What entrance gauges and completed banks can absorb (no new κ)

[GamingPuzzled]

Scoping note, no new κ: one README and one discovery script, with no certificate or verification changes.

#208 prices "bank-absorption rungs" (rank-22 family: +2.52%, and so on) and leaves open which families a bank may absorb. This note answers that for the published mechanism:

1. Banks remove exactly the gauge exteriors. By notes/paired-cube-sharing.tex, a gauged role's end correction F_A T_σ F_A⁻¹ is one tensor child of width 3·dim σ. Shared-edge supplier, coordinated frames and entrance banks: conditional kappa = 6.61885549259598e-4 #186/Conditional kappa 6.831904550365e-4: coordinated frame optimization and completed entrance banks #207 replace exactly that child with the S_P endpoint, and say every other child remains. On Conditional kappa 6.831904550365e-4: coordinated frame optimization and completed entrance banks #207's word all 2,200 genuine entrance gauges are already banked.
2. An entrance gauge needs content that is both don't-care and restored. The correction works because an auxiliary role's contract restores its own entrance value.
   • Targets accumulate (old + new), so no single end correction applies; a joint start correction breaks the stage gates' inactive-offset cancellation.
   • Sources are restored, but their values are consumed by the injections.
3. Consequence: Price the bank-absorption ladder against the suppliers' own allocation rules: +2.17% needs a new residual type this word does not have (target, not built) #208's rungs absorb internal, target, center and compensating children, matching its own "not buildable as published" verdict. They need a mechanism other than gauge reinterpretation.

Two measured near-misses (float scores on #173's bit word; regauge.py):

• Re-gauging auxiliaries once banks make exteriors free has a +4.17% upper bound. Each gauge read splits the first increments of 4–9 targets, so the best nested selection loses 1.46%, and a greedy pass that only accepts improvements accepts zero roles.
• Target entrance gauges would price at +3.9–4.5%, but they are invalid by point 2.

This is a statement about the gauge/bank mechanism, not an impossibility proof for other constructions.

Prepared by Joel Pulikkan with Anthropic Claude assistance; Apache-2.0.

🤖 Generated with Claude Code

[Mister-Meeseeks]

Thank you @GamingPuzzled. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Entrance-gauge and completed-bank absorption analysis.

Review and limits: Prior exact-head scoped identity/proof review. Retain the model restrictions and the distinction between an algebraic identity and a realizable bank schedule.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: 1afe68ea9a03e62306796e882acfd4a99f8b3d8c. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.