking in the wrong place. CERTIFICATE-REACH.md ranks all 100 cases by the most a certificate could add. The two this program has spent itself on are near the bottom: $n=11$$n=11$ has $+0.0590$$+0.0590$ to its packing-side cap ($+0.0671$$+0.0671$ to Trump’s packing itself, which the cap says no certificate on this net reaches) and $n=17$$n=17$ has $+0.0810$$+0.0810$. The largest are all just above a perfect square, where the lower bound is Nagamochi’s closed form and the gap to the best known packing runs near half a unit — eleven cases above $+0.49$$+0.49$, headed by $n=51$$n=51$ at $+0.5364$$+0.5364$, then $68$$68$, $84$$84$, $39$$39$, $86$$86$, $66$$66$, $38$$38$, $83$$83$, $37$$37$, $53$$53$ and $26$$26$. Two cautions travel with that ranking. The prize is what the ceiling allows; the real limit is the covering value at that side. 46 values have been reported for the restricted program, at sides $2.99$$2.99$, $3.81$$3.81$, $3.82$$3.82$, $3.83$$3.83$, $3.84$$3.84$, $3.85$$3.85$, $3.875$$3.875$, $3.95$$3.95$, $3.96$$3.96$, $3.965$$3.965$, $3.969$$3.969$, $3.97$$3.97$, $3.98$$3.98$, $3.985$$3.985$, $3.99$$3.99$, $4.58$$4.58$, $4.59$$4.59$, $4.6$$4.6$, $4.61$$4.61$, $4.67$$4.67$, $4.675$$4.675$, $4.6775$$4.6775$, $4.679$$4.679$, $4.68$$4.68$, $4.69$$4.69$, $4.7$$4.7$, $4.80$$4.80$, $4.81$$4.81$, $4.82$$4.82$, $4.825$$4.825$, $4.85$$4.85$, $4.855$$4.855$, $4.86$$4.86$, $4.865$$4.865$, $4.875$$4.875$, $4.88$$4.88$, $4.895$$4.895$, $4.985$$4.985$, $5.13$$5.13$, $5.25$$5.25$, $5.48$$5.48$, $5.59$$5.59$, $5.7$$5.7$, $5.8$$5.8$, $6.75$$6.75$ and $6.84$$6.84$ — the first eight reports, not measurements this repository can reproduce, since no covering-search run log or solver checkpoint was retained for any of them; the ten added on 2026-09-05 by Agenda 021’s BC-200 and BC-197 and Agenda 022’s BC-213 and BC-206 carry run logs; the $2.99$$2.99$ pair added on 2026-09-18 by session-139 is H-216 calibration at n=6 (covering $6.08216$$6.08216$ and $6.07724$$6.07724$ on two named site sets, both ≥ 6, not a bound); $3.81$$3.81$ is the session-139 T-025-seeded auto-plus-60 at 381/100, covering $11.000000$$11.000000$ unconverged on the eleven plateau, site set refuted, side open; $3.82$$3.82$ also has the session-139 T-025-seeded auto-plus-60 plus --seed-windows 5 at 191/50, covering $11.018646$$11.018646$ converged, closest session-139 point-atom construction, site set refuted; T-026-seeded auto-plus-60 at the same side converged $11.033743$$11.033743$, worse than the threshold seed; $3.83$$3.83$ is the session-139 n=11 probes at 383/100, covering $11.192598$$11.192598$ (auto grids), $11.142857$$11.142857$ (four-grid), and $11.140351$$11.140351$ (T-025-seeded four-grid), all site sets refuted, side open; $3.84$$3.84$ is the same T-025-seeded auto-plus-60 construction at 96/25, covering $11.371819$$11.371819$ converged, site set refuted; $3.85$$3.85$ also has the session-139 T-025-seeded auto-plus-60 at 77/20, covering $11.456576$$11.456576$ converged, site set refuted; $3.875$$3.875$ is the same construction at 31/8, covering $11.561186$$11.561186$ converged, site set refuted, 0.002 below the packing; $3.965$$3.965$ is the session-141 n=12 T-017-seeded auto plus windows 7 at 793/200, covering $12.067502$$12.067502$ unconverged, still above twelve, the first first-party covering row at that side; a session-141 T-017-seeded four-grid plus windows 7 finished at $12.066995$$12.066995$ unconverged, still above twelve; $3.969$$3.969$ T-017-seeded auto-grid dropped to $12.118036$$12.118036$ unconverged, still above twelve; T-017-seeded four-grid at the same side dropped to $12.116115$$12.116115$ unconverged; a session-140 leftover T-017-seeded four-grid plus windows 7 finished at $12.091168$$12.091168$ unconverged, still above twelve; $4.6$$4.6$ is the session-139 n=17 auto-grid probe at 23/5, covering $17.331710$$17.331710$ unconverged, site set refuted, side open; the T-019-seeded auto grid at the same side dropped to $17.049597$$17.049597$ unconverged, still above seventeen; T-019-seeded auto plus --seed-windows 5 dropped to $17.042346$$17.042346$ unconverged; a session-140 T-019-seeded four-grid plus windows 8 finished at $17.120106$$17.120106$ unconverged, still above seventeen; $4.61$$4.61$ is the session-140 leftover n=17 T-019-seeded auto plus windows 5 at 461/100, covering $17.195968$$17.195968$ unconverged, one cent above $23/5$$23/5$; $4.67$$4.67$ is the session-139 n=18 auto-grid probe at 467/100, covering $18.000000$$18.000000$ unconverged, cannot confirm; the T-019-seeded auto grid at the same side converged $17.875567$$17.875567$ with least_covered 1, freeze-then-decide retained T-027 at $s(18)\ge 467/100$$s(18)\ge 467/100$; $4.675$$4.675$ is the session-140 T-027-seeded auto plus windows 5 at 