What the conformal marked seam axioms fix
Original ledger classification: Exact [E] rigidity/census/genus identities (sympy) + [C] the residue typing
Recorded statement: The seam forcing round -- the conformal seam axioms force the mu3-cover y^3 = x^4 - 1 up to the conjugate sheet (one module, 14 checks, <1 s; discovery probe seam_cover_forcing_probe.py 14/14, verdict SEAM-FORCES-COVER; a constructive…
Statement, assumptions and sources
Paper context: TFPT — Introduction and reading guide
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QGEO.SEAMFORCE.01
Original ledger classification: Exact [E] rigidity/census/genus identities (sympy) + [C] the residue typing
Original claim text
The seam forcing round -- the conformal seam axioms force the mu3-cover y^3 = x^4 - 1 up to the conjugate sheet (one module, 14 checks, <1 s; discovery probe seam_cover_forcing_probe.py 14/14, verdict SEAM-FORCES-COVER; a constructive slice of the bedrock premise QGEO.SYM.01). Z4-MOBIUS RIGIDITY [E]: any 4-point configuration on P^1 cyclically permuted by an order-4 Mobius map is Mobius-equivalent to mu4 (multiplier forced primitive); the cross-ratio census is the HARMONIC orbit {2, 1/2, -1} (must-fail: 4/3 not in the orbit). THE WEIGHT CENSUS [E]: among 81 mu3-weight vectors exactly FOUR are clock-equivariant; the mark-EQUIVALENCE demand kills the alternating pair -- weights FORCED uniform, j in {1,2} = the conjugate sheet pair (v613). THE CURVE [E]: j = 1 gives y^3 = x^4 - 1 EXACTLY; full ramification at infinity (v603); Riemann-Hurwitz genus 3 exactly. THE SEAM GEOMETRY [E]: marks ON the unit circle, doubling reflection fixes seam and marks; the OS-cut (bond) reflection z -> -i conj(z) permutes the marks by EXACTLY the (k,5-k) pattern of the v599 real structure and meets the circle at the two v519 cut points; the mark-fixing reflection is the site-type axis v519 excludes. THE READING [C]: the seam axioms (disk + Z4 clock + four equivalent marks + cyclic-3 grading) force the cover; the bedrock residue narrows to (i) the cyclic-3 choice (N_fam = 3, anchored in the E8 glue 240 = 16 x 5 x 3) and (ii) the physical-seam <-> conformal-seam identification. GATE.QGEO does not move. [2026-08-01 XXXVI: residue (i) is made CONDITIONAL -- v620: the cyclic-N census shows the seam admits exactly N in {3, 5} as primitive-Lorentz orders (N = 6 reduces to N = 3), and the compiler's machine-checked integral constants (27 = 3^3 deck determinant, 81 = 3^4 saturation) pin N = 3 uniquely; the residue moves to N_fam = 3 (E8-anchored); see QGEO.NCENSUS.01.] [2026-08-01 XXXVII: residue (ii) closes at the kernel + dictionary level -- v622: the v519 seam kernel is EXACTLY the discrete NS chiral mode sum (flat band = NS spectrum, Ramond must-fail), the mark-bond midpoints sit exactly at mu4, the group dictionary is exact, and the straddle law is literal geometry (straddled = axis through marks); the remaining continuum residue is the covering-level identification; see QGEO.SEAMID.01.]
Original classification detail
SEAM-FORCES-COVER: Z4-Mobius rigidity (mu4 forced, harmonic CR orbit); weights forced uniform j in {1,2}; y^3 = x^4-1 exact, genus 3; seam reflections = the v599 (k,5-k) pattern with the v519 cut points; residue = cyclic-3 choice + physical<->conformal identification; 14/14 checks
Dependencies as recorded
QGEO.COVER.01; QGEO.REAL.01; QGEO.SEAMMARKS.01; QGEO.PERNORM.01; v597; v599; v603; v613
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- Architecture, E8 and the electromagnetic fixed point
- Standard Model and flavor structure
- E8 audit and bootstrap
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- Front matter / supportE8 audit and bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- =150 2026-08-01 (XXXV) (the seam identification lands ( v622 promoted) — THE PHYSICAL SEAM IS THE CONFORMAL SEAM: the v519 chiral seam kernel is EXACTLY the discrete NS (antiperiodic) chiral mode sum on the 16-site circle, including the even-distance zeros (the flat band IS the NS spectrum; the Ramond sum fails as must-fail control); the four mark-bond midpoints sit EXACTLY at [formula in source] under the site map [formula in source] (no site touches a mark — the v519 ``marks at bond midpoints'' becomes literal geometry); the group dictionary is exact (clock [formula in source] , RP reflections [formula in source] diameter reflections); and the v534 STRADDLE LAW becomes geometry — straddled cuts [formula in source] exactly the through-mark axes; the second v617 bedrock residue closes at the kernel [formula in source] dictionary level, leaving the covering-level identification)Research changelog; TFPT — Introduction and reading guide
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- Front matter / supportE8 audit and bootstrap
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Registered verification modules
- v617_seam_cover_forcing.pyRegistered verification module · core
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QGEO.SEAMFORCE.01: die Seam-Forcing-Runde — **DIE KONFORMEN SEAM-AXIOME ERZWINGEN DEN μ₃-COVER** (konstruktive Scheibe der Bedrock-Prämisse QGEO.SYM.01): ℤ₄-MÖBIUS-RIGIDITÄT — jede zyklisch ℤ₄-symmetrische 4-Punkt-Konfiguration auf ℙ¹ ist Möbius-äquivalent zu μ₄ (Multiplier ±i erzwungen; Cross-Ratio-Zensus = harmonischer Orbit {2, ½, −1}; must-fail: 4/3 nicht im Orbit); GEWICHTS-ZENSUS — unter allen 81 μ₃-Monodromie-Vektoren sind genau 4 clock-äquivariant, die Mark-Äquivalenz killt das alternierende Paar: **Gewichte UNIFORM erzwungen, j ∈ {1,2} = das konjugierte Blatt-Paar (v613)**; j = 1 gibt EXAKT y³ = x⁴−1, volle ∞-Verzweigung (v603), Riemann–Hurwitz Genus 3 exakt; die Seam-Geometrie passt: Bond-Reflexion z ↦ −iz̄ = das (k,5−k)-Muster von v599s R, Schnittpunkte = die zwei v519-Cut-Punkte; Bedrock-Rest verengt auf (i) die Zyklisch-3-Wahl und (ii) die physisch↔konform-Identifikation [C] (14 checks, <1 s)
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