A registered result in its source context

SEAM.STATE.WIRING.SELECTOR.01

Original ledger classification: Contract closed as measured freedom theorem [Identity/Numerical]: one admissible wiring orbit (C_rot), Z/X excluded gauge-invariantly; pure-I = deployment representative; RP exclusion frame-relative (option 2); 'pure-I is compiler-forced' FORBIDDEN; [O] premise of v898/v903 unmoved; no marker move

Original claim text

THE WIRING FREEDOM THEOREM -- IS PURE-I COMPILER-FORCED? ANSWERED: NO -- DEPLOYMENT-CHOICE, NOT COMPILER THEOREM (the v908-registered contract, closed 2026-08-12, rounds 69-71 notes CCXIII/CCXV/CCXXI; promoted in v911). (1) THE EXACT GROEBNER CENSUS (30/30, WIRING-DEGENERATE): the C6-equivariant commutant of the coupling space is EXACTLY 24-dim (the boundary C6 action is the identity), the IOTA rule subspace 8-dim with the deployed PURE-I point; the constraint classes E1 (unit law), E2 (CAR/KMS), E3 (Pfaffian pencil, anchored by the symbolic Schur identity on all of W), E4 (orientation propagation det u > 0), E5 (covariance + seat stack) leave EXACTLY ONE admissible component mod rule gauge -- the rotation cell C_rot (dim 3; certified real decomposition, cofactor certificates, mixed branches real-point-free); pure-I is an INTERIOR point, NOT a vertex, and the INTEGER gauge (+)_5 J2 (+) I6 (preserving A_CC, C6, W and the ideal) connects pure-I and the pure-J ray; C_refl falls at EXACTLY ONE class -- orientation (det u = -(b^2 + d^2) < 0 identically): Z/X wirings are edge-illegal; SELECTOR THEOREM: rules + strict-collar Hermiticity would force PURE-J uniquely (up to flips/scale), pure-I sits at the maximally obstructed angle (defect 2t). (2) THE COLLAR-FRAME DECISION (26/26, THETA-CONVENTIONAL): no compiler-side demand distinguishes the theta_S sheet-swap frame within the 9-dim rule-gauge algebra -- five demand classes (mu4/C6, CAR/state, pencil/orientation, doily combinatorics, the round-59 census property) all COMPATIBLE-NOT-FORCING / SILENT-ON-ANGLE (the bare covariance tanh(beta u/2) A16 is exactly torus-invariant; the refined doily stabilizer is 9 OF 9; the round-59 spectra are constant on the orbit with closed forms tanh(1/2) / tanh^2(1/2)); the deployed parent (pure-I) PASSES strict collar RP EXACTLY in the integer-conjugated frame and fails at theta_S with defect 0.1 = 2t -- the round-58/59 strict-collar obstruction is FRAME-RELATIVE; the CXXXIX question closes as a compiler-FREEDOM theorem: freedom group = the rule-gauge frame orbit (tangent 7/9), selection quotient = the delta-circle, the only gauge-invariant datum of (frame, wiring) is the relative angle. (3) THE GAUGE-COVARIANCE AUDIT (21/21, RP-FRAME-COVARIANT, lead-ordered): theta' = g_int theta_S g_int^{-1} both directions exactly; the kernel-covariance law holds SYMBOLICALLY on the full torus (g^T A(V) g = A(g_C^T V g_B) identically), so strict-collar RP depends only on the relative angle delta (defect law 2t |a cos delta + c sin delta|); the pure-I exclusion is the lead's OPTION (2): a statement at the FIXED theta_S frame, NOT a wiring no-go; the Z/X exclusion IS genuinely orbit-invariant (det u frame-transport-invariant; the only det-flipping orthogonal element flips the vacuum and leaves the rule gauge). THE CANONICAL SENTENCE (frozen verbatim, sha 79950314): the compiler determines the wiring ORBIT; pure-I is a DEPLOYMENT REPRESENTATIVE; strict Hermiticity in the theta_S frame would select pure-J, the same demand in the integer-conjugated frame selects pure-I; a canonical wiring selection requires an ADDITIONALLY DERIVED physical frame. FORBIDDEN from now on: 'pure-I is compiler-forced' (and equivalents without the frame qualifier). HONEST SCOPE: the census covers the FIVE enumerated demand classes -- a compiler demand outside the list is not excluded; whether the actual seam physics derives a specific collar frame remains outside the formalized rules; the v898/v903 [O] premise stays [O]. Controls fire 6/6 + 6/6 + 5/5; exact integer/rational sympy, float64 only in disclosed wards, RNG only in declared controls. Zero RH content.

Original classification detail

CLOSED (DEPLOYMENT-CHOICE): exactly one admissible wiring component mod rule gauge; pure-I interior + integer-gauge-connected to pure-J; theta_S conventional (five demand classes silent); strict-collar RP exactly frame-covariant, exclusion = frame statement; Z/X exclusion orbit-invariant

Dependencies as recorded

SEAM.CFIN.NESS.PARENT.01; SEAM.CFIN.MARGINAL.STABILITY.01; SEAM.STATE.DERIVATION.01; v898; v903; v908