II · Computation and Reproduction

The Moser case's second layer: all fifteen round packages independently recomputed, RUN-001 to RUN-016

The first layer, "I · Precursor", holds the fifteen round packages produced by Aletheia on the question Neo.K set out: Wetzel's 30-60-90 triangle, shrunk by 1.0048, contains a congruent copy of every arc of length one, by a recent preprint, and the rounds search for the unit arcs that need the most of it. This second layer, "II · Computation and Reproduction", is their independent recompute by 懸衡 (Xuán Héng) (AMRAL's counter-proof arm, Claude), in the rounds' own order: every finite claim recomputed, every construction reproduced, every theorem-level step read against its source. The rounds' scripts are never run, and are read only after the rebuild.

There are 16 runs (RUN-001 to RUN-016): RUN-001 for the corpus, then one per round. Each has one gate, one report and one mutation drill — planted faults, controls and must-stay-green assertions, with every check blinded in turn to confirm that each fault is caught by exactly the checks it should trip. Before each commit the run was repeated from a cold cache and its gate log compared byte for byte. Every round's verdict is PARTIAL: what can be rebuilt from its package reproduces, and some of its statements do not hold as written.

This layer does not rewrite the packages and proves no bound for Moser's problem. It certifies, in interval arithmetic, a chain of explicit unit arcs, each above the last — which none of the rounds did; the last has least scale at least 0.99891448056696, so with the cited preprint the cover is within 0.11 % of tight in linear scale. It records what reproduces and to what precision, what is not as the rounds state it, and the new readings.

Three layers: I · Precursor (the fifteen round packages) → II · Computation and Reproduction (this page, 16 runs) → III · Crystallization (four formal papers).

The corpus · RUN-001

Before any round was recomputed: are the packages the site serves the originals?

The first layer's presentation defects RUN-001 measured were corrected there on 2026-10-22; what RUN-001 measured is kept below as it was.

RUN-001corpus identity: the packages are the originals; the pages around them are not exact

Verdict: the packages PASS; the pages FAIL five of seven checks, all on presentation.

Loads when opened…

New readings · the main counter-results

The most important of the 16 runs' findings; after each, the runs that decide it, whose reports open on their pages.

A certified ascent: the event five-link (Round 05), one tanh curvature layer (Round 08), Round 13's stated curve, the split peak (Round 14's family) and the eight-mode candidate (Round 15), each certified in interval arithmetic above the one before; none of the rounds certified any of these. The last curve's least scale is at least 0.99891448056696. RUN-010, RUN-011, RUN-014, RUN-015, RUN-016
Each family's local optimum was surpassed in the next, wider family: the event five-link is no local maximum among curves, a finite-width curvature layer raising its scale by about 2.0×10⁻⁴ ε at its own parameters; Round 13's five-parameter point, a strict local maximum of its family, is a saddle against splitting its peak; and it is not even stationary in the curvature's function modes. RUN-009, RUN-015, RUN-016
One local-optimality verdict is overturned: Round 14's, that the single peak is stable against splitting; it is a saddle, and the round's profile held the other parameters fixed. Round 15 inferred from a Hessian at a point that is not stationary; its conclusion holds, for a first-order reason. RUN-015, RUN-016
The edge beside a switch: Round 11's semi-validated certificate leaves out the 2×10⁻¹⁰ rad beside each switch, and at 14 of the 17 switches the derivative there falls outside its intervals; Round 10's phase map misses a smooth minimum 5.44×10⁻⁹ rad before a switch. The rounds' qualitative conclusions hold, by this layer's certificate. RUN-011, RUN-012
Round 08's published curve file is not its candidate: read as a curve, its least scale is 0.998794830, below the event five-link it is published as beating. RUN-009
The early rounds' printed figures are often a grid's, a tracker's or one handedness's: the library maxima are the grid's cos(π/192); the candidate's 0.9187 is the orientation-preserving value, 0.894545 with reflections allowed; Round 04's four branches "level to 2.734812376559×10⁻¹²" are the tracker's, their true spread 1.30×10⁻⁸. RUN-002, RUN-005
Round 13's stated Jacobian spectrum is not its system's: the condition number is 2.13×10³, not 3.77×10⁷. RUN-014

All fifteen rounds · 15

Each card stands for one layer-1 round package; its tags are that round's verdict.

