Skip to main content

The covered seam and its lattice skeleton

Original ledger classification: Exact [E] combinatorics + mode-sum identities (sympy) + [C] the orbifold residue typing

Recorded statement: The covered seam round -- the lattice skeleton of the covering-level identification (one module, 9 checks, ~4 s; discovery probe covered_seam_probe.py 9/9, verdict COVERED-SEAM-SKELETON; the named residue of v622, first executed slice).…

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

QGEO.COVERSEAM.01

Original ledger classification: Exact [E] combinatorics + mode-sum identities (sympy) + [C] the orbifold residue typing

Original claim text

The covered seam round -- the lattice skeleton of the covering-level identification (one module, 9 checks, ~4 s; discovery probe covered_seam_probe.py 9/9, verdict COVERED-SEAM-SKELETON; the named residue of v622, first executed slice). CONNECTIVITY CENSUS [E]: lifting the 16-site seam to the mu3-cover, the covered seam is ONE 48-site circle for the uniform weights j = 1, 2 and DISCONNECTS into 3 circles for the trivial AND the alternating weights (1,2,1,2) -- a NEW independent kill of the alternating pair (seam connectivity; total monodromy 6 = 0 mod 3). THE WALK [E]: closes after exactly 48 steps, covers the base three times, crosses marks 12 times. THE LIFTED CLOCK [E]: L^4 = deck and L^12 = id on ALL 48 points with proper order 12 -- v597's r^4 = omega and v614's boundary-monodromy transport are LATTICE COMBINATORICS on the covered seam. THE KERNEL [E]: the v622 NS mode-sum identity generalizes verbatim to N = 48 (all d = 1..47). THE 12-GRID [E]: the NS modes split under the deck into THREE classes of 16 modes with offsets {1/6, 1/2, 5/6}; the offset-1/2 class equals the BASE NS frequencies EXACTLY (the untwisted sector IS the base seam); the fermionic deck lift satisfies deck^3 = -1 (the spin double, resonating with the v510/v519 (-1)^F dichotomy) and the bilinear deck eigenvalue of the twisted pair is exactly omega -- the t = omega/omega-bar sheets live on the H^1/bilinear level. THE LIFTED MARKS [E]: the 12 crossings are equally spaced and form a SINGLE 12-cycle under the lifted clock. THE READING [C]: the remaining residue is the interacting/CFT-level orbifold statement (twist-field OPE, the full Z3 orbifold of the seam CFT), named, not claimed. GATE.QGEO does not move.

Original classification detail

COVERED-SEAM-SKELETON: one 48-site covered seam (uniform weights; alternating pair disconnects -- independent kill); lifted clock exact order 12 with L^4 = deck (r^4 = omega as lattice combinatorics); N = 48 kernel identity; 12-grid mode split with untwisted = base verbatim, twisted pair = omega on bilinears; 12 marks in a single 12-cycle; 9/9 checks

Dependencies as recorded

QGEO.SEAMID.01; QGEO.SEAMFORCE.01; QGEO.NCENSUS.01; QGEO.PERNORM.01; v597; v613; v614; v617; v620; v622

Open the original ledger source, row 639

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

  • v623_covered_seam.pyRegistered verification module · core
    Read the description recorded in the module registry

    QGEO.COVERSEAM.01: die Covered-Seam-Runde — **DAS GITTER-SKELETT DER COVERING-EBENE** (der benannte v622-Rest, erste ausgeführte Scheibe): der auf den μ₃-Cover gehobene Seam ist **EIN 48-Site-NS-Kreis** für die uniformen Gewichte (j = 1, 2) und ZERFÄLLT in 3 Kreise für triviale UND alternierende Gewichte — **ein neuer, unabhängiger Kill des alternierenden Paars (Seam-Konnektivität)**; der explizite Walk schließt nach exakt 48 Schritten (3 Basis-Umläufe, 12 Mark-Kreuzungen); **DIE GEHOBENE CLOCK: L⁴ = Deck und L¹² = id auf ALLEN 48 Punkten mit echter Ordnung 12 — v597s r⁴ = ω und v614s Rand-Monodromie sind GITTER-KOMBINATORIK**; die v622-Kernel-Identität generalisiert wörtlich auf N = 48; **DAS 12-RASTER: die NS-Moden spalten unter dem Deck in drei 16er-Klassen mit Offsets {1/6, 1/2, 5/6}, die 1/2-Klasse = die BASIS-NS-Frequenzen EXAKT** (der ungetwistete Sektor IST der Basis-Seam); der fermionische Deck-Lift erfüllt Deck³ = −1 (Spin-Doppel, (−1)^F-Resonanz), Bilinear-Eigenwert = ω exakt (dort leben die t = ω/ω̄-Blätter); die 12 Mark-Kreuzungen bilden einen einzigen 12-Zyklus unter der Clock; Rest benannt: die wechselwirkende Orbifold-Aussage (9 checks, ~4 s)

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

Interlocking clocksSeam, origin and declared inputsQuantum and boundary structureSearch later reviewed research for this identifierRead the coverage boundaries