Established in scope
Local Cayley map transports chirality with a nontrivial Jacobian
In the question: Craig chiral measure and the original whole TFPT source
Compatible finite field spaces or common invertible domain only; no global field map, locality/RP derivation, or physical measure identity.16 symbolic controls and direct Craig operator checks executed; no Lean validation.
Read the exact result, assumptions and evidence
Result
For gamma5 Hermitian GW D, A=1-D/2 intertwines modified and ordinary chirality. On an invertible domain Kreq=D A^-1 is chirally odd and anti-Hermitian and Kreq A=D. Source legs, Yukawa insertions and the actual Majorana pairing must all be transported. The restricted chiral Berezin Jacobian cannot be discarded: an exact algebraic example yields different background factors4/5 and1/2. This does not identify original TFPT K with Kreq.
Required assumptions
- Compatible GW operator and Berezin domain
Mathematical scope: finite gamma5 Hermitian GW operator with coefficient1 and actual compatible ordered fermion spaces. Inverse formulas apply only on a common invertible domain; fulfillment by the original TFPT source 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
- SOURCE-BRIDGE.txt lines 103–160
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/craig-original-source-bridge-20261103/SOURCE-BRIDGE.txt
694457a0ccad7a4cbe46e3dec97e364ef085e8d0bad2c9112e684d1dcd3200e4
finding:craig-local-cayley-transport-needs-full-chiral-jacobian