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A registered result in its source context

Original ledger classification: Lattice/Lie [L] (derived selection + explicit conjugacy/obstruction) + [P] (realisation premise unchanged)

Recorded statement: DECK SELECTION THEOREM (R5's Z_3 choice DERIVED, executing the v140 residue): the established integer deck G=T_A*Sigma (v97 anchor-forced conjugation; v98 integer mu4 on generation space) pairs the Q_+=1 cusp line with the SELF-CONJUGATE…

Statement, assumptions and sources

Paper context: Standard Model and flavor structure

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FLAV.QGEO.06

Original ledger classification: Lattice/Lie [L] (derived selection + explicit conjugacy/obstruction) + [P] (realisation premise unchanged)

Original claim text

DECK SELECTION THEOREM (R5's Z_3 choice DERIVED, executing the v140 residue): the established integer deck G=T_A*Sigma (v97 anchor-forced conjugation; v98 integer mu4 on generation space) pairs the Q_+=1 cusp line with the SELF-CONJUGATE character 2 (G e1=-e1 exact eigenline; E-plane carries {1,3}); of the three Z_3 rotations only the sheet-twisted assignment (2,3,1)=chars(-U) is compatible - the cusp exponential i^{Q_+} (1,2,3) and the third rotation are EXCLUDED (same eigenvalue multiset, wrong grading pairing: (-1)-eigenlines on Q_+ degrees 1 vs 2). Explicit Q_+=1-line-preserving conjugacy S G S^-1 = -U constructed. SHEET ROBUSTNESS: under k->-k the B1 pairing (1->2) and plane set {1,3} are invariant - the only remaining freedom is the plane orientation = the established sheet Z_2 (v92 chirality pair), NOT a new residual. CONSEQUENCE: the H^1 Euler degree pulls back to Q_+ o rho (rho=(123)=coker-Q triality, v72): cusp grading and Euler grading differ by exactly one family rotation. STATUS: GATE.QGEO's discrete Z_3 residue CLOSED [L]; what remains of R5 is the realisation premise [P] the gate always carried (integer D4 model = parabolic geometry), with no discrete freedom left

Original classification detail

Lattice [L]: Z_3 choice derived - geometric deck = sheet-twisted class; residual = realisation premise only

Dependencies as recorded

FLAV.QGEO.05; FLAV.QGEO.04; v97; v98; v72

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Registered verification modules

  • v141_deck_selection.pyRegistered verification module · registry
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    deck selection: the v140 ℤ₃ choice DERIVED — the integer deck G=T_A·Σ (v97/v98) pairs the Q₊=1 line with the self-conjugate character 2, excluding i^{Q₊} and selecting the sheet-twisted −U assignment (2,3,1); only the established sheet ℤ₂ remains; Euler grading = Q₊∘ρ

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