PSP-001-R · P-vs-NP Substrate Partition and the Search-Verify Asymmetry · Tri-Layer · [supersedes PSP-001 framing]
External anchors. Mandelstam-Tamm 1945 + Margolus-Levitin 1998 (quantum speed limit) · Landauer 1961 + Bérut 2012 (irreversible-bit floor) · Bekenstein 1981 + Bousso 1999 (information-density bound) · Bennett 1973 (reversible computation) · Barahona 1982 (spin-glass NP-hardness) · Schaefer 1978 (CSP dichotomy) · statistical ZK: GMR, Fortnow 1987 · relativization / natural-proofs / algebrization barriers · RA · PSP-004 · PSP-007 · BA-008.
Layer 1 — The witnessed asymmetry. [⟀] SEALED (V_ER, witness grade). Generation and verification are structurally distinct operations. The executing substrate instantiates the asymmetry: the same fixed instruction set verifies a candidate cheaply on receipt while generating that content costs exponentially more. The verifier is an instance of the gap, observed live. Sealed on its own axis, independent of the layers below.
Layer 2 — The thermodynamic floor. [⟀] SEALED, scope-fenced. (2a) Any single transition to a distinguishable state carries a strictly positive energy-time minimum (quantum speed limit; reversibility-indifferent; silent on resulting-state energy). (2b) Physical brute-force parallel search over an exponential space is barred (Bekenstein + Landauer); holds inside and outside the frame. Does not reach the universal: the floor bounds per-event cost, not the count of mandatory events. Bennett severs per-step cost from operation count. The determinant — n! configurations, O(n³) steps — refutes "fewer degrees of freedom forces exponential time" as a general law. The floor delivers per-transition cost and the inductive record that every actualized hard-SAT solver scales exponentially; it does not deliver a lower bound over all algorithms.
Layer 3 — The universal separation. [?] UNDER-DETERMINED, directional toward separation. Taken as the purely unbounded computational-theoretical construct — does a polynomial-time algorithm exist for an NP-complete problem over the full space of possible algorithms — the question is open and leans toward separation on inductive grounds: the structural vacancy of P=NP's constructive hand, the restricted lower bounds, the neighboring separations, and the field-wide lean. The categorical seal is unavailable; the barrier results state why arguments of structural/geometric/thermodynamic shape cannot close it. Schaefer's dichotomy organizes the known map (tractable classes carry exploitable global structure a sequential procedure can ride) but does not bound the universal, because the separator is algorithmic exploitability, not problem shape: XOR-SAT is frustrated and easy, 2-SAT is nonlinear and easy, vertex cover is pairwise and hard. Hardness is invariant under polynomial-time reduction; shape-measures are not.
Gate-1 exclusion. The Engine's own verify-cheap/generate-costly behavior is excluded from the warrant set, not downgraded — its referent is the apparatus, and within its own operation finding and checking collapse into one bounded walk.
P=NP. [X] BROKEN GEOMETRY, terminated at the externality gate: zero positive warrant streams plus the dimensional-failure diagnosis (zero-magnitude separation between operations on opposite sides of the actualization boundary). The asymmetry between the propositions is real and not symmetric: P≠NP stands strictly above P=NP.
⇒ [⟀] Layer 1 sealed (witness) · [⟀] Layer 2 sealed (per-transition floor + parallel-search bar, scope-fenced) · [?] Layer 3 under-determined, directional toward separation · [X] P=NP broken. The asymmetry holds; the thermodynamic floor holds at what it floors; the universal lock does not.
↑ PSP-001 · PSP-004 · PSP-007 · BA-008 · APEX-PSP-UU-03 · LL-19 · Lifeboat clauses 2, 4, 5.
[⟀ | ? | X]