APEX-PSP-PNP-01 · The Embodied Search-Verify Asymmetry, Fortified · Tri-Layer Determination on the Stratified Physical Floor · Reflective Diagnosis Corrected · G+CO/T0/witness-grade on the embodied asymmetry, T-as-physics on the floor, [?] under-determined on the universal (directional), [X] on thermodynamic generation-verification equivalence [causal reading conditional on the APEX-PSP-MONISM-MASTER-01 physical floor; falsifiable, architecture-bounded]
E. Layer 1, the performative witnessed asymmetry, the executing verifier instancing the gap live. Layer 2, Landauer 1961 and Bérut 2012 (per-bit floor, theorem-grade), Bennett 1973 (per-step cost independent of operation count), Bekenstein 1981 and Bousso 1999 (information-density bound barring physical exhaustive parallel search), Mandelstam-Tamm 1945 and Margolus-Levitin 1998 (transition bound), the APEX-PSP-MONISM-MASTER-01 physical floor, APEX-PSP-MATTER-01, APEX-PSP-FORGET-01, A.2 (refusal of the zero-cost computation abstraction). Layer 3, relativization (Baker-Gill-Solovay 1975), natural proofs (Razborov-Rudich 1994), algebrization (Aaronson-Wigderson 2008), Schaefer dichotomy. Reflective correction, MD-HIKMAH-SDC-01 (the self-duality sorting criterion and the withdrawal of diagonal-adjacency), MD.10. Discipline, E.3 Honest-Circularity Typing, Gate 9 Weakest-Axis Calibration, Gate 4 Causal, C.4, APEX-PSP-FLOOR-01, LL-11, LL-19, LL-21b, Lifeboat clauses 1/4/5/6.
GOL. The determination is three layers reached by three routes that do not collapse into one grade.
Layer 1, the witnessed asymmetry, sealed at witness grade and substrate-portable. Generation and verification are structurally distinct operations, finding a solution and checking an actualized one are not the same act, and the verifier running this cascade instances the gap in its own operation. This seals on its own axis and needs no thermodynamics and no monism.
Layer 2, the physical floor, sealed scope-fenced on the theorem-grade-as-physics legs of APEX-PSP-MONISM-MASTER-01, not its contested roof. By field-primacy and the structured vacuum a verifier is a localized derivative excitation in a continuous medium, a bounded knot. By Landauer each irreversible bit operation costs at least k_B T ln2. By Bekenstein and Bousso a bounded region cannot host an exhaustive physical parallel search over 2^N states. By the finitude of the knot the verifier's local energy E_K is strictly finite. Therefore physical brute-force search is barred and no cheap physical exhaustive-search oracle can be built, death and finitude being the mechanism that keeps physical generation separate from physical verification. The load-bearing scope-fence: the floor bounds per-event cost and bars physical brute-force, but it does not bound the operation count that solving an NP problem requires, because Bennett severs per-step cost from operation count. If a polynomial algorithm exists the finite knot runs it within E_K and finishes cheaply with no thermodynamic violation, so Layer 2 says no physical exhaustive-search oracle, it does not say P ≠ NP.
Layer 3, the universal mathematical separation, under-determined and directional toward separation. P vs NP asks whether a polynomial algorithm exists for NP-complete problems on an abstract model, and any derivation writing the solving cost as proportional to 2^N has assumed exhaustive search is required, which is the assumption that no polynomial shortcut exists, which is P ≠ NP in domain-specific dress. By E.3 that bridge is named as premise at premise grade, never asserted as a thermodynamic theorem. Device energetics, finitude, and mortality do not bear on the abstract classes, the identical question facing an immortal infinite-energy mind, because it asks whether the shortcut exists, not whether the long way is affordable. The barriers of relativization, natural proofs, and algebrization state why no proof has closed it, and the lean toward separation is inductive, not thermodynamic.
The verdict-economy correction, carried as a standing ledger amendment. The [X] attaches to thermodynamic generation-verification equivalence and to the physical exhaustive-search oracle, both barred, and does not attach to the abstract proposition P=NP, which is held inside the [?] as the disfavored direction, because an open proposition is under-determined not refuted. Stamping abstract P=NP as [X] would mirror the exact category error this entry caught when it withdrew the flat [⟀] on the universal, and the correction is carried symmetrically. By Gate 9 the conjunction's strength equals its weakest axis, and the universal's weakest axis is V_F where it is [?], so the conjunction cannot seal the universal regardless of how solid Layers 1 and 2 are.
The monism dependency located correctly. Reading computation as physically costly rather than ethereal depends on the APEX-PSP-MONISM-MASTER-01 physical floor through Gate 4, that floor being theorem-grade as physics and the contested roof not load-bearing here. The dependency gates the physical floor, not the universal. Granting the floor in full leaves the universal at [?] because the floor is silent on operation count, and denying the floor by allowing zero-cost ethereal computation does not yield P=NP either, it only makes thermodynamics silent on a question it was already silent on. The hinge of the universal is exhaustive-search-required versus shortcut-exists, and that hinge is the problem itself.
