Skip to main content

A registered result in its source context

Original ledger classification: Geometric premise [O] (reduction, not closure)

Recorded statement: RAW-SEAM => MARK-LOCALITY REDUCTION (2026-06-18): composes v216+v201+v198 on the canonical pillowcase metric to make the converse implication explicit and isolate the bedrock. The flat pillowcase has curvature only at the 4 marks…

Statement, assumptions and sources

Paper context: tfpt research contracts

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

QGEO.ENERGY.03

Original ledger classification: Geometric premise [O] (reduction, not closure)

Original claim text

RAW-SEAM => MARK-LOCALITY REDUCTION (2026-06-18): composes v216+v201+v198 on the canonical pillowcase metric to make the converse implication explicit and isolate the bedrock. The flat pillowcase has curvature only at the 4 marks (Gauss-Bonnet), so the DtN sub-principal symbol is a mu4-orbit sum, Z4-invariant (Fourier on 4Z), block-diagonal, [rho,M_f]=0; with |k| commuting (v198) [rho,Lambda]=0 => omega o rho=omega ON THIS METRIC. Reduces the whole bedrock to the single statement 'the raw RP seam carries the uniformising flat pillowcase metric' (= QGEO.SYM.01). A reduction/sharpening, NOT a closure -- the converse (raw RP forces the metric) stays the irreducible postulate.

Original classification detail

[E] Gauss-Bonnet 4 marks + block-diagonal/state-invariance chain on the pillowcase; [N] Z4-Fourier support (4Z) of the pillowcase curvature; [O] the metric-realisation premise (QGEO.SYM.01) stays open -- a reduction to one metric statement, NOT a closure (NEG control: curvature off the mu4 orbit breaks the chain).

Dependencies as recorded

QGEO.SYM.01; QGEO.SUBPRIN.01; QGEO.MODULAR.01; QGEO.MARKS.03; QGEO.PILLOW.01

Open the original ledger source, row 350

Location 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.

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.

Navigation through a shared verification script

These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.

Registered verification modules

  • v264_raw_seam_marklocal.pyRegistered verification module · registry
    Read the description recorded in the module registry

    QGEO.ENERGY.03 — the raw-seam => mark-locality REDUCTION (NOT a closure of QGEO.SYM.01). Composes v216+v201+v198 on the canonical pillowcase: [E] Gauss-Bonnet 4 cone points (deficit pi each, sum 4pi=2pi chi(S^2)), curvature ONLY at the 4 marks; [N] a curvature sourced at the mu4 orbit {0,pi/2,pi,3pi/2} has Fourier support ONLY on 4Z (FFT), so mark-locality is automatic for the pillowcase; [E] M_f then commutes with the clock rho=diag(i^n), [rho,M_f]=0; [E] with |k| already commuting (v198), [rho,Lambda]=0 => omega o rho=omega ON THIS METRIC; [O] the residual IS the metric -- the chain assumes the raw seam carries the uniformising flat pillowcase metric (= QGEO.SYM.01), NEG control (curvature off the mu4 orbit) breaks it. A reduction/sharpening, NOT a closure.

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries