NP Program

Research corpus and governance workspace for P vs NP, proof complexity, lawful morphology, closure, monodromy, renormalized defect, and Stokes / wall-crossing data.

Status

This repository does not claim P = NP, P != NP, or a solution to any Clay problem. It codifies the discipline P vs NP imposes on our proof, agent, search, and trust infrastructure: verification and generation are different operations; evidence must carry morphology; lower-bound claims require barrier analysis; empirical claims require tranche and distribution metadata.

The current framework claim is narrower and constructive: lawful mathematical artifacts can be studied through a singular-germ regime stack — exact closure, monodromy residue, renormalized finite defect, and Stokes / wall-crossing data — with explicit basis, provenance, and stage discipline.

Current lanes

1. Doctrine. Lawful Morphology Doctrine: the methodological constitution for proof, witness, agent-plan, hyperedge, attestation, and empirical-record morphologies.
2. Singular geometry. Singular germs as the unifying home for scale, phase, finite-part, and wall-crossing data.
3. Proof dynamics. Conditional bridge from proof-character generating functions to monodromy/Floquet signatures, with the p = 2 obstruction as first implementation target.
4. Gate minimality. Theorem target for making the SO(3) / Spin(3) gate realization canonical in the half-integer case.
5. Polarization compatibility. The load-bearing condition tying the singular-germ pairing to the active constraint complex.
6. Empirical observables. Proof-character and certificate-discovery generating functions over declared corpora, augmented with Stokes / chamber signatures.
7. Scope control. Singularity-class taxonomy restricting base claims to algebraic isolated singularities unless an extension is declared.
8. Barrier registry. Relativization, natural proofs, algebrization, and program-specific analogs attached to every lower-bound-shaped claim.
9. Implementation target. Catalan/square-root mu_2 toy protocol: encode, ledger, recompute monodromy, verify Spin lift, and check committed Stokes normalization.

Repository map

docs/
  conventions/
    stokes.md
  doctrine/
    lawful-morphology-doctrine.md
  research/
    proof-dynamics-bridge.md
    singular-germ-regime-decomposition.md
    gate-minimality-theorem-target.md
    polarization-compatibility.md
  scope/
    singularity-classes.md
  barriers/
specs/
  catalan-mu2-reference-implementation.md
experiments/
ledgers/

Claim discipline

Permitted:

• measuring proof and certificate morphologies;
• separating verifier cost from generator cost;
• defining basis-relative generating functions;
• building tranche-conditioned empirical registries;
• treating singular germs as the organizing object for the four-regime decomposition inside declared scope;
• implementing falsifiable toy protocols such as the Catalan p = 2 monodromy test.

Forbidden:

• claiming P vs NP movement without a formal separation or algorithm;
• claiming agentic search bypasses complexity barriers;
• claiming full canonicity of the SO(3) gate target before the gate-minimality theorem is proved;
• comparing proof lengths across bases without a translation cost;
• reporting empirical solver performance without input distribution and tranche;
• treating cryptographic hardness as a metaphysical guarantee;
• treating convention-dependent Stokes constants as intrinsic outside a committed normalization;
• extending the Milnor-fiber argument beyond algebraic isolated singularities without declaring an extension theory.

Seed documents

• docs/doctrine/lawful-morphology-doctrine.md
• docs/research/proof-dynamics-bridge.md
• docs/research/singular-germ-regime-decomposition.md
• docs/research/gate-minimality-theorem-target.md
• docs/research/polarization-compatibility.md
• docs/conventions/stokes.md
• docs/scope/singularity-classes.md
• specs/catalan-mu2-reference-implementation.md