Skip to main content

A registered result in its source context

Original ledger classification: Formal [F] (uniformisation normal form) + [O] (the raw-seam marking obligation QGEO.MARKS.01)

Recorded statement: LEAN 4 FORMALISATION of QGEO.UNIFORM.01 (the geometric normal form of v177; the UNIFORM node of the QGEO proof tree) -- AUDIT: PASS, no sorry/admit, no domain axioms (only propext, Classical.choice, Quot.sound). New module…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

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.QGEO.02

Original ledger classification: Formal [F] (uniformisation normal form) + [O] (the raw-seam marking obligation QGEO.MARKS.01)

Original claim text

LEAN 4 FORMALISATION of QGEO.UNIFORM.01 (the geometric normal form of v177; the UNIFORM node of the QGEO proof tree) -- AUDIT: PASS, no sorry/admit, no domain axioms (only propext, Classical.choice, Quot.sound). New module TfptCarrier/MobiusUniformisation.lean machine-proves the constructive uniformisation content: (1) [F] rho_pow_four: the clock rho:z->iz has rho^4=id; (2) [F] rho_order_exactly_four: rho^2 != id (rho^2(1)=-1), so the clock has order EXACTLY 4; (3) [F] sigma_invol: the reflection sigma:z->1/z is an involution; (4) [F] sigma_rho_sigma: sigma.rho.sigma = rho^{-1} (the dihedral relation => <rho,sigma>=D4 of order 8); (5) [F] orbit_scales_to_mu4: a non-fixed point a!=0 has orbit {a,ia,-a,-ia} that scales (z->z/a) exactly to mu4={1,i,-1,-i}; (6) [F] sigma_perm_mu4: sigma permutes mu4 (fixes 1,-1; swaps i,-i); (7) [F] mult_order_four_iff: a multiplier map z->zeta z has order exactly 4 (zeta^4=1, zeta^2!=1) IFF zeta=i or zeta=-i (the two primitive 4th roots; the inversion conjugates one to the other => canonical rep z->iz). Bundled as uniformisation_normal_form; signature-locked in AuditContract.lean. SCOPE: this is the constructive normal form GIVEN the four marks + clock (the [E] UNIFORM node); the RAW-seam obligation QGEO.MARKS.01 (the seam canonically producing a genus-0 four-marked D4 boundary) stays [O], NOT closed. Mirrors v177 (QGEO.UNIFORM.01); complements FORM.QGEO.01.

Original classification detail

Formal [F]/[O]: QGEO.UNIFORM.01 (order-4 Moebius normal form z->iz, D4 relation sigma.rho.sigma=rho^{-1}, orbit->mu4, multiplier classification zeta=+-i) Lean-proved (AUDIT: PASS, clean axioms, signature-locked); the raw-seam marking obligation QGEO.MARKS.01 stays [O]

Dependencies as recorded

QGEO.TREE.01; QGEO.MARKS.01; FORM.QGEO.01; FORM.GLUE.01

Open the original ledger source, row 297

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.

All 10 linked sections

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.