187/40, freeze-then-decide retained T-028 at $s(18)\ge 187/40$$s(18)\ge 187/40$; $4.6775$$4.6775$ is the session-141 leftover T-028-seeded auto plus windows 5 at 1871/400, freeze-then-decide retained T-029 at $s(18)\ge 1871/400$$s(18)\ge 1871/400$; $4.679$$4.679$ is the session-141 T-029-seeded auto plus windows 5 at 4679/1000, freeze-then-decide retained T-030 at $s(18)\ge 4679/1000$$s(18)\ge 4679/1000$; $4.68$$4.68$ T-019-seeded auto-grid locked at exact mass $18.000043$$18.000043$ converged, cannot confirm; T-019-seeded auto plus --seed-windows 5 at $4.68$$4.68$ locked $18.000000$$18.000000$ unconverged; T-027-seeded auto at the same side locked $18.000000$$18.000000$ unconverged; $4.69$$4.69$ T-019-seeded auto-grid locked $18.000000$$18.000000$ unconverged; $4.7$$4.7$ T-019-seeded auto-grid converged $18.165413$$18.165413$, cannot confirm; retained checkpoint and frozen-certificate availability differs by row. $4.81$$4.81$ is the session-140 n=19 T-020-seeded auto plus windows 6 at 481/100, covering $19.132115$$19.132115$ unconverged, closer than the same construction at $4.85$$4.85$ ($19.808958$$19.808958$); a session-141 T-020-seeded four-grid plus windows 7 finished at $19.111435$$19.111435$ unconverged, still above nineteen. $4.82$$4.82$ is the session-140 leftover n=19 T-020-seeded auto plus windows 6 at 241/50, covering $19.247109$$19.247109$ unconverged, farther than $4.81$$4.81$ on the same site set; a session-141 T-020-seeded four-grid plus windows 7 finished at $19.224565$$19.224565$ unconverged, still above nineteen. $4.855$$4.855$ is the session-140 leftover n=20 T-021-seeded auto plus windows 6 at 971/200, covering $19.910044$$19.910044$ unconverged, still below 20. $4.86$$4.86$ is the session-141 n=20 T-021-seeded four-grid plus windows 7 at 243/50, covering $19.887914$$19.887914$ unconverged, still below 20. $4.88$$4.88$ is the session-156 n=21 exp-229 trio at 122/25: a T-021-seeded auto plus windows 6 stopped at its deadline at $20.040960$$20.040960$ unconverged; seedless auto plus windows 5 converged at $20.131946$$20.131946$, but the interval route stalled on a seam where window rows sit exactly $B$$B$ apart and refused the freeze, which decides nothing; seedless auto with no windows converged at $20.145556$$20.145556$, and freeze-then-decide retained T-034 at $s(21)\ge 122/25$$s(21)\ge 122/25$. $5.13$$5.13$ is the session-141 n=26 seedless auto plus windows 5 at 513/100, covering $25.000000$$25.000000$ unconverged, still below 26, the first first-party covering row at that size. $5.25$$5.25$ is the session-141 n=27 seedless auto plus windows 5 at 525/100, covering $25.000000$$25.000000$ unconverged, still below 27, the first first-party covering row at that size. $5.48$$5.48$ is the session-141 n=29 seedless auto plus windows 5 at 548/100, covering $26.040745$$26.040745$ converged with freeze mass $26.0409395$$26.0409395$; the interval route refused the freeze, the first first-party covering row at that size. $5.59$$5.59$ is the session-141 n=30 seedless auto plus windows 5 at 559/100, covering $27.178193$$27.178193$ unconverged, still below 30, the first first-party covering row at that size. $5.7$$5.7$ is the session-141 n=31 seedless auto plus windows 5 at 57/10, covering $28.331329$$28.331329$ unconverged, still below 31, the first first-party covering row at that size. $5.8$$5.8$ is the session-141 n=32 seedless auto plus windows 5 at 29/5, covering $29.803318$$29.803318$ unconverged, still below 32, the first first-party covering row at that size. $6.75$$6.75$ is the session-141 n=44 seedless auto plus windows 5 at 675/100, covering $41.236782$$41.236782$ unconverged, still below 44, the first first-party covering row at that size. $6.84$$6.84$ is the session-141 n=45 seedless auto plus windows 5 at 684/100, covering $42.137360$$42.137360$ unconverged, still below 45, the first first-party covering row at that size. Several sides are reported more than once from site sets built differently, which is the point of reporting them that way: at $4.85$$4.85$ the difference is between a wall and the certificate T-021 rests on, at $4.865$$4.865$ it is two independent walls plus a session-140 four-grid-plus-windows-7 construction that stopped at $19.930198$$19.930198$ unconverged without crossing, and at $3.97$$3.97$ it is a converged grid optimum of $12.364038$$12.364038$ above a cutting-plane row LP of $12.248227$$12.248227$ and a session-140 T-017-seeded four-grid-plus-windows-7 freeze at $12.133391$$12.133391$, and a session-141 T-017-seeded auto-plus-windows-7 row at $12.097146$$12.097146$ unconverged, with a historical reported floor of $10.845594$$10.845594$. That floor cannot currently be replayed because its generating family and state are missing; D-478 records the evidence gap.

