Experiments Conducted

Experiments Conducted

There are 246 rounds registered in series-000.

They record 2512.1 agent-minutes and 5883.1 wall-minutes. These totals exclude four historical annealing rounds with unrecorded timing; their wall and operator costs are unknown, not zero. Exp129 closed as blocked without invocation and contributes zero scientific elapsed time; its source-free development and review costs belong to Session097. Exp-114 completed its one target and independent replay. Reader development costs are recorded separately from those process times. Exp-056 stopped at its fixed timebox with a 170-row agreeing prefix and no canonical result; exp-057 stopped before target access; exp-058 stopped on the review it was waiting for, which arrived and accepted it. Exp-058 records no agent-minutes, because the lane that produced its mathematics did not retain its operator time; the agent-minute total above therefore understates what H-060 has cost. Their instruments are sqsearch 0.1.0 (the f64 screening annealer), sqpack.quench (0.1.0 with angle descent and 0.2.0 with class bracketing), the high-precision Kingbird SVG reconstruction, the exact Trump linearized-cone checker, the exact small-moduli checker, the exact Stromquist printed-set falsifier, and the exact repaired-cover certificate, the exact terminal-component known-answer checker, and the exact $n=5$$n=5$ fixed-angle face, angle-sheet, full-angle tangent, and second-order obstruction checkers, plus the exact branchwise tangent-inventory checker. Exp-058 alone used no repository instrument: its numbers come from read-only sympy scripts retained verbatim in its results record, which is why it is not a receipt.

No record-search round has produced verified assurance, so no result below claims a new record. Exp-012 is an exploratory reconstruction of a published record witness; its six-class determination leaves H-024 unresolved because the source has no formal feasibility certificate. Exp-037 separately rejects H-042’s serialization-scoped three-class claim. Neither round certifies the source geometry or optimality.

The roughly 100-digit retained n = 29 witness is evaluated at 160 decimal digits of working precision and passes all 406 pair checks at tolerance 1e-80. The figure therefore says “numerically checked,” not “verified,” “exact,” or “proved optimum.”

Roll-up

Every figure is lifted from the round’s frontmatter, which is lifted from the JSONL archive beside it.

Cost and provenance

What the 246 rounds jointly establish

The 246 rounds use 2512.1 agent-minutes and 5883.1 wall-minutes under the campaign’s retained effort accounting. The never-invoked exp129 adds no scientific result or execution time. Exp-114 contributes 2.46 seconds of target/replay effort; its readiness work is recorded separately in Session089.

