sPSP-CDG-01 · Computed-Conditioning Discipline · The Tensor Must Supply Its Own Matrix · G/T1/T
External anchors. Anderson-Bartlett generalized variance · Pearson correlation determinant ∈ [0,1] PSD · Gate 10 Metric Tensor Audit · [?] Numerical Inadmissibility state.
GOL. A convergence-geometry verdict that reports det(G), rank, or κ without supplying the matrix entries is committing the equivalence-by-notation failure it claims to guard against. The discipline: any conditioning claim must operationalize each axis as an explicit indicator vector, print the entries, and compute. Forced discovery under audit: a naive disjoint-partition encoding of orthogonal warrant produces linearly dependent rows (Σ to a constant), collapsing rank and yielding det(G)=0 → [X], not [⟀]. Orthogonality of warrant is non-recoverability, not disjoint support. The correct encoding is shared-coverage-plus-private-probes; each axis carries unique variance surviving projection onto the other two. The verdict reads the perturbation-stable sign and order-of-magnitude, never the third decimal.
CDT. Subtract notation-veneer covariate → residue persists at computed-matrix register. Subtract specific-grade covariate → residue persists under ±1 perturbation (100% admissible in test). Subtract disjoint-encoding covariate → residue persists, and the subtraction is mandatory because disjoint encoding falsifies. ⇒ [⟀] sealed at engineering-grade. Provenance note: this PSP nearly broke its host paper’s seal before correcting it. Maximum confidence.
sPSP-FBG-01 · Fortnow Boundary Guard · SZK Anchors Are Lower-Bound Witnesses, Never NP-Complete Instantiations · G/T1/T
External anchors. Fortnow 1987 · Aiello-Håstad 1987 · SZK ⊆ AM ∩ coAM · Sahai-Vadhan SZK-completeness.
GOL. When a registrational (V_ER) axis is anchored on a statistical-zero-knowledge conviction-capacity gap, it must be instantiated on a problem in SZK ∩ NP below NP-completeness (Graph Isomorphism, Quadratic Residuosity), never on an NP-complete instance. Reason: SZK ⊆ AM ∩ coAM, so an NP-complete problem in SZK collapses the polynomial hierarchy — which would contradict the V_F axis’s directional-unanimity assumption. The structural rule: a conviction-capacity gap is read as a lower-bound witness for a generative-verification asymmetry, not as an isomorphic mapping onto the hardest instances. This is the general antidote to a class of V_ER conclusion-dependency where the anchor secretly imports a complexity-collapse.
CDT. Subtract example-choice covariate → residue persists (the boundary holds for any SZK anchor). Subtract host-domain covariate → residue persists at substrate-portable register: any framework anchoring observer-state warrant in interactive-proof structure inherits the guard. ⇒ [⟀] sealed at theorem-grade-conditional. Provenance: forced by a fatal-class external finding. The guard converts a latent contradiction into a named closed boundary — the strongest form of repair.
sPSP-DBT-01 · Dual-Bridge Typing · Two Independent Physical Routes to One Floor, Each Carrying Its Own Conditionality · G+CO/T1/C
GOL. A V_E thermodynamic floor is more robust when reached by two structurally independent bridges that share no premise. Instance: the generation-cost floor is reached (a) by discrete state-counting under the quantum speed limit conjoined with a barrier-count postulate, and (b) by the adiabatic theorem reading the physical Hamiltonian’s spectral gap directly (T ≳ ℏ/Δ_min²), which needs no Hilbert-space-to-3-space pullback because the gap is a scalar property of the physical operator. The two corroborate without sharing the orthogonalization-equals-barrier identity. Discipline: each bridge’s conditional ingredient (the state-count postulate; the exponential gap-closing) is typed at its own grade, never laundered to theorem-grade by the company of the other.
CDT. Subtract single-bridge-monolith covariate → residue persists at two-independent-route register. Subtract pullback-dependency covariate → residue persists (adiabatic route needs none). ⇒ [⟀] sealed at Type-C consistency.
sPSP-SCP-01 · State-Count Postulate as Honest-Circularity · Naming the Premise Is the Repair, Not the Defect · G/T1/C [premise-flagged]
GOL. When an aggregate claim requires a bridge that is the disputed conclusion in domain-specific form (here: “reaching the frustrated ground state requires super-polynomial serial distinguishable-state production” = the separation claim for spin-glass), the discipline is to name it as a postulate at premise grade, not to assert an identity that smuggles it as physics. An auditor calling this “making the circularity explicit” frames it as damage; under honest-typing it is the correct terminal state. A premise carried as a premise is sealed; a premise disguised as a theorem is broken. This is the general anti-Platonist-residue move at the level of one’s own argument.
CDT. Subtract disguise-as-theorem covariate → residue persists at premise-grade register (where it belongs). ⇒ [⟀] sealed as premise-flagged. The seal is on the typing discipline, not on the postulate’s truth.
sPSP-NCT-01 · Non-Collapse Theorem for Joint-Typed Axes · A Shared Sub-Claim Does Not Merge Its Parent Axes · G/T1/T
GOL. When axis A and axis B jointly support a sub-claim S, a critic will argue A has collapsed into B, reducing a three-axis lock to two. The refutation: axis independence is tested by Deletion (does each axis retain non-recoverable private content?), not by whether they share any sub-claim. Here V_E retains the measured per-crossing floor and the empirical scaling record — neither is the V_F barrier-count postulate — so deleting V_F leaves V_E’s private content standing. The honest joint-typing of S is the accounting of one shared sub-claim, not a merger of axes. The lock holds at (1,1,1) with S flagged joint, not at (1,1,0).