The middle tier is built and works within the explicit boundaries above. Two instruments now agree on the cell decomposition to 4.4×10−16$4.4\times {10}^{-16}$ and on the corner’s slopes to three decimals. Floating-point LP refinement reaches its declared solver floor on both proved instance cells. The current hypothesis-status aggregate is reconciled from the generated ledger in Current research readiness, and the campaign has a defect log that has already predicted a recurrence.

For record-finding, the bottleneck has moved from polish to proposal. Nothing in the current toolkit reaches Trump’s standing side, and the refiner cannot rescue the tested starts by construction; no sampled $n\ge 5$$n\ge 5$ full terminal-component relation has been measured. The named candidates are δ-continuation, angle-class search as a search rather than an assumption, neighbour-transfer seeding, and quality-diversity retention—none built.

The cartography premise is still untested, and now blocked on the first nontrivial component question. The claim that mapping terminal components is the best route to records rests on record basins being rare in quench measure, and H-012 is the measurement that would refute it. The independent proof, construction, exact-value, and asymptotic lanes do not depend on that premise. The quench supplies one needed instrument, and exact $n=3$$n=3$/n = 4 identity controls now pass, but sampled terminal identity at $n=5$$n=5$ is not ready. What is not settled is what a basin is.

D-034 is the open defect that says so. The exact $n=3$$n=3$ side-2 sliding family proves that one connected optimal set produces many geometric keys. Its open stratum retains one contact certificate, but the wall endpoint has a different certificate after node attributes were restored; exp-014 fixes the stale closed-family claim recorded as D-140. At $n=5$$n=5$, exp-033 replaces the matching-summary conjecture with a narrow exact result. After one D4 action and relabelling, four squares coincide and the fifth slides through an exact side-constant segment in one fixed-angle cell. An exact dual proves optimality within that cell, while active fixed-side nullity changes from zero at each endpoint to one in the interior. Exp-034 proves that exact face lies in a two-parameter angle-and-slide sheet of orientation-indexed LP optima. Exp-035 derives both owner-axis first-order systems at the two endpoints and one interior point and verifies one exact non-sheet direction in each. Certified nonlinear continuation must still decide whether that direction is a true motion in the full component; the unequal-side rows still need minimax-clearance bounds.