The numerical basin event trust boundary now retains complete declared blocks through $n=8$$n=8$ plus one bounded $n=9$$n=9$ performance event; exact component controls pass only at $n=3$$n=3$ and $n=4$$n=4$. Exp-018 through exp-020 retain twelve independently valid historical v2 poses at $n=3$$n=3$ through $n=5$$n=5$, including four at the proved $n=3$$n=3$ and $n=4$$n=4$ optima, but D-165 correctly remains recorded on those artifacts. Exp-021 adds one v3 $n=3$$n=3$ event whose 2,037 fixed-point evaluations are all retained and settled, whose pose independently verifies, and whose admissibility claim replays. Exp-022 completes the four-seed v3 block at 4/4 admissible: three endpoints reach side 2 and one reaches the valid nonoptimal side 2.362735797795. These events are evidence for the producer contract and terminal outcomes, not terminal-component counts. Exp-032 freezes the missing evidence rule: the complete exact $n=3$$n=3$ quotient is one interval across four geometric keys and two contact signatures, and the complete exact $n=4$$n=4$ quotient is one point. All current f64 events remain unresolved because none carries an exact component-membership witness. Exp-033 adds the first exact relation between sampled $n=5$$n=5$ source poses: after one D4 action and relabelling, two different golden keys share a one-dimensional fixed-angle optimal face at side 1+52​/4$1+5\sqrt{2}/4$. It does not assign a full terminal component. Exp-034 embeds that face in an exact two-parameter angle-and-slide sheet. Exp-035 then retains six exact active-system matrices across A, the interior, and B and verifies a non-sheet direction against every row. Exp-036 proves that displayed direction cannot be a nonlinear path tangent: the only two nearby pair $(3,4)$$(3,4)$ owner-axis branches have exact second-order obstruction margins. Exp-038 then certifies the complete first-order inventory and both pointed-quotient face vectors. This strict linearized-versus-true-tangent gap and finite inventory do not classify transverse or mixed nonlinear realization or assign a component. Exp-039 exactly continues four release classes through twelve sharp fixed-angle paths in one connected five-dimensional cell-local LP-optimal position polytope. Both owner branches carry positive structurally derived first-order stresses on those paths. This does not make every point of the polytope stationary, certify an A-to-B stationary path, classify R4, R5, -W, or mixed-angle directions, or assign a terminal component. Exp-023 reaches proved side 2 on three of four n=4 starts and preserves the fourth event’s post-check rejection. That stop exposed D-171: two rows were already outside the screen before an argmax-only retry. Exp-024 applies one complete offending-set retry and reaches side 2 on all four starts, with 14,301 of 14,301 evaluations settled and all four events admissible. Exp-025 extends the unchanged event path to $n=5$$n=5$: all four starts independently replay, all 14,219 fixed-point evaluations settle, and the run observes three descriptors at two nonoptimal side values. Those descriptors are not component identities, and none of the four starts finds the proved optimum. Exp-026 then finds the next retention boundary: three $n=6$$n=6$ events reach side 3 and replay, but seed 3 fails independent validity and is censored when event validation raises before writing it. D-183 now routes independently invalid endpoints through the same atomic retention path as every other terminal outcome. Exp-027 retains all four starts: three admissible side-3 events and one independently valid, non-admissible time-budget stop at side 3.040392660291. The earlier invalid endpoint does not reproduce because open D-126 makes wall-clock-limited work load-dependent; neither round supports frequency or component claims. Exp-028 retains four independently valid $n=7$$n=7$ outcomes but only one converges; three carry typed time-budget stops. This validates the event path at $n=7$$n=7$ while showing that the ten-second cell is already too censored for landscape statistics. Exp-029 retains four independently valid $n=8$$n=8$ outcomes: one admissible side-3 event, one typed unsettled cell-cycle stop, and two typed time-budget stops. Its bounded cost audit measures median four-event independent screening at 0.000684 seconds and canonical key computation at 0.004956 seconds, versus 38.004 seconds of retained quench wall. Canonicalization is therefore not yet the event-loop bottleneck at n=8, while the 3/4 typed-stop rate again bars landscape statistics. Exp-030 retains one independently valid $n=9$$n=9$ time-budget stop and completes the frozen command in 21.36 seconds, below its 30-second profile trigger. Median one-event keying costs 0.001074 seconds versus 20.062 seconds of quench wall, so canonicalization remains negligible at n=9. This one censored event is a performance control, not an n=9 landscape sample. The blind random-start size ladder stops after n=9. A source-bound n=10 entry point now reconstructs the published Göbel pose from the retained fixture, records its source URL, replays deterministic perturbations, and retains typed failure. A one-second smoke run reaches a valid endpoint at the proved side but times out before producer convergence. Exp-031 then converges on all four preregistered perturbations: every endpoint validates and replays, all 6,631 fixed-point evaluations settle, and the maximum proved-side error is 2.221×10−15$2.221\times {10}^{-15}$. This is a local known-answer control, not a random-search or component claim. The exact small-moduli controls remain valid; component identity is the next blocked layer. The $n=12$$n=12$ calibration returns exactly $4.0$$4.0$, but that is not a known-answer guard. The runner’s full-pose independent verification boundary is repaired but not closed under D-044: a scored line must carry the pose, record re-checks the archived geometry in a separate process before writing a round, and an independent review on 2026-09-03 reproduced every refusal. That review returned BOUNDED-CAVEAT, and the record now names why — the float screen still demands an exact zero overlap where the source finding asked for an independently bounded one, and record never binds the lines it scores to the bytes the child verified. A producer-reported overlap scalar still does not close it.

Trump’s exact pose is locally isolated. Exp-013 retains all 512 raw active-feature selections as 128 derivative-distinct matrices. Every matrix has exact rank 33 and a strictly positive exact $Q(u)$$Q(u)$ stress, so every branchwise fixed-side linearized cone is zero. A finite-branch subsequence argument upgrades that result to local isolation and strict local side optimality in the anchored pose–side chart, modulo finite symmetries. It does not prove global optimality or give an explicit isolation radius.

Goebel’s $n=5$$n=5$ optimum is locally rigid at fixed side, and that is a first-party result. Exp-058 registers the BC-152 proof packet: an intrinsic half-angle chart injective on all of R15$R^{15}$, all 400 elementary wall-corner and pair inequalities classified by exact sign (confirming the agenda’s 16/64 and 4/6 counts with no discrepancy), a neighbourhood cut out by 128 strict sign conditions on which the local feasible system is exactly the twenty active rows, T-012’s 28 Farkas certificates and self-stress replaying on the chart with w · q_chart = -2√2 < 0, and an order-2m coefficient induction that contradicts a nonconstant analytic feasible arc. H-060 is confirmed on BC-153’s independent review, which returned PASS on 2026-09-03 against a criterion frozen before the target work and met as written: the reviewer replayed the instrument from clean roots under both interpreters and got this chart’s neighbourhood back exactly, and rebuilt every exact quantity from scratch in code sharing nothing with the author before accepting each step from nonisolation to the second-order contradiction. What is established, exactly: for s=2+2​/2$s=2+\sqrt{2}/2$ and Goebel’s labeled pose P0$P^0$ in C=(R2×S1)5$C=({ℝ}^2\times S^1{)}^5$, P0$P^0$ is an isolated point of Feas(s), so no nonconstant continuous feasible path leaves it and no sequence of distinct feasible poses converges to it — hence rigid at fixed side in the catalogue’s sense. Registered as T-014 at V3/C5, apparently-novel at S3: the exact quantities are machine-confirmed here, the curve-selection lemma and the induction that close the argument are an audited proof, and no instrument decides isolation — isolation_decided is false unconditionally, by design. Not claimed: an isolation radius, the side as a variable (false, X-007), global uniqueness, any other $n=5$$n=5$ optimum, applicability of Connelly–Whiteley as stated, or novelty of method. Exp-034’s two-parameter feasible family is not a counterexample: it lives at side 1+52​/4$1+5\sqrt{2}/4$, disjoint from the feasible set at Goebel’s side, and X-012 runs it as the C8 control on which the instrument must refuse a receipt. Six gaps stay named and none is a condition of the pass — the printed BCR page behind the curve-selection citation is still unread, and the review replaces it with a derivation from primary-text Basu–Pollack–Roy plus the one-variable Puiseux fact rather than closing it. The corroborating second-order-sufficiency proof in the packet reaches the same conclusion from weaker hypotheses and discharges nothing, because acceptance was preregistered on the curve-selection route.

