GATE D22

Implicit global-signature elimination

partialEvidence I2Verify: doublePublic claim: No2026-07-19

What changed

D21-S showed that writing down the complete family of starting fingerprints is astronomically large, but that only blocks the two explicit ways to materialize it, not every method. The product of the per-prime fingerprint sets is not a state space anyone must build; constraints linking the primes can rule out most states before they are ever generated. D22 reverses the order once more. Instead of listing all starting fingerprints and then filtering, it keeps the unknown bounded object as symbols, projects it onto one prime at a time, asks the fast narrowed local feasibility question, and cuts away impossible states with a proof for every cut. Two symbolic pictures are piloted in parallel: a coefficient master carrying the symmetric functions of the squared speeds, and a root master carrying the squared speeds themselves. Each local subproblem returns a match witness, a certified empty, or an honest open, and every pruning cut must carry a theorem and a proof hash, so nothing is discarded without justification. No compute budget increase is authorized, and nothing about the conjecture is decided by opening this gate. LRC(13) remains open.

Evidence

check 1Do NOT materialize the initial signature family; keep the bounded global object symbolic while prime constraints are added incrementally. Two master representations piloted in parallel: coefficient master on E_j = e_j(V_i^2), root master on X_i = V_i^2

check 2Loop: project the symbolic state to each prime, ask the narrowed local feasibility subproblem returning MATCH-WITNESS / EMPTY-CERTIFIED / OPEN-INCOMPLETE, then generate an exact cut. Every pruning cut must carry a theorem and a proof hash

check 3D22-PARTIAL (measured): one-way soundness proved (a counterexample survives every certified cut) and two verifiers plus 179 of 179 corruption accept the engine, BUT cross-prime CRT compatibility alone prunes nothing, so with a global check only at the reconstruction threshold the implicit master still grows as the product of local signature counts, the same wall as D21-S. Cuts close the impossible regions; the compatible-unreconstructed bulk stays open. The frontier moves to D23 early cuts. LRC(13) OPEN

Verification: double · I2 · 8 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)

Graph impact

introducedC-D22-IMPLICIT-STATEProved (internal)introducedC-D22-PILOTValidated (bounded)introducedC-D22-CRT-NO-PRUNINGSupported (internal)changedC-D21-SEED-BLOCKEDSupported (internal)

← All gates