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A registered result in its source context

Original ledger classification: Identity [I] (exact census) + [P] (scoping conclusion)

Recorded statement: NS/R SECTOR CENSUS (R2 scoped honestly; corrected same day - the first version graded the Ramond labels by the sum q_D+q_A, which is not the glue label): (1) NS CENSUS [I] - every Neveu-Schwarz state of the 16 carrier Majoranas has INTEGER…

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GATE.METRIC.10

Original ledger classification: Identity [I] (exact census) + [P] (scoping conclusion)

Original claim text

NS/R SECTOR CENSUS (R2 scoped honestly; corrected same day - the first version graded the Ramond labels by the sum q_D+q_A, which is not the glue label): (1) NS CENSUS [I] - every Neveu-Schwarz state of the 16 carrier Majoranas has INTEGER (D5, SO(6)) weights, and integer weights lie in discriminant classes 2x(sum parity): the NS module supports ONLY the even pairs {(0,0),(2,0),(0,2),(2,2)} - the odd glue elements (1,1),(3,3) have ZERO NS support; (2) R CENSUS [I] - the Ramond zero-mode module (2^8=256 ground states; D5 spinor weights (+-1/2)^5, SO(6) spinor weights (+-1/2)^3) carries exactly the four odd class pairs (1,1),(1,3),(3,1),(3,3), 64 each; (3) SHEET SPLIT INSIDE R [I] - the R module splits 128+128 into the odd sectors of the TWO Lagrangian glues <(1,1)> and <(1,3)> (v92): choosing the glue IS choosing the R-projection (128 = one SO(16) spinor chirality), and E8 assembles as 248 = 120 (NS adjoint) + 128 (R, one chirality). SCOPING CONCLUSION [P]: the index-4 Q-system extension is invisible to the untwisted (NS) module - its odd sectors are twisted (Ramond-type) modules and the glue choice is the Ramond projection; R2's one remaining statement is irreducibly about the twisted-sector structure of the seam-Calderon net; the finite shadow is exhausted (v113 kernel theorems, v125 Q-system axioms, v143 graded-Frobenius hull, this census) [2026-08-03 LIII: the NS/R grading acquires an arithmetic home (v722, 9/9, GNET.RAMIFIED.01): it IS the parity character of E8(Z[i])/(1+i) = F2^4 -- (1+i)L lies in the even sublattice (Z-basis proof), all 15 root classes are parity-PURE (7 NS + 8 R), parity is a homomorphism, and both controls fire; the Ramond projection is (1+i)-adic at the one ramified edge of the Z[i]-E8 Hecke tower. With v726 (index 4 + state-preserving Klein dressing; chi = 1 <-> half-integer labels on both sides, ramified defect in ker(chi)) the groupoid reading of G_net has its first exact witnesses. No status move.]

Original classification detail

Identity [I]: odd glue sectors are Ramond modules; glue choice = R-projection; R2 = a twisted-sector net statement

Dependencies as recorded

GATE.METRIC.09; GATE.METRIC.08; CAR.QFREE.01; v113; v125; v143

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Registered verification modules

  • v148_fock_census.pyRegistered verification module · registry
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    NS/R census (R2 scoped, corrected): the untwisted (NS) module carries only even classes {0,2}×{0,2} — the odd glue sectors are RAMOND modules; the R zero-mode module (256) splits 128+128 into the odd sectors of the two Lagrangian glues: choosing the glue = choosing the R-projection; 248 = 120(NS)+128(R)

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