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Prove uniform precision-depth bounds and a stronger low-precision range - #80

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GoGoKo699 merged 1 commit into
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research/uniform-precision-depth
Oct 3, 2026
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GoGoKo699 merged 1 commit into
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research/uniform-precision-depth

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@GoGoKo699 GoGoKo699 commented Oct 3, 2026 •

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The fixed-accuracy blocked-query theorem hides precision-dependent constants. Its balanced indicator allocation also loses a square root of word precision in the count ledger.

This change proves absolute-constant same-circuit bounds for every L ≥ 6 and b ≥ 17(L+n+7), using two clean flags:

  • T = O(sqrt(NL) + NL/b + nL), G = O(NL), and T-depth = O(NL/b² + nL).
  • For 6 ≤ L ≤ log₂(n+2)/16, the sharper bounds are T = O(sqrt(NL) + NL/b) and T-depth = O(NL/b² + n).
  • The corresponding simultaneous matching intervals end at sqrt(N/n) and sqrt(NL/n), when nonempty.

The proof uses rectangular dimensions for the existing exact query, exposes the unary-source cutoff uniformly, and uses the existing hybrid at larger precision. Native circuit identities, full initialized-isometry error, dirty/reference return, charged preparation and actual inverses are preserved. The original width threshold is unchanged.

Five new exact allocation checks cover 15,024 bounded tuples, rounding boundaries, asymmetric addresses, Q < m, and the helper-free one-row query. They test resource interfaces; the asymptotic proof remains analytic. No scalable native frame emitter or unrestricted depth lower bound is claimed. The high-precision constant-clean endpoint remains open.

Validation: focused presentation/provenance checks and the new allocation checks pass; the walkthrough, all native examples, all four exact fault-tolerant receipt suites, offline upstream verification and resource ledgers pass. All 476 regression tests pass locally and on CI Python 3.11 and 3.13. All five head checks are green, including rendered presentation; CI also reproduces all four exact fault-tolerant receipt suites. Independent proof audits found no blocking issue.

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GoGoKo699 merged commit 7a3fc01 into main Oct 3, 2026
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