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
Open the original ledger source, row 667Location recorded in the ledger
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- Architecture, E8 and the electromagnetic fixed point
- E8 audit and bootstrap
- Research contracts
Sections that explicitly cite this claim
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- Front matter / supportE8 audit and bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Research Contract 2 — [formula in source]tfpt research contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- The [formula in source] compiler: [formula in source] as a closure, not an inputtfpt 1 architecture e8
- Research Contract 2 — [formula in source]Research contracts
- The [formula in source] compiler: [formula in source] as a closure, not an inputtfpt 1 architecture e8
Navigation through a shared verification script
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- 2026-10-18: Project separation and retained physics historyResearch changelog; TFPT — Introduction and reading guide
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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