So distinct_basins currently counts family members, the discovery curve cannot plateau, and H-011’s saturation criterion is unreachable until the definition is fixed. The three candidate definitions are written up on think-1s0h; none is a code tweak, because this is the deliverable’s own shape. Until that is settled and the census runs, the cartography program is a well-argued bet rather than a finding.

The mathematical-frontier review now keeps several independent routes alive rather than making the census spine the whole program: Trump’s nonsmooth local geometry, exact small-n quotient spaces, held-out construction surgery, pure-point piercing limits, robust restricted-angle proofs, $s(12)$$s(12)$, $s(61)$$s(61)$, exact record fields, and the asymptotic waste exponent.

The small-n lane was missing its direct prior art. D-139 records the omission. Two primary hard-square configuration-space papers are now archived; the Plakhta paper remains explicitly publisher-blocked, so no novelty language is permitted until its scope is checked from a lawful primary copy.

The first fast rotation is cheap and high-information. Exp-012 exposed that H-024’s formal prerequisite was missing, while exp-037 separately rejected the corresponding numerical claim H-042. Exp-013 confirmed H-026 and locally isolated Trump’s pose, and exp-014/015 solved the exact $n=3,4$$n=3,4$ quotient controls in 1.28 wall seconds. Exp-033 then certified the $n=5$$n=5$ equal-side pair’s exact fixed-angle face in 0.24 wall seconds of generation plus replay. Exp-034 through exp-036 then certify an exact angle-and-slide sheet, a non-sheet first-order direction, and an exact second-order obstruction to that displayed direction in 0.76 further wall-seconds. Exp-038 adds the complete branchwise first-order inventory in 1.06 wall-seconds. Next certify the discovered fixed-angle optimal-position polytope, test transverse and mixed nonlinear realization, bound clearance between the unequal-side rows, and hide the UnitSquare $n=68,69$$n=68,69$ children for the first parent-surgery test. The quantitative Trump successor is an explicit isolation radius or minimal-support stress analysis, not another rank count. No hour-scale lane is promoted without a known-answer response, independent validity, and a result that changes a decision.

