Later convergence handoff; Draft 3 unchanged

Equations in these preserved Markdown records retain their TeX notation where present; this is not a newly typeset proof edition.

CM Structural Computation C1–C4 — frozen Phase 2 T3 handoff

Status: RETURN COMPLETE BOUNDED EVIDENCE TO MASTER FOR THE NEXT CONVERGENCE GATE. Draft 3 remains unchanged. This is an empirical handoff, not a novelty claim, manuscript rewrite, or publication approval.

Answers required by the gate

1. T3 correctness reproduced: YES within the exact tested contract. The independent implementation retains coordinate moments and metadata only, discards factor references, reduces the cumulative horizon after distinct-coordinate destructive updates, and returns exact counts after every tested prefix. Both orientations, dense/sparse layouts, noncontiguous coordinates, source poisoning and residual binary round trips pass. All 7,445,928 executed campaign counts and 70,662 updates passed the exact oracle. The independent Theory checker also reproduced its original 3,749,102 checks exactly. Finite verification supplements the supplied proof; it does not replace its universal quantifier.
2. Frozen dense storage prediction: payload formula SUPPORTED; unqualified serialized-byte crossover FALSIFIED in finite cases. All 9,712 successful initial payload checks and 34,582 recorded update-work checks match the frozen formulas. Of 133 successfully realized dense case/depth pairs, 32 satisfy the original row-anchored inequality. Nine of those 32 do not beat the actual raw-factor serialization after headers/alignment; 22 do not beat ideal raw-factor payload bits when the complete T3 file is charged. The primary inequality was never replaced by a sparse/adaptive one. These metadata exceptions do not falsify correctness or the asymptotic formula with its metadata term.
3. Sparse/orientation-adaptive layouts change the practical picture: YES, as a secondary result. Observed-support layouts avoid many unused dense profile blocks, and choosing the smaller row/column sparse payload adds favorable cases. On the natural corpus at k=1, the primary dense criterion holds for only two cut cases in one design; sparse adaptive payload favorability holds for 18 cut cases across four designs. These are different criteria and are reported separately. No k>=2 natural cut satisfies either criterion in this bounded slice.
4. Favorable cases occur naturally: narrowly. The corpus contains 20 distinct EPFL source designs in two application families, not 20 outputs of one circuit. All 2,861 outputs are retained: 1,088 eligible outputs from 11 designs, 1,773 support-cap exclusions, 2,119 fixed-cut cases. At k=0 the dense criterion holds in 1,067 cut cases across six designs, heavily concentrated in decoder and memory-controller outputs. At k=1 only two memory-controller cut cases qualify. These counts are descriptive within support<=12 and two fixed cuts, not evidence of broad incidence across high-support circuits.
5. Any advantage survives full lifecycle accounting: YES against some baselines, not generally. Sparse adaptive T3 beats direct supplied-factor counting and the retained histogram path in many executed reuse cells and has lower design-median full lifecycle than the measured CUDD compilation path. However, compiled packed binary has lower full-lifecycle design medians on every natural timing design. Neither dense nor adaptive T3 beats it on a nonconstant natural warm/fresh-object paired cell; the separately measured fixed sparse orientations have three small k=0, batch=1 wins in controller/decoder cases. Some bounded synthetic cells also win; they are not natural-design evidence. Two repetitions per in-process cell support descriptive comparisons only.
6. Any advantage survives credible optimized comparators: qualified and endpoint-dependent. The comparator is a sifted CUDD representation with a new -O3 C++ exact-integer residual-count kernel and repeated-count caching; the historical Python ROBDD is not called optimized. T3 construction can be cheaper than compiling this representation, but its online phase loses to native CUDD at every natural design median. Compiled packed persistence remains stronger overall in the admitted natural slice. A broad best-comparator runtime advantage is not established.

Completed and preserved evidence

• C1: the unchanged prior 4,912-file delivery verified at intake; original Astra attribution, coordinate-convention regressions, class/rank checks and historical results retained. No redundant restart of that phase.
• New correctness: 122,120 T3 prefix/round-trip checks; 117,792 explicit update-work checks; 592,960 compiled/baseline prefix checks; source-disposal and gauge checks. No correctness counterexample found.
• Main campaign: 16,752 PASS trials and 400 preregistered dense allocation-cap exclusions. Complement-control completion: 3,072 PASS trials. Cold panel: 115 PASS trials and five identical-cap exclusions. No failed or timed-out experiment trial was discarded; none occurred.
• Cold loads: separate consumer processes observed zero resident artifact pages via mincore before reading a separately fsynced/evicted Linux-local file. This verifies OS page-cache coldness, not physical-device-cache coldness. Consumer peak RSS is isolated; in-process and producer high-water RSS histories are explicitly distinguished.
• Additional isolated full-lifecycle memory panel: 115 PASS and five cap exclusions on the same fixed cases/methods, with 21,056 additional actual counts and 214 updates. These instrumentation timings are not pooled with the campaign. Fresh-process construction-through-query RSS ranges are approximately 22.7–28.6 MB for adaptive T3 and 53.2–54.2 MB for CUDD/native on this panel; these are absolute process peaks, not persistent payload size or isolated object allocations.
• Raw phases: construction, verification/oracle preparation, serialization, load, indexing, each update and count, total method phases and wall times. Source-factor payload, mathematical counters, binary file size and RSS remain separate. A separate recorded BLIF-to-factor preparation supplies the larger raw-circuit input boundary.
• The only protocol addendum completes an accidentally omitted complement for every parity control dimension. It was frozen before extension results, preserves the original grid/criterion, and replaces no earlier data. Main runner v1 is retained under source_snapshots/; the subsequent change only charges additional cold-path oracle/hash verification.

Limits and next gate

The measured artifact-input campaign reaches n=20; natural exact validation is restricted to support<=12. It does not establish large-circuit scaling, optimal decomposition, a blind previously unseen corpus, hardware-general timing, or firstness. The earlier suite exposure is disclosed. Supplied factor rank is recorded separately from actual rank; source discovery is not smuggled into the artifact-input theorem. The Python state has object overhead beyond mathematical bits. Cold panel cells have one repetition and should not support a stable comparative latency claim.

Review DESIGN_LEVEL_RESULTS.md, THEOREM_EXPERIMENT_CROSSWALK.md, LIFECYCLE_SUMMARY.csv, the raw results, manifests and counterexample note. The nine byte-crossover exceptions require precise finite-size wording at the next Theory/Master gate. The timing losses do not refute T3.

Next: Master should conduct the convergence/priority gate on this evidence, using the existing Master task and GPT-6-Astra/high. No new computation campaign or manuscript change is recommended before that decision. Closely related measurement questions should return to the current computation task to reuse the frozen state and evidence.