A registered result in its source context
Original ledger classification: Formal [F] (Lean kernel; the entrywise forcing iff (uniform in N), the exact commutant dimension and the order discriminator kernel-proved axiom-free, the operator-level clock-invariance named)
Recorded statement: LEAN 4 FORMALISATION of the rigidity FORCING converse (2026-06-30; the kernel-hardening of v445/SEAM.RIGIDITY.FORCING.01, also hardening v442/SEAM.RIGIDITY.UNIFORM.01) -- new module TfptCarrier/SeamRigidityForcing.lean, lake build OK,…
Statement, assumptions and sources
Paper context: Red-team audit
The exact identifier, original classification and full claim are available below.
The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.
Read the exact registered claim and its dependencies
FORM.SEAM.RIGIDITY.FORCING.01
Original ledger classification: Formal [F] (Lean kernel; the entrywise forcing iff (uniform in N), the exact commutant dimension and the order discriminator kernel-proved axiom-free, the operator-level clock-invariance named)
Original claim text
LEAN 4 FORMALISATION of the rigidity FORCING converse (2026-06-30; the kernel-hardening of v445/SEAM.RIGIDITY.FORCING.01, also hardening v442/SEAM.RIGIDITY.UNIFORM.01) -- new module TfptCarrier/SeamRigidityForcing.lean, lake build OK, #print axioms CLEAN. It kernel-checks the load-bearing forcing algebra over Fin 4 / Z: [F] commutator_zero_iff (the ENTRYWISE forcing clock4 a = clock4 b <=> a=b, i.e. i^a=i^b <=> a==b mod 4 -- residue-only, hence UNIFORM in N, which is exactly v442's uniformity), [F] clock_injective + four_distinct (the four eigenphases are pairwise distinct = nondegeneracy), [F] commutant_dim_16 + proper_16 (dim = sum n_s^2 = 4*4^2 = 64 < 256 = N^2, a PROPER subspace), [F] order2_dim_16 + order_discriminator_16 (the order-2 commutant 128 is strictly larger than the order-4 64 -- the four marks force strictly more structure), [F] marks_eq_four (|mu4|=h(A3)=4), bundled as forcing_kernel_facts -- ALL by kernel decide (axioms propext/Classical.choice/Quot.sound only, NO domain axiom). The lift of the finite-N forcing to the full operator L^2 (the cited rigidity/MMST step) is the single named premise ClockInvariantOnFullL2; forcingClosesRigidity pins the rigidity closure to EXACTLY that one premise -- which v446 (SEAM.RIGIDITY.CLOCKINV.01) further reduces to mu4-symmetry of the seam RP data. So the linear-algebra core is machine-checked; only the operator-level clock-invariance is assumed -- no sorry. Mirrors v445 (and Wolfram-mirrored in tfpt_readouts_extension.wl).
Original classification detail
Formal
Dependencies as recorded
SEAM.RIGIDITY.FORCING.01; SEAM.RIGIDITY.UNIFORM.01; SEAM.EQUIV.01; v445; v442
Open the original ledger source, row 509Location recorded in the ledger
These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.
- Research contracts
Sections that explicitly cite this claim
A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.
- OutcomeRed-team audit
- 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
No separate module is linked in this claim record. This is a coverage statement, not a verdict about its truth.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.