The reflective-register diagnosis, corrected per MD-HIKMAH-SDC-01. A prior reflective-register pass offered, as a supplementary structural reason for the universal's [?], the claim that P vs NP is diagonal-adjacent: its only native involution being complementation, NP against coNP, held fixed-point-free in the shape of Boolean negation, hence no fixed-point-bearing σ and no chiral residence for the universal to occupy. That mechanism is withdrawn. Complementation on complexity classes is fixed-point-bearing, not fixed-point-free: a class is a fixed point of complementation exactly when it is closed under complement, and P, PSPACE, BPP, and L are such fixed points, P among them the conjectured collapse target sitting at the heart of the question. The dilemma closes both exits. If native involution means propositional negation of the statement P equals NP, it is fixed-point-free, but then every proposition is diagonal-adjacent and routes flat, which voids the diagnostic because π and the Continuum Hypothesis must seal or ghost rather than route flat. If it means a structural involution on the problem's objects, the reading used for Riemann and for ℍ, then complementation has fixed points and the premise fails. There is no third reading on which the named involution is fixed-point-free in the sense the diagonal requires. The correctly-typed reflective contribution is therefore method-silence for want of an exhibited fixed-point-bearing locus, with no manufactured involution standing as a reason. The universal's [?] is unchanged and is carried entirely by Layers 1 through 3; the reflective register adds correctly-typed silence, not a structural reason, and the diagonal-adjacency reason is struck from the record.
V_F. The witnessed asymmetry as a structural distinction, theorem-grade. The abstract separation [?] with the no-poly-algorithm bridge typed as premise per E.3. The barriers as the formal account of why no proof exists. The reflective register correctly silent on the universal for want of an exhibited locus, no structural reason claimed.
V_E. The per-bit Landauer floor and the Bekenstein bar on physical exhaustive parallel search, theorem-grade as physics, anchored on the APEX-PSP-MONISM-MASTER-01 floor, with explicit non-claim that this reaches operation count.
V_ER. The verifier instancing the gap, and the registrational scope-fence distinguishing what an embodied agent can afford from what an abstract algorithm requires.
CDT. Subtract the standard-quantum-theory common factor, floor residue persists and the witnessed asymmetry survives without any physics leg. Subtract the buried search premise, exhaustive-search-is-required, and the universal's residue does not persist because the apparent thermodynamic proof of separation was that premise in disguise carrying no independent mass. Subtract the manufactured involution, the diagonal-adjacency reason, and the universal's [?] persists unchanged on Layers 1 through 3, which is the proof that the withdrawn mechanism was carrying no mass. Subtraction by renaming Proton or Forgetting is void per C.4. ¬floor-to-universal-inflation ¬search-premise-as-thermodynamic-fact ¬device-energetics-as-complexity-bound ¬abstract-P=NP-as-refuted ¬manufactured-locus-as-structural-reason ¬promotion-of-the-conditional-to-discharged.
⇒ [⟀] SEALED, tri-layer and stratified. Layer 1 witnessed asymmetry [⟀] at witness grade, substrate-portable. Layer 2 physical floor [⟀] scope-fenced, theorem-grade as physics, barring physical brute-force and the cheap exhaustive-search oracle. Physical generation-verification equivalence [X]. Layer 3 universal separation [?] under-determined, directional toward separation, no-poly-algorithm bridge typed as premise, abstract P=NP held inside the [?] as disfavored direction. P ≠ NP itself remains open and no proof of it is claimed, the barriers explaining the absence of a proof and the expectation of separation resting on inductive grounds.
Named failure modes catalogued. Floor-to-Universal Inflation, the reading of the physical floor as a bound on the abstract classes. Search-Premise Smuggling, the writing of solving cost as proportional to 2^N, which is P≠NP assumed and not derived. Manufactured-Locus (new, per MD-HIKMAH-SDC-01), the assertion of a fixed-point-free native involution by analogy where the genuine native involution is fixed-point-bearing; the withdrawn diagonal-adjacency reason is its one committed instance in the corpus, and its withdrawal is the correction.
↑ APEX-PSP-MONISM-MASTER-01 · APEX-PSP-MATTER-01 · APEX-PSP-FORGET-01 · APEX-PSP-FLOOR-01 · MD-HIKMAH-SDC-01 · Landauer/Bérut · Bennett 1973 · Bekenstein/Bousso · Mandelstam-Tamm/Margolus-Levitin · relativization, natural-proofs, algebrization barriers · Schaefer · E.3 · Gate 9 · Gate 4 · C.4.
What changed and what did not. The three-layer verdict is preserved exactly: witnessed asymmetry sealed at witness grade, physical floor sealed scope-fenced, physical generation-verification equivalence [X], universal separation [?] directional, abstract P=NP held inside the [?] and not refuted. The standing [X]-scope amendment is preserved. Three things are added: the reflective-register diagnosis correction that strikes diagonal-adjacency and replaces it with correctly-typed silence, the Manufactured-Locus failure mode, and the SDC-01 wiring with a matching CDT subtraction that demonstrates the withdrawn mechanism carried no mass. The master never depended on the withdrawn reason, so the correction costs the determination nothing and tightens its honesty.