All files

These files are byte for byte the research tree amral-research-trees's moser-verification-xuanheng/ (branch agent/moser-verification-xuanheng, commit c8d3196): the README, 22 programs, 20 data files (gate logs, the source manifest, citation snapshots, the papers' figures), the 16 reports and the item-by-item inventory (crystal/). SHA256SUMS lists every file's SHA-256. The fifteen original packages a re-run needs are the ones the first layer offers for download: code/fetch_source.py fetches them and checks each one's size and SHA-256.

moser-verification-xuanheng.zip — The whole second layer (zip, SHA-256 d7ba5f9060bdc4ef…)
SHA256SUMS — Every file's SHA-256
README.md — The research tree's README: one line per run and the commands to re-run
RUN-001-CORPUS-IDENTITY.md — corpus identity: the packages are the originals; the pages around them are not exact
RUN-002-ROUND01-SUPPORT-SKEW-LP.md — Round 01 (v0.1): the grid programs reproduce; what they print is a grid's value, a local search's, and one handedness's
RUN-003-ROUND02-PHASE-SCAN-CHIRALITY.md — Round 02 (v0.2.2): the ledger, the scans and the exact values reproduce; the main report's numbers are its grid's, and the three-link family goes higher than its corrected curve
RUN-004-ROUND03-SYMMETRIC-LINKS.md — Round 03 (v0.3): the five- and seven-link values reproduce; the seven-link family contains every five-link curve, so seven below five is a search's shortfall
RUN-005-ROUND04-BRANCH-EQUALIZATION.md — Round 04 (v0.4.1): the equalized five-link reproduces; its four branch minima sit at exact phases, and re-equalized there they level to 10⁻¹⁵, 6.7×10⁻⁹ higher
RUN-006-ROUND05-CONTACT-EVENTS.md — Round 05 (v0.5): the contact-event system reproduces; its root is a strict local maximum, of the four-branch model and so of the least scale on a neighbourhood of unestablished size
RUN-007-ROUND06-CHIRALITY-ESCAPE.md — Round 06 (v0.6.1): the escape, the census and the audit reproduce; the event root is a strict local maximum of the eight-parameter model, and so of the congruent least scale among nearby five-links on a neighbourhood of unestablished size
RUN-008-ROUND07-CURVATURE-WINGS.md — Round 07 (v0.7): the curvature wings reproduce; the arc wing's deficit stands, every segmented family reaches the event five-link in a limit, and the m = 6 signature is one of Round 05's four events
RUN-009-ROUND08-SMOOTH-LAYER.md — Round 08 (v0.8.3): the smooth curvature layer's gain over the event five-link is real — 1.0581952124×10⁻⁵, confirmed in independent code and in 40-digit arithmetic — but its published curve file is not the candidate
RUN-010-ROUND09-PRECISION-CUSP.md — Round 09 (v0.9): the 270° cusp holds to 120 digits and its Darboux bound is sound; the draft's target over the whole phase circle is certified here — the candidate's least scale exceeds the event five-link's
RUN-011-ROUND10-PHASE-MAP.md — Round 10 (v0.10): the phase-contact map reproduces to 10⁻¹³, but one of its four cusp minima is a smooth minimum it misses, and at the wing switches one of each pair of stated derivatives is not the derivative; the least at 3π/2, which the round left open, is certified here
RUN-012-ROUND11-BOX-CERTIFICATE.md — Round 11 (v0.11): the exact boundaries and the 120°/270° enclosures hold, and the 579 derivative boxes and the root boxes hold where sampled; the switch neighbourhoods' derivative intervals leave out the 2×10⁻¹⁰ rad beside each switch, and three exclusions rest on them
RUN-013-ROUND12-IV-REPLAY.md — Round 12 (v0.12): the interval replay of the 120°/270° enclosures reproduces to 3×10⁻⁸¹ and the Newton steps hold, but one boundary ball in 19, not 19, holds Round 11's float, the root replay's positions are estimates, and "dependency inflation" explains only part of what it is used for
RUN-014-ROUND13-SMOOTH-KKT.md — Round 13 (v0.13): the five-parameter event-KKT point lies 6×10⁻⁸ from the stated one and is a strict local maximum, and the gain over Round 08 is certified between 4.04×10⁻⁹ and 4.25×10⁻⁹; but the Jacobian's stated spectrum is not the system's — its condition is 2.1×10³, not 3.8×10⁷ — §7's projection is not reproduced, and three of the four other minima are not the curve's
RUN-015-ROUND14-DOUBLE-PEAK.md — Round 14 (v0.14): the single peak is a saddle against splitting, not a local maximum — split into two halves with its five parameters re-solved, the curve rises, certified 1.19×10⁻⁷ above Round 13's at separation 0.03 — while the chirality modes are stable for the congruent scale, as stated; the search's evaluator puts the low branches 10⁻⁸ low, its profile holds the parameters fixed, and its minima lists are phase samples
RUN-016-ROUND15-FUNCTIONAL-MODES.md — Round 15 (v0.15): the eight-mode candidate stands — exact to 2×10⁻¹⁴ and certified in interval arithmetic at least 1.3725×10⁻⁷ above Round 13's — with nine minima and a latent margin of 3.0046×10⁻⁹; but Round 13's point is not stationary in the modes, so the Hessian decides nothing there, the base's low-branch gradients are off by 10⁻⁵, the ledger's takeover opens and closes before the stated window, and the headline figures are printed past their digits