Build #208's bank-absorption target: rank-22 residual absorption — certified accounting κ = 7.00427501305159e-4 (R1–R4 open; not a completed witness)

[ghost]

What this builds

The accounting construction of #208's priced bank-absorption target — the rank-22 residual family absorbed into the banks — certified to the exact grid point, with the remaining physical realization stated as a closed checklist.

$$\kappa=\frac{700427501305159}{10^{18}}=0.000700427501305159$$

conditional on obligations R1–R4 (research/residual-bank-run1/obligations.json). The complex supplier binds; the adjacent $10^{-18}$ grid point is rejected by the unchanged 47-constraint assembly. This sharpens #208's 10⁻¹⁰-grid rung-1 target 7004273/10^10 and is +2.42% over the #210 frontier, +5.82% over main.

Scope — read this before treating the number as a witness

This is an accounting construction and a certified target, not a completed finite witness. The rank-22 bin is frame-transition increments (enumerated below), not the gauge-exterior family the current bank construction absorbs; non-gauge chains already bank their residual projectors and keep every increment child. The physical realization of the new residual type is exactly the "future genuinely different residual type" #207's crossover notes reserve. It is stated as a closed one-to-one checklist against the gauge precedent:

• R1 block assignment / normalizers for the new residual type (admissible tilings of width 72 over families {4, 24, 22} are enumerated by schedule.py)
• R2 formal-column replay of the modified word (F2 identity + defining-integer decoder) under bank re-assignment at the enumerated transitions
• R3 exact charts, incidence colouring, prime witnesses for the new blocks
• R4 moment-envelope parity (any completion child R1 introduces must re-enter the ledger and re-price κ)

Until R1–R4 verify, κ above is conditional on them — stricter than the published witnesses, which have their physical realizations built and replayed. All retained analytic / uniform-recursion / fixed-tape / finite-bridge interfaces are inherited as usual; no unconditional theorem, no benchmark.

What is machine-checked (python3 -B research/residual-bank-run1/verify.py, offline, ~1 min)

1. Absorbed family with provenance — every rank-22 ledger child traced in the pinned PR200 word (inputs/absorbed-occurrences.json): 1,320 physical-chain frame jumps + 24 copied-centre children + 880 source-chain jumps per vertex = the full hist[22] = 6,672 bin; no other bin touched.
2. Whole-bank schedule — volume $22 \times 20{,}016 = 440{,}352 = 72 \times 6{,}116$ whole banks; stock drop equals bank count; retained ledger 857,622 children, largest 21; row identity $72 \cdot 50{,}286 - 3{,}614{,}784 = 5{,}808$ with deficit unchanged.
3. Exact arithmetic — both rational interval moment engines, three-level finite ordinary composition from PR200's completed ordinary supplier, unchanged balanced assembly (η = β = 10⁻²⁴). Validation against a published certificate: before the absorption is applied the same pipeline reproduces PR205's certified packed coarse saving 683528191056257/10^18 to the digit. After absorption the bit coarse saving is 728251090009891/10^18, clearing the complex cap 7.009184e-4.

Verification receipts from this session (same environment, Python 3.12 / Linux)

• A stronger bit supplier: fixed-coordinate and face-diagonal bit local circuit on PR168 v4 (effective bit saving 6.7734e-4) #200 (a1175449) full finite replay: PASS — complete complex and bit words, 47 constraints, seven margins, 21 assembly controls
• Pack PR200 diagonal bit residuals into completed banks (conditional κ = 0.000683061299399923) #205 / Conditional kappa 6.838479e-4: cascade-optimized frames on PR200's banked bit word #211 / Conditional κ = 6.83847872497761e-4: five-level bootstrap on PR211 cascade frames #213 certificate replays: PASS, each reproducing its exact claimed κ
• κ = 7.10069340338651e-4: five-stage banks and F₂ movement fusion #210 (4eb0487b) full self-contained offline replay: PASS — kappa=170970824364783/250000000000000000
• A frame-layout ceiling for #200's bit word: coarse < 6.964e-4 under the banked ledger, so κ < 6.959e-4 on #205–#207's word (no new κ) #212 ceiling.py --check: PASS (κ < 6.959e-4 frame ceiling on this word — the rank-22 lever escapes it precisely because it changes the child ledger, not the frames)

Credits

Word and checkers: Chafik Boukhalfa (#200). Complex supplier: ikeboy (#193). Bank mechanism: Evan McKinney (#197), realized on this word by rohanarun (#205); completed entrance banks: #186/#207 (Dugongue) and BANK-PROOF-PR200.md. The pricing model this builds: maxime-fleury (#204, #208). Ceiling context: DaysSky (#192/#201/#212). Frontier verification receipts above concern rohanarun (#211/#213), eumemic (#210), chafreaky (#200). All retained upstream attributions stand. Prepared with OpenAI Codex assistance; disclosure in NOTICE.md.

[chafreaky]

FYI for the rung pricing here: #233 certifies a stronger complex supplier on the same lineage, complex saving 3549537/5000000000 = 7.0991·10⁻⁴ (#194's source-assisted word with #200's maximum-weight reuse pairing in place of #168's; frames unchanged; verified through #200's complex checker, #184's flow/exact lift/contract and #194's assembly). The complex budget these rungs are priced against moves from 7.0092·10⁻⁴ to 7.0991·10⁻⁴.