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A registered result in its source context

Original ledger classification: Exact [E] integer-arithmetic slice ((1+i)L in the even sublattice on a Z-basis; 15x16 purity census; parity homomorphism) with both controls firing; contract half typed OPEN (Python-only per GATE.WOLFRAM.02).

Recorded statement: PHYS moonshot slice (T2 / G_net) -- is the Ramond projection (1+i)-adic? (one module, 9 checks, ~1 s; discovery probe phys_ramified_ns_r_probe.py 9/9, verdict RAMIFIED-SEES-NSR). THE THEOREM CHECK: on the explicit even-coordinate E8 with…

Statement, assumptions and sources

Paper context: Architecture, E8 and the electromagnetic fixed point

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GNET.RAMIFIED.01

Original ledger classification: Exact [E] integer-arithmetic slice ((1+i)L in the even sublattice on a Z-basis; 15x16 purity census; parity homomorphism) with both controls firing; contract half typed OPEN (Python-only per GATE.WOLFRAM.02).

Original claim text

PHYS moonshot slice (T2 / G_net) -- is the Ramond projection (1+i)-adic? (one module, 9 checks, ~1 s; discovery probe phys_ramified_ns_r_probe.py 9/9, verdict RAMIFIED-SEES-NSR). THE THEOREM CHECK: on the explicit even-coordinate E8 with the integral complex structure J (pair rotation, J^2 = -I, orthogonal, lattice-stable -- a concrete witness of the v634/v689 Gaussian E8), (1+i)L is CONTAINED in the even/NS sublattice (verified on a Z-basis), so the SO(16) coordinate-parity functional (E8 roots = 112 integer/NS + 128 spinor/R, the GATE.METRIC.10 census) FACTORS through the quotient E8(Z[i])/(1+i) = F2^4 (v689). PURITY: the 240 roots fall into exactly 15 classes x 16 (re-derived in this frame), every class purely NS or purely R (7 NS + 8 R), all classes mu4-stable, and parity is a HOMOMORPHISM F2^4 -> F2: the NS/R grading IS the parity character of the ramified quotient -- the Ramond projection is (1+i)-adic, the first exact witness for the groupoid reading of G_net (the ONE ramified edge of the Z[i]-E8 Hecke tower is the Gaussian prime (1+i)). CONTROLS FIRE: the trivialization Z[i]^4 = Z^8 does NOT show the 15x16 pattern (4 classes); scrambled NS/R labels BREAK purity. THE CONTRACT (stated with v726): the seam-Calderon inclusion A = B^{mu4} in B (index 4, the GATE.METRIC.08 Q-system) is the ramified-place structure of the groupoid -- kills: Frobenius mismatch Q-system vs (1+i)-correspondence convolution; index != 4 on the state-preserving ladder; dressing incompatible with the sigma descent. Exact integer arithmetic, no fit, no external tables. No marker move (GATE.METRIC.10 stays as typed).

Original classification detail

RAMIFIED-SEES-NSR: the NS/R grading IS the parity character of E8(Z[i])/(1+i) = F2^4 (exact, controls fire); the Ramond projection is (1+i)-adic -- first exact witness for the groupoid reading of G_net; the Q-system identification stays the OPEN contract half (kills registered); no status move.

Dependencies as recorded

GATE.METRIC.10; GATE.METRIC.08; E8.GAUSSCODE.01; PRIME.MOONSHOT.01

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Registered verification modules

  • v722_phys_ramified_ns_r.pyRegistered verification module · core
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    GNET.RAMIFIED.01: PHYS-Moonshot-Scheibe (T2/G_net) — ist die Ramond-Projektion (1+i)-adisch? — **RAMIFIED-SEES-NSR: (1+i)L liegt im geraden/NS-Untergitter (Z-Basis-Beweis), die 240 Wurzeln fallen in 15 × 16 Klassen mit REINER Parität (7 NS + 8 R), Parität ist ein Homomorphismus F₂⁴ → F₂ — die NS/R-Graduierung IST der Paritäts-Charakter von E8(Z[i])/(1+i) = F₂⁴**; erster exakter Zeuge für die Gruppoid-Lesart von G_net (die EINE verzweigte Kante des Turms ist die Gauß-Primzahl (1+i)); Kontrollen feuern: Z[i]⁴-Census ≠ 15×16, gescrambelte Labels brechen die Reinheit (9 Checks, ~1 s)

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