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Bound retained backing across the selected complex and BIT backend stack with history-safe stock reserves - #7151
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…lls and complete stock histories
This was referenced Nov 11, 2026
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Exact result and novelty
A per-tape finite-stage Bellman certificate M_i=max(c_i/(1-rho_i), c_i+a_ij M_j) bounds retained backing across the selected complex/BIT backend stack, including suspended parents, erased tails, and full stock reservations. A symbolic stock-boundary counterexample blocks replacing the full stock envelope by endpoint-only stock. This composes but does not reprove the underlying backends of #7000/#7001.
Reproduction and independent checks
Independent descending-path review, 1,068 certificates, 4,920 paths and negative controls. Replay: python3 -B scripts/research_package.py --package research/stratified-owned-reserves
Limitations and bound status
No new kappa. Local per-tape physical coefficients, completed selected B0 implementation and overall supplier admission remain premises. Selected conditional kappa remains 0.00363005817; the five framework assumptions remain.
Attribution
Prepared for @CubeJerry with substantial OpenAI assistance; credit #7000, #7001, #6879 and inherited source owners.
Complete review packet
Full PR description, proof and source pins
Base:
e54523517d0f03e58352e647c403a5af3e525a57. No upstream PR is opened by this link.