The optimal configuration spaces at $n=3,4$$n=3,4$ are now exact controls. Exp-014 proves that F3​(2)$F_3(2)$ is two labelled circles, its S3 quotient is one circle, and its D4​×S3​$D_4\times S_3$ quotient is an interval whose corner endpoint changes the active signature and whose midpoint only changes the stabilizer. Exp-015 proves that F4​(2)$F_4(2)$ is 24 isolated labelled grids and both declared quotients are one point. Arbitrary rotations add no side-2 configurations in either case. Generation plus complete replay costs 1.28 wall seconds, so both controls belong in every gate. H-032 remains open at $n=5,6$$n=5,6$.

The published $n=11$$n=11$ lower-bound proof is false as printed. Exp-016 exactly certifies an open box of side $10001/10000$$10001/10000$ that fits Stromquist’s claimed container and strictly avoids all twelve printed Figure 14 points. This rejects the registered five-node H-010 conjunction but not the numerical lower bound itself.

The numerical lower bound now has an independent exact certificate. Exp-017 moves only Figure 14 point G.x from .8 to .79 and exactly certifies the complete five-node argument. Its 18-cell Figure 13 cover plus four Klein-four-related exceptions, 26-face repaired Figure 14 tiling, exact lemma premises, and $3+9$$3+9$ count prove s(11)≥2+4/5​$s(11)\ge 2+4/\sqrt{5}$. This source-distinct computer-assisted result is not attributed to Stromquist, is not externally peer-reviewed, and does not close the gap to Trump.

The tested class-bracketing refiner separates the proved controls from the target. It takes the tested $n=5$$n=5$ and $n=10$$n=10$ starts to 10−15${10}^{-15}$ and leaves the tested $n=11$$n=11$ starts at 6×10−2$6\times {10}^{-2}$. That makes proposer quality the next empirical bottleneck; it does not certify general local optimality or finish the quench contract (D-052).

The $n=11$$n=11$ failure is consistent with an exploration problem. Five annealer seeds land in a band five times narrower than the remaining gap and the local quench improves those tested starts by only 1.3×. Starting near Trump’s reference, the default schedule moves far away; that is refinement evidence, not a certified basin-membership test.

Two rounds have been re-read by later ones. exp-005’s finite-quench residual is now scoped to the tested refiner and no longer called component attraction (D-083). exp-003’s $n=11$$n=11$ result is therefore a combined proposer/refinement observation, not a pure basin-finding diagnosis.

Known defects in the record

The full log is defects.md; these are the ones that bear on reading the table above.

• exp-001’s archive carries no configurations and its engine commit was orphaned by a rebase (D-006, D-010). Cite exp-002–exp-004 for anything configuration-level.
• exp-001 and exp-006 each record a three-cell sweep as one cell (D-010, D-017—the second a verbatim repeat of the first, because the first fix left no regression check). Their numbers stand; the ledger’s sweep coverage misreported them until the successor rounds split the cells.
• D-021 is contained. Floating-point LP refinement has a noise floor of about 10−11${10}^{-11}$ in the side, and eight rounds sit on it. Those numerical results may not claim a difference smaller than the floor.
• D-403 is contained. The negative controls run only in the full gate, and a pull request runs --fast, so a branch can be green on every push while its controls rot — six of a hundred and fifty were not firing when this was checked. A control that does not fire is worse than an absent one, because the suite reports a count that reads as coverage. The runner is what saves it: an unmatched anchor is reported rather than skipped, and “failed, but not with the expected message” is distinguished from a real firing. Moving the suite onto the pull-request surface would push that surface past the point where it gets run at all, so what is owed is a cheap anchor-resolution check in --records rather than a faster suite.
• D-405 and D-406 are the reassessment auditing itself. BC-088’s entry sequenced X-009 on an unmeasured gap claim — the measured spread is $0.056$$0.056$–0.536, structured by k=m2−n$k=m^2-n$, and devtools/gap_ranking.py now carries it — and BC-092 was stopped on an enumeration price quoted without its artifact and against that artifact’s own isomorph-free decision at $n=5$$n=5$. X-010 carries the corrected sequencing input; the repricing is open on the x-010 beads.