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Original ledger classification: Uniform-in-N rigidity [E]/[C]: the band-limited mu4-character rigidity of v398 is uniform in N -- exact 4-sector commutation to N=256, a uniform gap, and an N-independent clock-breaking lower bound ||[rho,V]||=2; not a small-N artifact. SEAM.RIGIDITY.01/SEAM.EQUIV.01 stays [O] (the full-L^2 forcing is the cited rigidity/MMST step)

Recorded statement: The uniform-in-N hardening of the Seam State Rigidity Theorem (2026-06-30; hardens SEAM.RIGIDITY.01/v398) -- the band-limited mu4-character rigidity is NOT a small-N artifact. v398 verified [rho,K]=0 by a finite sweep N=4..64; this module…

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SEAM.RIGIDITY.UNIFORM.01

Original claim text

The uniform-in-N hardening of the Seam State Rigidity Theorem (2026-06-30; hardens SEAM.RIGIDITY.01/v398) -- the band-limited mu4-character rigidity is NOT a small-N artifact. v398 verified [rho,K]=0 by a finite sweep N=4..64; this module makes it uniform in N and adds an N-independent rigidity bound. [E] EXACT UNIFORM 4-SECTOR COMMUTATION: rho=diag(i^n) has EXACTLY 4 distinct eigenvalues {1,i,-1,-i} for ALL N (an order-4 clock, N-independent), and a genuinely character-block-diagonal K (random Hermitian within each n mod 4 class, not merely diagonal) satisfies [rho,K]=0 EXACTLY for N=4..256 (extends v398's N<=64). [E] UNIFORM GAP: the gapped collar proxy has Delta(N)=const>0 across N=20..160 (the Nachtergaele-Sims uniform gap, shared with v439). [E] N-INDEPENDENT RIGIDITY BOUND: a FIXED local clock-breaking perturbation (single off-mu4-block Hermitian entry) gives ||[rho,V]||=2 EXACTLY for all N=4..256 -- a uniform lower bound; any fixed-size clock-breaking is detected with N-independent strength. [E] NEG CONTROL: a clock-PRESERVING (same-sector) perturbation gives ||[rho,V']||=0; an order-2 (Z2) clock has only 2 distinct eigenvalues, not 4 -- the ORDER of the clock (the four Gauss-Bonnet marks) is the discriminator, uniformly in N. [C]/[O] VERDICT: the band-limited rigidity of v398 is uniform in N (exact 4-sector commutation to N=256, uniform gap, N-independent detection) -- not a small-N artifact; SEAM.RIGIDITY.01 / SEAM.EQUIV.01 stays [O]: that RP+gap+holomorphy FORCE Lambda_Sigma block-diagonal on the FULL L^2 (rather than merely permit it) is the cited rigidity/MMST step.

Original classification detail

Numerical

Dependencies as recorded

SEAM.RIGIDITY.01; SEAM.EQUIV.01; QGEO.MODHAM.01; v398; v439; v309; v199

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Research contracts
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Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
2026-06-30 (six convergent attacks on the one SEAM.EQUIV.01 continuum residual — intrinsic Bisognano–Wichmann, a Lieb–Robinson continuum motor, the [formula in source] -homotopy, an applicability audit, uniform rigidity, and falsifiable kill tests; none closes the keystone, together they reduce it to a single analytic fact and make the claim falsifiable)Research changelog; TFPT — Introduction and reading guide

Navigation through a shared verification script

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2026-06-30 ( v445 — the rigidity FORCING converse: commuting with the order- [formula in source] clock is exactly [formula in source] -block-diagonality, upgrading the rigidity step from ``permit'' to ``force'')Research changelog; TFPT — Introduction and reading guide
Research Contract 1 — [formula in source]tfpt research contracts
Front matter / supportResearch contracts
Front matter / supportResearch contracts
Research Contract 1 — [formula in source]tfpt research contracts
2026-06-30 ( v446/ v447/ v448 + Lean + Wolfram — deriving clock-invariance from [formula in source] -symmetry, an independent topological reading of the edge [formula in source] , and pinning the one external MMST fact at four-point order)Research changelog; TFPT — Introduction and reading guide

Registered verification modules

v442_seam_rigidity_uniform.pyRegistered verification module · frontier
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SEAM.RIGIDITY.UNIFORM.01: the uniform-in-N hardening of the Seam State Rigidity Theorem (v398) -- the band-limited rigidity is NOT a small-N artifact. [E] EXACT UNIFORM 4-SECTOR COMMUTATION: ρ=diag(i^n) has EXACTLY 4 distinct eigenvalues for all N, and a genuinely character-block-diagonal K (random Hermitian within each n mod 4 class, not merely diagonal) has [ρ,K]=0 EXACTLY for N=4..256 (extends v398's N≤64). [E] UNIFORM GAP: Δ(N)=const>0 across N=20..160 (Nachtergaele-Sims, shared with v439). [E] N-INDEPENDENT RIGIDITY BOUND: a FIXED local clock-breaking perturbation gives ||[ρ,V]||=2 EXACTLY for all N. [E] NEG CONTROL: a clock-PRESERVING perturbation gives ||[ρ,V']||=0; an order-2 clock has only 2 sectors -- the order (4 marks) is the discriminator. [C]/[O] band-limited rigidity is uniform in N; SEAM.RIGIDITY.01/SEAM.EQUIV.01 stays [O]: the full-L² forcing is the cited rigidity/MMST step. Python-only (numpy).

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