A registered result in its source context
Original ledger classification: Numerical certification [N] (implication on realistic profiles + state level) + premise [O] (the physical seam being mark-local)
Recorded statement: MARK-LOCAL DtN CERTIFIED ON REALISTIC STEKLOV PROFILES + AT THE STATE LEVEL (2026-06-15): a numerical SHARPENING of QGEO.SUBPRIN.01/v201, carried to the quasi-free STATE (the actual omega o rho = omega, not just [rho,Lambda]=0); NOT a…
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QGEO.MARKLOCAL.01
Original ledger classification: Numerical certification [N] (implication on realistic profiles + state level) + premise [O] (the physical seam being mark-local)
Original claim text
MARK-LOCAL DtN CERTIFIED ON REALISTIC STEKLOV PROFILES + AT THE STATE LEVEL (2026-06-15): a numerical SHARPENING of QGEO.SUBPRIN.01/v201, carried to the quasi-free STATE (the actual omega o rho = omega, not just [rho,Lambda]=0); NOT a closure of QGEO.SYM.01. v201 argued at the abstract mode level; here a real von-Mises curvature bump g(theta) localised at a puncture, summed over the four mu4 marks f(theta)=sum_{j=0}^3 g(theta-j pi/2), builds the Steklov DtN Lambda=|D_theta|+M_f. (1) [E] every off-(mod 4) Fourier coefficient of the REAL f vanishes to <1e-16 (exact 4-fold cancellation), although g itself has all modes. (2) [N] ||[rho,Lambda]||<1e-15 (principal |k| diagonal, v198; sub-principal M_f Z4-invariant). (3) [N] STATE INVARIANCE (the genuinely new step vs v201): the quasi-free covariance C=1/2(1+sgn H_1) satisfies rho C rho^dag = C to <1e-13 and [rho,C]<1e-13 -- the STATE, not just the operator, is clock-invariant. (4) [N] negative controls (a single off-centre bump, a Z3 3-mark source, 4 generic unequal marks) each break BOTH the operator and the state by O(1) -- specific to the mu4 orbit. (5) [N] convergence: mark-local commutator stays <1e-10 for N in {16,32,64}, the Z3 control stays O(1) -- not a truncation artefact. (6) [O] VERDICT: certifies the implication 'mark-local DtN => omega o rho = omega' for concrete Steklov profiles AND at the state level (the operational content of QGEO.SUBPRIN.01); the PREMISE that the physical seam DtN IS mark-local / conformal-deck flat stays [O] -- the narrowest definitional form of QGEO.SYM.01, NOT its closure (net existence + full-cone RP remain the [E] of v175). Python-only (numerical; the exact mark-sum identity is Wolfram-mirrored via v201)
Original classification detail
Numerical/premise [N]/[O]: mark-local DtN => omega o rho = omega certified for realistic von-Mises Steklov profiles AND at the quasi-free state level (rho C rho^dag = C to 1e-13); negative controls (off-centre, Z3, generic) break by O(1); the seam being mark-local stays [O], the narrowest form of QGEO.SYM.01, not a closure
Dependencies as recorded
QGEO.SUBPRIN.01; QGEO.STATE.01; QGEO.MODULAR.01; v201_seam_subprincipal_marks.py; v198_modular_commutator_reduction.py
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- Research contracts
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- 2026-06-15 (QGEO sharpening: mark-local DtN certified on realistic profiles)Research changelog; TFPT — Introduction and reading guide
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- Honest statusinput 4 origin theory
- Research Contract 1 — [formula in source]tfpt research contracts
- Honest statusorigin theory
- Honest statusOrigin Theory
- 2026-06-15 (Lean: the QGEO.SYM.01 conditional theorem machine-proved)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Honest statusinput 4 origin theory
- Front matter / supportFrontier and open physical interfaces
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Registered verification modules
- v210_mark_local_dtn.pyRegistered verification module · registry
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a numerical SHARPENING of v201/QGEO.SUBPRIN.01 on REALISTIC Steklov curvature profiles, carried to the quasi-free STATE level (the actual ω∘ρ=ω, not just [ρ,Λ]=0); NOT a closure of QGEO.SYM.01. A real von-Mises curvature bump g(θ) localised at a puncture, summed over the four μ4 marks f(θ)=Σ_{j=0}^3 g(θ−jπ/2), builds the Steklov DtN Λ=|D_θ|+M_f. [E] every off-(mod 4) Fourier coefficient of the REAL f vanishes to <1e-16 (exact 4-fold cancellation), although g has all modes. [N] ‖[ρ,Λ]‖<1e-15. [N] STATE invariance (new vs v201): the quasi-free covariance C=½(1+sgn H₁) satisfies ρCρ†=C to <1e-13 — the STATE, not just the operator, is clock-invariant. [N] negative controls (a single off-centre bump, a Z3 source, 4 generic marks) break BOTH operator and state by O(1); [N] convergence stable for N∈{16,32,64}. [O] verdict: certifies 'mark-local DtN ⟹ ω∘ρ=ω' for concrete profiles AND at the state level; the premise that the physical seam IS mark-local stays [O] — the narrowest definitional form of QGEO.SYM.01, NOT its closure.
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