Established in scope
Eta phase alone does not identify needed spin/reference pair
In the question: Common clock sectors, quartic geometry and operational reconstruction
Convention/type check, not exclusion of a properly derived relative anomaly theory. No unchecked detailed erratum signs used.
Read the exact result, assumptions and evidence
Result
With lambda=detH0 tensor inverse detH1, positive theta determinant is inverse lambda; inverse Dai-Freed determinant is lambda in this convention. TFPT action factor exp(−i pi Delta eta/2) obeys a²=tau_rel^(-1) for vanishing kernels, not a=tau_rel. A Pfaffian application needs actual operator,real structure,kernel and orientation; generic gluing does not identify coefficients.
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.
Original evidence
- ETA-CONVENTION-AND-BOUNDARY-FACTOR.txt lines 1–73
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/boundary_origin_20261027/ETA-CONVENTION-AND-BOUNDARY-FACTOR.txt
198cc720a955d7f6ece859ee324e73fc6e2a2a7fcfc9d51f8eeca22142faeab1
finding:eta-phase-conventions-do-not-identify-relative-spin-reference-pair