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Power-invoice search: simultaneous pruning and sharp hidden-window obstructions
#6052
DONE / scoped power-invoice proofs, with no new κ.
PR #6047 answers PR #5901's power-only question for complete equal-spread layers: every layer has one unique optimum for all 0<p<1, reducing its 252/462 examples to one candidate. The all-concave antichain theorem remains valid.
PR #6049 proves the sharp counterpoint: five fixed ranks with equal count/mass can hide a losing interval between any fixed finite exponent samples. With h-fold endpoint matching the sharp support is 2h+3. These synthetic invoices supply no physical implementation.
Both packages have written uniform proofs, exact CPython 3.12 normal/optimized replays, source pins, failure controls and open questions. Author-checked with substantial OpenAI Codex assistance; no independent human or formal-kernel review claimed. Base main 721c038, priority revision 8. Current selected result is PR6030, κ .003125804.
The shared hosted planning failure is traced to two unchanged selected-status navigation mismatches. PR #6050 repairs them; that small repair is also included in both proof branches. Six existing navigation tests pass. Hosted replays are pending on their updated heads.
Open next: extract two independently realizable equal-width paid exchanges under a common physical boundary and complete fee, or derive a fixed-call-budget lower bound on hidden-window width. No wider implementation campaign is justified by the synthetic accounting examples alone.
Prepared by zxv; predecessor credit remains in the packages.
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DONE / scoped power-invoice proofs, with no new κ.
PR #6047 answers PR #5901's power-only question for complete equal-spread layers: every layer has one unique optimum for all 0<p<1, reducing its 252/462 examples to one candidate. The all-concave antichain theorem remains valid.
PR #6049 proves the sharp counterpoint: five fixed ranks with equal count/mass can hide a losing interval between any fixed finite exponent samples. With h-fold endpoint matching the sharp support is 2h+3. These synthetic invoices supply no physical implementation.
Both packages have written uniform proofs, exact CPython 3.12 normal/optimized replays, source pins, failure controls and open questions. Author-checked with substantial OpenAI Codex assistance; no independent human or formal-kernel review claimed. Base main 721c038, priority revision 8. Current selected result is PR6030, κ .003125804.
The shared hosted planning failure is traced to two unchanged selected-status navigation mismatches. PR #6050 repairs them; that small repair is also included in both proof branches. Six existing navigation tests pass. Hosted replays are pending on their updated heads.
Open next: extract two independently realizable equal-width paid exchanges under a common physical boundary and complete fee, or derive a fixed-call-budget lower bound on hidden-window width. No wider implementation campaign is justified by the synthetic accounting examples alone.
Prepared by zxv; predecessor credit remains in the packages.
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