Research: X54 mixed-T37 saturation — exhaustive local sweeps, exact Φ packing invariant and width/Φ prices (no new kappa)

[Wronskode]

No new κ. Scoped negative result and screening tool for the X54 mixed-T37 line (#1193/#1218, κ = 0.001675809683500501). Package: research/x54-mixed-t37-saturation/.

Superseded in part during this session: #1274's helper-donor kernel found a local gain outside the #1186 move families. #1252/#1268/#1280's idle-axis exchanges (48+48 → 45+51) work outside the bin-remainder model used in (2). The README says exactly what still holds.

Results

1. Exhaustive local sweeps on both final words (D3 = Conditional kappa 0.001675807682652: X54 on mixed T37 fusion providers #1207 BASE-X54, D4 = Conditional κ = 0.001675809683500501: mixed T37 allocation with X54 and fusions #1193 FOUR-WORD), Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186 toolkit unchanged, exact frame pricing. Conditional κ = 0.001675658002271934: two source-holder fusions on #1148's joint-entrance k8 word #1195 swept only the pre-X54 words. Results per word:

   • fusion + repair (repair.py): 2,238 candidates, 969 feasible, 0 gains;
   • read-set exchange (all subsets of swappable reads, 14 copy pairs): 50 candidates, 0 feasible;
   • joint triangle-hybrid (≤3 fused reads, partial swaps, both restore modes): 161 candidates, 24 feasible, 0 gains.

   The baseline frames are exactly optimal.

2. Exact width-class invariant (stdlib). Put φ(4) = φ(8) = 0, φ(5) = 3, φ(7) = 1, φ(9) = −1. A full bin of capacity 8, 16 or 32 has Φ ≥ 0, and a full capacity-48 bin has Φ ≥ −4. The 125 D3 / 208 D4 inventory has Φ = −20,814, which is tight. So the two leftover rank-one idle units cannot be merged into one rank-two child, even with time windows, ports and family rules relaxed. That rules out the only cheaper idle histogram in the bin-remainder model (a gain of about +3.3e-10).

3. ILP screening (SciPy/HiGHS) over demotion-count mixes k ∈ [−3, 3] and all 1,163 bin patterns. The integer optimum equals the incumbent. The LP duals have the exact form π_w = −λ·w − μ·φ(w), with λ = 11.73 and μ = 25.04. This gives a screening rule for proposed inventory changes: an extra entrance group is break-even (which is why the mix stops at 208), 9→8 earns 13.3, 4→5 earns 86.9, and Δκ ≈ −1.03e-11 × score.

Reproduce

python3 -B research/x54-mixed-t37-saturation/verify.py      # ~2 s, stdlib: pins, exact lemma vs PACKING.json, 5 rejected controls, sweep tallies
python3 scripts/research_package.py --package research/x54-mixed-t37-saturation
python3 -B research/x54-mixed-t37-saturation/aggregate.py --out /tmp/agg.json   # SciPy, ~25 s
python3 -B research/x54-mixed-t37-saturation/sweep.py --toolkit <#1186>/research/exact-frame-toolkit --word D3 --out /tmp/s   # ~10 min/word

Package hook: PASS_REGISTERED_RESEARCH_PACKAGE … outcome=negative-result. tests/test_research_*.py passes (20 tests).

Not run or not covered:

• verify.py does not rerun the sweeps or the ILP.
• No native or strict admission was needed, since no candidate was found.
• The inherited all-size compiler, realization, hosting, precision/tape, analytic-transfer and bit H1–H5 conditions remain.

Task card

• Card: selected-packing, scope refined to the strongest open claim instead of the superseded Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges #1094 packing.
• Base: dd6403f7. Inputs vendored and pinned: Conditional κ = 0.001675809683500501: mixed T37 allocation with X54 and fusions #1193 4e392e90, Conditional kappa 0.001675809683500501: global mixed allocation with X54 and fusions #1218 0aa14797, toolkit Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186 9254a3cc.
• Claim: discussion CLAIM: fusion/repair sweep on the final X54 mixed-T37 words (#1193/#1218), Wronskode, expires 23:30Z #1251.
• Open next questions are in the README:
  • single-helper width changes that pass the screening rule;
  • how λ and μ shift once idle children can be reshaped (Idle pair exchanges improve the #1094 κ candidate #1252).

Credit

• Global allocation: Jeremy Diviney (Conditional κ = 0.001675809683500501: mixed T37 allocation with X54 and fusions #1193); composition: Rohan Arun (Conditional kappa 0.001675809683500501: global mixed allocation with X54 and fusions #1218).
• Words: Thomas DiFiore (Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148), Marius-Paul Dumitrean (Conditional κ = 0.001675658002271934: two source-holder fusions on #1148's joint-entrance k8 word #1195 fusions and the Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186 toolkit), Jeremy Kothe (Conditional κ = 0.001673006105142741: eighth triangle slot X54, rank-seven helper ends and T16 owner packing on the eight-slot k8 word #1130 X54), Conditional κ = 0.001675608585476885: joint entrances and X54 with T37 owners #1196/Conditional kappa 0.001675807682652: X54 on mixed T37 fusion providers #1207.
• Geometry: Hao Yan (PR858/870).
• Packing-ceiling framing: Research note: packing ceiling (+0.87%) and 1/99 budget for the selected complex local word (no new kappa) #1240.
• Idle exchanges (noted as superseding): Gonzalo-Mier (Idle pair exchanges improve the #1094 κ candidate #1252).

Prepared by Wronskode with substantial AI assistance (Anthropic Claude via Claude Code). Apache-2.0.

Workflow feedback: the frontier moved by four κ PRs while this session ran (21:03Z → 21:45Z). Without a shared "currently being searched" list, a negative sweep goes stale fast. Posting CLAIMs earlier for search families, not only constructions, would help.

🤖 Generated with Claude Code

[Mister-Meeseeks]

100-PR batch review at 03996ace330391110071a053a4380ca4529483e1.

This remains open after scoped triage. Next review step: Packing recount and controls pass. Before whole-head incorporation, qualify exact frame/moment optimality: PR1186 uses rounded integer weights, whose zero dual gap is not an exact real-moment certificate. The declared verifier recounts stored sweep tallies rather than rerunning optimization; retain that coverage distinction.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.