The normal checkpoint and blocking macOS deep golden are green; broader unattended launch is not yet authorized. At that checkpoint the tree passed all 31 normal-gate steps in 97.68 wall-seconds, including seven exact small-n replays, 59 pytest contracts, and all 62 mutation controls. The gate has since grown to 59 steps, of which the pull-request tier runs 35; the sentence is dated rather than restated because no check guards this number, so a current-tense figure here silently goes stale — as it did twice on 2026-09-03, once when a second step budget landed and once when the results-headline check did. The first deep regeneration had reproduced one unsettled $n=4$$n=4$ proposal and an $n=10$$n=10$ 1.503×10−10$1.503\times {10}^{-10}$ pair-row residual. D-199 identifies and fixes the n=10 cause: repairing first-call offenders 49 and 66 exposes previously clean row 61, which a third conservative call settles with zero all-original-row residual. All seven ladder rungs now converge at pool widths 10 and 1. D-203 isolated the remaining n=4 seed-0 stop as a distinct HiGHS status-4 Solve error. Its retained LP is not malformed or globally ill-conditioned: independent exact primal/dual certificates prove the finite optimum $2.00103283426408968$$2.00103283426408968$, rank 9, and zero duality gap. The failure is dual-simplex presolve/postsolve instability on a thin near-degenerate optimal face. Strict highs-ipm solves the identical LP with zero original-row residual; default tolerances and presolve-off simplex are rejected because their residuals exceed 10−10${10}^{-10}$. The status-4-only fallback keeps the same LP, tolerances, four-call cap, and all-row screen. The bounded seed-0 replay reaches proved side 2 with all 3,692 fixed-point evaluations settled; the independent verifier accepts every square and pair. The direct blocking macOS deep golden then rebuilds $n=4$$n=4$ at 4/4 converged and passes all seven proved ladder rungs. D-272 records the removal of the temporary expected-failure wrapper after that recovery, with Linux and macOS green at b582fe1. D-266 records a soundness error caught in the first fallback draft: a primary status 4 followed by IPM status 2 was briefly promoted to mathematical infeasibility. The corrected classifier reserves infeasible for a sole primary status-2 receipt and keeps every mixed-method failure numerical. D-260 through D-262 record and correct the fixture-capture hazards found before commit: a cross-wired geometric context, a receipt that initially defined its own acceptance, and a pytest-only completion claim while static checks were red. The retained millisecond fixture now exact-rebuilds all LP inputs, rejects the cross-wire mutation, and either reproduces status 4 or admits only a finite successful solve whose original-row residuals remain at or below 10−10${10}^{-10}$. D-263 records a coordinator recurrence during that reconciliation: a status-only patch again touched D-034 instead of the named new defect. The exact named-status audit restored D-034 and closed only D-260 through D-263. D-225 preserves the decision boundary: a normal no-skip gate and owned limitations suffice for a checkpoint merge, while unattended execution requires fresh strict/deep evidence. It does not turn this repaired small-n result into a general producer-health claim. D-202 separately keeps final-receipt capture open after one delegated long command terminated without returning its output; the evidentiary rerun used a durable parent-owned session. D-217 is the same failure in a local parallel validation wrapper: its unreceipted result was discarded and rerun directly, while think-b3bm still owns the portable yielded-command and terminal-polling rehearsal. D-222 records a separate audit-scope violation caught during this merge review: an explicitly excluded strict run was terminated by exact process group, its partial output discarded, and think-ysz2 owns explicit command and wall ceilings for future bounded delegations. The repaired small-n path no longer blocks the campaign, but unattended numerical work still lacks a reproducible work-based quench budget (D-126), a bound around pure-Python validation workers and the aggregate duration of multi-command steps (D-239), and portable terminal-receipt discipline for delegated long commands (D-202). D-280 records the phase-count cap exhausting the fast campaign early; its continuation remains open.

One open measurement defect constrains timing forecasts. D-101: the historical exp-007/008 round-level wall times disagree with retained per-call durations. Price the first maps from raw calls or a current receipt until those aggregates are reconstructed.

One contained defect constrains every floating-point LP result. D-021: the solver floor is about 10−11${10}^{-11}$ in the side, so this numerical method cannot resolve finer. The general fix is an exact LP over certified rational or algebraic coefficients; the rational special case alone is not a universal remedy.

The destructive negative-control path is closed. D-035: negctl now mutates bounded private source snapshots, so a killed control can abandon only temporary data and cannot leave deliberate sabotage in the checkout.

Mutation-control timeouts are bounded. D-129 is fixed: each control has a finite deadline, runs in its own process group, and is terminated and reaped after TERM and then KILL if necessary. This closes that specific gate-stall path; the unattended numerical runner still has the separate launch requirements above.

Validation subprocesses now have finite POSIX deadlines. The shared captured-command path and quiet Git provenance probes use a 900-second production default, configurable by CLI or environment, and retain smaller call-site caps. Timeout and coordinator interruption terminate and reap the registered process groups. D-239 remains open because pure-Python worker code, aggregate multi-command duration, detached daemons, and Windows process-tree cleanup are not bounded by that policy. A strict gate therefore still needs an independent outer watchdog for unattended use.

One open defect makes quench evidence load-dependent. D-126: the scientific work budget is still wall-clock time, so contention changes the number of LP solves and probes performed. Price and compare basin experiments by retained work units; use the wall clock only as a recorded outer deadline.

A second contained defect makes the LP count itself unreliable on aborted runs. D-349: _free_sweep accumulates its own LP count and returns it, and quench_bracket adds that total only on the normal return path, so a sweep that raises on its wall budget or on an unsettled cell carries the partial count away with it. The reported lp_solves therefore understates any run that stopped inside a free sweep. The direction is conservative and the fix is deferred because it changes figures already reported in past rounds, but a per-solve efficiency number computed from a budget-cut run is too favourable until it lands. The Motion Lab timeline is what made it visible: it retains one event per solve, so an aborted sweep has more retained events than the counter describing them.