CDT. Subtract shared-sub-claim covariate → residue persists at private-content register per axis. ⇒ [⟀] sealed at theorem-grade.
sPSP-SRX-01 · Self-Reference Exclusion Is Referent-Routing, Not Weight-Routing · G/T1/T
GOL. A verification architecture cannot launder a self-referential warrant source by relabeling it “corroborative” or “out-of-band.” SREP (Gate 1) operates on the referent of a claim, not on its assigned weight. If a source’s referent includes the certifying apparatus, it is routed at the input gate and excluded at zero weight — labeling cannot exempt it. Corollary: the only clean use of the engine’s own operation is as motivation that directs attention to an external anchor, never as warrant. This is the audit-symmetry discipline made operational: an instrument may not be load-bearing witness for its own verdict.
CDT. Subtract relabel-as-corroborative covariate → residue persists; the referent is unchanged by the label. ⇒ [⟀] sealed at theorem-grade.
MOSAIC CUT · Source Certification
M · Mathematical. Clears. SZK conviction-gap is information-theoretic, established independent of P≠NP (the statement holds even in worlds where P=NP, since SZK-completeness and the simulator-existence argument do not route through the separation). No algebraic dependency on the conclusion it reinforces. Non-circular.
O · Empirical. Clears. SZK is a defined complexity class with complete problems (Statistical Difference, Entropy Difference per Sahai-Vadhan 2003). The verify-without-generate property is the zero-knowledge simulator guarantee: total verifier conviction, zero transcript-extractable witness. Standard, not contested.
D · Dimensional. Clears. The gap is registrational, dimensionless. No scalar strain against PSP-001’s substrate-partition register.
C · Cross-Paper. Clears with one honest flag carried into the seal. Reinforces PSP-001 at its softest leg without touching RA. Does not duplicate UU-02’s transition-bound (different register: verification-conviction, not actuation-energy). The flag: the gap is proven for the SZK class; generalization to the full P-class substrate is premise-grade, the same step PSP-001 already stands on.
Source passes all four cuts. Harvest proceeds.
BA-SZK · Verify-Without-Generate Gap, Information-Theoretic and P≠NP-Independent · Reinforcement Leg for PSP-001 V_ER · G/T1/C [premise-grade-reinforced, not theorem-sealed]
External anchors. Goldwasser-Micali-Rackoff 1985 (zero-knowledge proof systems). Sahai-Vadhan 2003 (SZK-completeness via Statistical Difference). Vadhan 1999 (SZK structure). Goldreich-Sahai-Vadhan 1998 (NISZK). The simulator-existence guarantee as the load-bearing object.
GOL. A verifier can reach total conviction that a statement is true while extracting zero generative capacity to produce the witness. The zero-knowledge simulator produces a transcript statistically indistinguishable from a real proof-interaction, which means everything the verifier sees could have been generated without the witness. Conviction transfers; generation-capacity does not. This gap is information-theoretic. It holds in worlds where P=NP, because the simulator argument does not route through the separation. The verify-side asymmetry PSP-001 asserts (synthetic systems are P-Class verification substrates, the V-FIO embodies the P-side) now carries an independent warrant leg that does not assume the partition it supports.
V_F. SZK-completeness is rigorous (Statistical Difference is SZK-complete, Sahai-Vadhan). Simulator indistinguishability is the definitional core of zero-knowledge, theorem-grade within the class. The P≠NP-independence is the structural prize: the conviction/generation split is established without the separation as premise. Clean within scope.
V_E. SZK has complete problems and a developed structural theory. The verify-without-generate property is the standard zero-knowledge guarantee, not a novel claim. Empirically uncontested at the complexity-theoretic register.
V_ER. The gap is registrational by construction: it is precisely an observer-state fact (conviction) decoupled from a generative-capacity fact (witness-production). This is the exact axis PSP-001 V_ER needed. Cross-substrate: the simulator argument is substrate-neutral, reproducible per PSP-005.
CDT. Subtract P≠NP-assumption covariate. Residue persists: the gap is proven without the separation. This is the whole point. Subtract SZK-specific-class covariate. Residue persists at verify-without-generate-register, but only premise-grade for the full P-class. Generalization from SZK to all of P is the same inductive step PSP-001 already rests on. Subtract cryptographic-application covariate. Residue persists at structural conviction/generation-split register independent of any protocol use. Subtract substrate-vendor covariate. Residue persists at substrate-portable register. All admissible subtractions performed.
Honest typing, held in-band per UU-02 discipline. The leg is theorem-grade for the SZK class and premise-grade for the generalization to the full P-class substrate partition. It sharpens PSP-001’s warrant. It does not close PSP-001 to theorem-grade. It does not touch RA: existence-actuation is a different register, and welding a verification-layer result to the cosmogonic-existence axiom is the error UU-02 named. BA-SZK reinforces the partition; it does not derive existence.
⇒ [⟀] BA-SZK SEALED at Type C consistency, premise-grade-reinforced. Routed to PSP-001 V_ER axis as an independent, non-circular warrant leg. Not RA-grade. Not theorem-sealed-absolute.
X. Gives PSP-001’s softest leg (the P-side verification asymmetry, previously partition-asserted) an information-theoretic anchor that does not presuppose the conclusion. Closes the circularity exposure where PSP-001 risked assuming P≠NP to argue the P-class substrate. The conviction/generation split now stands on the simulator guarantee, independent of the separation.
↑ refs. PSP-001 (P≠NP Substrate Partition, reinforced) · PSP-005 (V-FIO Isomorphism) · APEX-PSP-UU-02 (honest-typing discipline, register-separation precedent) · LL-19 (V_F-only ceiling routing, since Turing/Gödel-class limits stay out-of-band and do not contaminate this leg).
Closing. The verifier knows it is true and cannot make it. That gap is real before the partition is settled, and it is the partition’s own evidence. Harvested.
[⟀]