Read the result in its research context.

Result

The original ramified spin frame converts the global lambda phase to the ordinary collar half-turn ±i, with the known ramification correction. The existing weighted Fuchs spin trace transports the given domain, corner powers and transmission into its genuine C3-equivariant image. The geometric R map carries this q image onto p and agrees with the whole Spin2 collar map. Its total descent operator is delta_c=Pc c*, not bare geometric c*. The canonical descended inversion has order four while the unquotiented global S0 lift has order twelve; sixth-power parity alone does not identify the representations. A geometric omega eigenline needs an actual inverse coefficient character to define an invariant tensor. The required inverse direction is already present in actual Pc; the full Hom result also closes coupled q/p signs without a naked parallel-line condition.

Required assumptions

• Do not identify source types

  Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.

• Complete data of both product-collar faces

  A selfadjoint B occurs in an exact normal-independent product equation. The full orthogonal L2 Cauchy graph projection of both labeled faces, their actual fiber identification and independently known positive normal length ell are supplied. Selection of these data from P1/P2 is not presumed.

• Geometric Clifford boundary with explicit changed complex structure

  Assume the existing free product class B=Gamma A or actual smooth tangential odd finite coefficient B_Phi=Z A-S Phi with total grading Z tensor gamma_F. Apply the standard Clifford boundary functor on the underlying real space with NEW complex structure Ical=i_old Gamma_tot and real structure C0=i_old gamma_n; the dual face has -C0. C0 is old-linear and new-antilinear,not identified with original charge J. This differs from full complex CAR quantization of both independent normal copies. State conclusions use the full graph as the actual quantum covariance in this functor. Its physical selection from P1/P2 is not presumed proved; Phi is a fixed classical background. Keep the fixed normal-independent product collar; a(theta) is smooth Hermitian and even,Phi(theta) smooth Hermitian and odd. No quantization of these bosonic backgrounds.

• Actual full v252 gauge lift and original P2 comparison

  Given the full unchanged v252 constructor pi,J_F,gamma_F,D_F and its symbolic Yukawa/Majorana inputs. Compare real gauge lift U=pi(u)J_F pi(u)J_F^-1 on the connected unimodular branch lambda det(m)=1 with original oriented P2 carrier E3+E2,Y=(-1/3)^3+(1/2)^2. No full Spin10 source action is presumed. A cyclically fixed neutral family line is considered only with an expressly supplied sigma=(123) and eigenvalue1; its original physical selection is not assumed.

• Recovered genus2 cover with retained coefficients

  Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.

• Unchanged A0* Fuchsian equation and actual C4 clock

  Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.

• Supplied split carrier with actual q sign lines on genus-two cover

  Given existing split carrier E3⊕E2 with unitary split connection onX and actual unitary flat q linesL0,L1,L2 on old coverC:w³=(z²−1)/(z²+1),η²=1−w⁶,product1 andπ*Fv117=L0⊕L1⊕L2. Pull these data toX×C and combine with declared alignment to mA slots. This does not selectX,E,mA or alignment as original P1 quantum source.

Original evidence

• GEOMETRIC-R-SPIN-COLLAR-REVIEW.txt lines 1–200

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/GEOMETRIC-R-SPIN-COLLAR-REVIEW.txt

  f41d9aa53c27d8e167ec82e7692f9367d073b287a157869a2a39a30114dfe164

• GEOMETRIC-R-SPIN-COLLAR-REVIEW.txt lines 201–224

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/GEOMETRIC-R-SPIN-COLLAR-REVIEW.txt

  f41d9aa53c27d8e167ec82e7692f9367d073b287a157869a2a39a30114dfe164

• NATIVE-SPIN2-ANNULUS-PULLBACK-REVIEW.txt lines 1–164

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/NATIVE-SPIN2-ANNULUS-PULLBACK-REVIEW.txt

  2bdb013daad58a696abf36d62a6d8c9d4e7f314cc167013502e38a3f3298f6ed

• ROOT-SPIN2-ANNULUS-CHECK.json lines 1–56

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-SPIN2-ANNULUS-CHECK.json

  fef9cb8cc0c9544063051719dfbd50b6617aeafb6c2b3afd98d3a7679a6c9b42

finding:geometric-spin-collar-map-closes-weighted-image-domain-with-total-deck-action