[Matarener]

Requested by Mark

Change and mathematical scope

This adds research/owned-centre-wire-floor/. It is a negative result for #4470's selected native word on the open question of #4534 (research/frame-aware-native). Retiming the owned C wire, which #4534's theorem allows when every C transition is paid, can neither lower the eight rank-8 centre transports nor fund #4534's rejected rank-5 merge candidate. No new κ.

• Floor (proof plus exact finite check). The model keeps the chronological scalar word, the coefficients, the warps and the helper boundaries fixed. L roles climb along nested frames, and the owned C register moves along nested frames in either direction, priced at |Δdim|. In this model, every centre block's C wire pays rank mass ≥ 8, in both orientations, which equals the current single rank-8 job. The proof combines two lemmas:

  • interval propagation of the lowest and highest legal chart of every scalar contact;
  • a path lemma: nested moves g_0 → … → g_n cost at least dim g_0 − dim(g_0 ∩ … ∩ g_n).

  In all 16 block-orientations, the source contact is forced into a frame of dimension 8, and the 22 targets' upper frames meet it in 0. A single target alone gives only 7, and at most 8 of the 22 targets share any nonzero line.

• Rejected candidate. On Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries #4470's complete invoice, 56 rank-1 + 56 rank-4 → 56 rank-5 jobs per full call raises the certified raw root from 0.0030201659 to 0.0030511780 (+1.03%). A net C charge between 0.42 and 0.43 rank-1 jobs per full call cancels this, and by the floor the C wire has no mass to give back.

• Bounded search (evidence only). A joint frame-retiming search with C contacts as variables, run in two unit models, covered all units, adjacent pairs and connected triples (about 95k and 108k moves) plus about 3.5 M annealing steps. It found 0 improving moves.

Remaining obligations, which are not covered: non-nested C transitions priced by their exact Clifford rank, changed scalar orders or warps, and joint moves of helper entrances and exits.

Task and overlap

Base: canonical main 4c0a359d88f22f05189d51f48387750b801a45d4. Card complex-new-helper-inventory (priority revision 7), scope changed. No helper inventory is built. The package closes the one new degree of freedom (owned-C retiming) that #4534 added to the fixed-inventory search space.

Nearest work: #4534 (retiming theorem and the rejected candidate) and #4539/#4540/#4549 (its noncommuting-stage question, a different part). #4470/#4447 are the native word and invoice. Earlier centre floors (PR968 decoders, #4417 nonlinear fresh observations) are about centre readout and not about chart retiming. This package does not duplicate them.

Validation

python3.12 -B scripts/research_package.py --package research/owned-centre-wire-floor --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/owned-centre-wire-floor
  PASS_REGISTERED_RESEARCH_PACKAGE research/owned-centre-wire-floor outcome=negative-result   (~9 s, stdlib only)

Run on Windows 10 with Python 3.12. No Linux run is claimed. verify.py checks the following:

• it rebuilds Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries #4470's word with joint-helper-lattice/native_joint.py and recovers {1:2237,2:388,3:494,4:147,5:36,8:8} from contact charts in both orientations;
• it checks the centre structure: 8 blocks, 22 targets and one rank-8 transport each;
• it checks propagation consistency at every contact and the floor in all 16 cases;
• it certifies raw roots with mixed_target_probe's interval series;
• it checks that RESULT.json is reproduced exactly.

Controls:

• the single-target bound of 7 and the 8-of-22 line count;
• a corrupted frame, which the propagation must reject;
• one extra rank-8 transport per call, which must lower the root.

The search script (search/cwire_joint.py) is evidence only. The registered replay does not run it.

Credit

Dugongue's #4534 owned-C retiming theorem and rejected candidate. Cinna Davis's #4470/#4440/#4441/#4447 native word and invoice, with zxv's native supplier and the retained scalar, Clifford, geometry and outer-ledger lineage. The interval engine comes from research/kappa-rebuild/architecture/mixed_target_probe.py. Prepared by Matarener with substantial Claude Code assistance. Apache-2.0.

Open next questions

1. Can a non-nested owned-C transition, priced by its exact Clifford rank, beat the nested floor of 8 per block? This is the only part of Frame-aware native construction lemmas and exact p16 certificates (no new κ) #4534's lemma that is not covered here.
2. Can helper entrances and exits move jointly with the C-contact charts? Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries #4470's own gain came from such joint helper moves.

🤖 Generated with Claude Code