Which cyclic orders the marked construction permits
Original ledger classification: Exact [E] ramification/genus/Chevalley-Weil/pinning identities (sympy) + [C] the conditional typing
Recorded statement: The cyclic-N census -- the seam admits N in {3, 5} as primitive-Lorentz orders and the compiler's integral constants pin N = 3 (one module, 9 checks, <1 s; discovery probe cyclic_n_census_probe.py 9/9, verdict N3-PINNED; makes the first…
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Paper context: input 5 tfpt 3 e8 audit bootstrap
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QGEO.NCENSUS.01
Original ledger classification: Exact [E] ramification/genus/Chevalley-Weil/pinning identities (sympy) + [C] the conditional typing
Original claim text
The cyclic-N census -- the seam admits N in {3, 5} as primitive-Lorentz orders and the compiler's integral constants pin N = 3 (one module, 9 checks, <1 s; discovery probe cyclic_n_census_probe.py 9/9, verdict N3-PINNED; makes the first v617 bedrock residue CONDITIONAL). RAMIFICATION [E]: points over infinity = gcd(N, 4): full ramification everywhere iff N in {3, 5} among N = 2..6. GENUS [E]: Riemann-Hurwitz table g = 1, 3, 3, 6, 7 with complete character decomposition. SHEET DIMENSIONS [E]: primitive sheets have the compiler's rank 3 exactly for N in {3, 5, 6}, rank 2 for N in {2, 4}. CHEVALLEY-WEIL [E]: N = 3 has BOTH primitive sheets Lorentz ((1,2)/(2,1), the v599/v613 signature); N = 5 has a Lorentz pair; N = 6 has NO primitive Lorentz sheet (its Lorentz content = the order-3 characters: N = 6 REDUCES to N = 3) -- the seam-admissible orders with a primitive Lorentz sheet are EXACTLY {3, 5}. THE PINNING [E]: det_Z(1 - deck) = Phi_N(1)^3 = N^3 for prime N: 27 for N = 3 (the machine-checked v597 constant) vs 125 for N = 5; saturation 81 = 3^4 vs 625 = 5^4: N = 3 UNIQUE. THE READING [C]: the residue moves one level down -- WHY the compiler is 3-adic is N_fam = 3, anchored in the E8 glue (240 = 16 x 5 x 3), named, not derived. GATE.QGEO does not move.
Original classification detail
N3-PINNED: seam-admissible primitive-Lorentz orders = {3, 5} exactly (N = 6 reduces to N = 3); compiler constants 27/81 pin N = 3 uniquely (vs 125/625 for N = 5); residue = N_fam = 3 (E8-anchored); 9/9 checks
Dependencies as recorded
QGEO.SEAMFORCE.01; QGEO.COVER.01; QGEO.PERNORM.01; v597; v600; v613; v617
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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
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- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- =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
Registered verification modules
- v620_cyclic_n_census.pyRegistered verification module · core
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QGEO.NCENSUS.01: der zyklisch-N-Zensus — **DER SEAM LÄSST N ∈ {3,5} ALS PRIMITIVE LORENTZ-ORDNUNGEN ZU, UND DIE COMPILER-KONSTANTEN PINNEN N = 3** (der erste v617-Bedrock-Rest, konditional gemacht): volle ∞-Verzweigung ⟺ gcd(N,4) = 1 ⟺ N ∈ {3,5}; Genus-Tabelle 1,3,3,6,7 (N = 2..6, Riemann–Hurwitz exakt); primitive Blatt-Dimension 3 genau für N ∈ {3,5,6}; **Chevalley–Weil: N = 3 hat BEIDE primitiven Blätter Lorentz ((1,2)/(2,1) — die v599/v613-Signatur), N = 5 ein Lorentz-Paar, N = 6 KEIN primitives Lorentz-Blatt (sein Lorentz-Gehalt = die Ordnung-3-Charaktere: N = 6 REDUZIERT auf N = 3)**; das Pinning: det_ℤ(1−deck) = Φ_N(1)³ = N³ — 27 für N = 3 (EXAKT die maschinell geprüfte v597-Konstante) vs. 125 für N = 5; Saturation 81 = 3⁴ vs. 625 = 5⁴: **N = 3 eindeutig**; der Rest wandert eine Ebene tiefer: warum der Compiler 3-adisch ist = N_fam = 3 (E8-Glue-verankert) (9 checks, <1 s)
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