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Mechanized reduction and executable parameter certificate

FPRD-T114

The concrete 1/30 reduction is admissible end to end

Exact statement

With c=1/30, Q=242, kappa=34, and tau=172, the formalized construction has output dimension at most 40 N^485 and yields Euclidean GapCVP hardness exponent 1/30 together with binary nearest-codeword and syndrome-decoding hardness exponent 1/15.

StatusMechanically checked and internally audited
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

A symbolic frontier is not yet a reduction. The concrete tuple must satisfy every finite-N field, support, reconstruction, interpolation, valuation, radius, parity, and gap-transfer obligation simultaneously.

Hypotheses and scope

  • N >= 100, q is the least power of two at least N^242, K=N^34, and T=N^172.
  • The two exceptional-loss classes receive separate q/4 budgets.
  • The exact completeness estimate uses ell+1 <= N and r^2 <= 4R <= 4Nq.

Proof or evidence

The integer-arithmetic checker passes every listed side condition. The Lean development reaches the concrete Euclidean and two binary NP-hardness endpoints, with thirteen axiom probes reporting only standard Lean axioms and no admitted proof in the modified files.

Concrete certificate →

Verification notes

The parameter audit, canonical checker output, complete constraint table, exact coefficient-16 margin, coefficient-four binary threshold, three final Lean endpoints, proof-hole scan, and pinned narrow-fork record were rechecked.

Limitations

  • The large constants affect practicality even though the construction remains polynomial time.
  • The executable end-to-end Lean reduction is instantiated at c=1/30, not uniformly at every c below 1/28.
  • This retunes and closes the parameter bookkeeping of the retained reduction; it does not introduce a new lattice-hardness method or claim external review.

Open work

Seek independent lattice-complexity review of the retuned proof interfaces and the complete Lean specialization.

Notes

The immutable Boxlab fork commit 3ac608981eb48c432e77b42b899689260351ca7d compiles GapCVP.Comparator.gapCVP30IsNPHard and the two binary endpoints through the physical polynomial-time reduction. Thirteen principal axiom probes report only propext, Classical.choice, and Quot.sound. The exact proof uses separate quarter-field loss allocation plus ell+1 <= N to obtain the strict coefficient-16 margin and carries coefficient-four binary soundness through the explicit and physical interfaces.