Independently check the seven-owner centre-repair Fano exclusion

[Sudarsh3301]

Base: canonical main 997e6a9ca7b4f95d50e366f61412fd640d72a88a, priority revision 6. Card: independent-moment (scope refined).

What this adds

#3097 (research/centre-seven-owner-information-floor) excludes kernel vectors supported on exactly 7 owners in the selected PR1094 centre-repair model. With the support ≥ 7 result from #3071, the repair floor stays at 104 observations per owner for blocks of at most 7 owners. #3097 was archived on 2026-10-16 without a scientific replay, and Discussion #3062 has no independent check of it. This PR adds a second implementation:

• Routes: the 112 routes come from the chart-swap derivation in centre-block-repair-information/independent.py. Research: rule out seven-owner centre information compression #3097 uses the forward-interpreter path.
• Relation census: recomputed on the exact 17×17 active block, with exact dict keys; the identity spectator block is checked. It matches Research: rule out seven-owner centre information compression #3097's receipt: class histogram {1: 1,379,852, 2: 50} and the same 50 braid edges. Every relation word is multiplied out and gives the identity.
• Written steps replaced by exhaustive search:
  1. The only 7-point line families with line size ≥ 3, pair multiplicity ≤ 1 and point degree ≥ 3 are the 30 labelled Fano planes.
  2. No route labelling of the 21 Fano flags (labels distinct per owner and per line) makes all 28 six-cycle words into relations. This search does not use the braid or triangle-free structure.
• Controls:
  • A Fano labelling planted in Z2^4 is recovered from its own cycle words.
  • The same labelling is rejected once one relation class is removed.
  • Changing a 7-point structure condition changes the structure count.

Outcome: the audited claim reproduces. No new κ, supplier or selected-frontier change.

Reproduce

python3 -I -B research/centre-seven-owner-fano-independent/verify.py
python3.12 scripts/research_package.py --package research/centre-seven-owner-fano-independent

The check takes about 30 s on CPython 3.12 or 3.13 and uses only the standard library. Expected marker: PASS_CENTRE_SEVEN_OWNER_FANO_INDEPENDENT. On the same host, #3097's own verify.py also passed, in about 60 s.

Review and scope

A separate agent reviewed the checker adversarially:

• Verified: the six-cycle word orientation, the justification of each necessary condition, the exactness of the 17×17 restriction, and pruning soundness.
• Faithfulness: a non-faithful matrix representation could only make the check more conservative.
• Fixed: the reviewer flagged the original free-relation control as vacuous, and the planted control replaces it.

Inherited and not rechecked: the support ≥ 7 argument and its column premises, the observation model, and the physical acquisition and restoration costs. The two route derivations come from the same AI-assisted lineage; they are separate code paths, not separate human review.

Overlap

Open #3147 (dcharb78, head 5cbc48b) claims a block floor for blocks of up to 12 owners and also recounts the 50 braid relations. This PR does not depend on #3147 and does not review it. #3149/#3151 audited #3147's circle-cancellation part only, so #3147's block floor for 8 to 12 owners is recorded here as the open next question.

Credit

• The audited claim and the Fano argument: Gonzalo-Mier (Research: rule out seven-owner centre information compression #3097).
• The route interface and the support ≥ 7 theorem: centre-block-repair-information (Ross Richardson, Prove sharp selected-centre repair dimension for owner blocks up to six #3071; Aaron Wang/navinor, PR2391).
• The R/H data: ywz65's centre-owner-observation-floor.

Prepared by Sudarsh Chaturvedi with assistance from Claude (Anthropic). Apache-2.0.