Established in scope
Oriented sewing continuation and genuine reversal satisfy distinct exact compositions
In the question: Common clock sectors, quartic geometry and operational reconstruction
Marked spin transport and existing two-object vertex functor. Full open P1 amplitude functor,its determinant line and identification of U_Gamma with normal spin transport remain to derive. No identification of group orders or two-object set with physical spacetime.
Read the exact result, assumptions and evidence
Result
alpha01=T,genuine reversal T^-1,continued positive quarter alpha10=beta0 T^-1. Hence alpha10 alpha01=beta0 and alpha01 alpha10=beta1,whereas forward/reverse yields1. Normalized central cocycle omega(1,1)=beta describes nonsplit1->C4->C8->C2 over mu4,with correct adjoint and defect-line dualization. Positive local spin quarter lift squares to+i independently of lift sign,matching marked q norm factor. Literal unextended D4 reflection s²=1 cannot map to alpha²=beta.
Required assumptions
- Marked oriented quarter spin and two-object vertex transport
Positively oriented marked quarter turn z->iz of normal two-plane with Spin(2) lift a=+/-exp(i pi/4),a²=i; existing genus2 source (C,S0,Dq,Q) and selected beta; existing lattice vertex objects F0,F1,unitary T:F0->F1 and beta1=T beta0 T^-1. Continued oriented quarter step and geometric reversal remain distinct arrows. An open P1 amplitude functor is not assumed.
- 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.
Original evidence
- SEWING-FUNCTOR-COCYCLE-TEST.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/dynamic_reconstruction_20261027/SEWING-FUNCTOR-COCYCLE-TEST.txt
6a20e16b3b8b58b44317b85707a896b6c1f03badedf30d7846180b22439ab489
- SEWING-FUNCTOR-COCYCLE-TEST.txt lines 201–378
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/dynamic_reconstruction_20261027/SEWING-FUNCTOR-COCYCLE-TEST.txt
6a20e16b3b8b58b44317b85707a896b6c1f03badedf30d7846180b22439ab489
- RELATIONAL-FOLD-AND-EMERGENT-E8.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/dynamic_reconstruction_20261027/RELATIONAL-FOLD-AND-EMERGENT-E8.txt
cf7ba7cfe48ac93486d3e9eedc1f8c2a11eb5dafd439e7acf6ea49e330bbcdd0
- RELATIONAL-FOLD-AND-EMERGENT-E8.txt lines 201–400
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/dynamic_reconstruction_20261027/RELATIONAL-FOLD-AND-EMERGENT-E8.txt
cf7ba7cfe48ac93486d3e9eedc1f8c2a11eb5dafd439e7acf6ea49e330bbcdd0
- RELATIONAL-FOLD-AND-EMERGENT-E8.txt lines 401–404
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/dynamic_reconstruction_20261027/RELATIONAL-FOLD-AND-EMERGENT-E8.txt
cf7ba7cfe48ac93486d3e9eedc1f8c2a11eb5dafd439e7acf6ea49e330bbcdd0
finding:oriented-sewing-cocycle-distinguishes-continuation-and-reversal