Established in scope
Fixed free product kernel differs from Craig at finite spacing
In the question: Craig chiral measure and the original whole TFPT source
Exact counterexample to the specified unblocked ordinary product identification at the stated momentum. No exclusion of derived nonunitary blocking, other regulators, continuum equivalence or TFPT; no already produced TFPT lattice kernel assumed.
Read the exact result, assumptions and evidence
Result
At the same free p=(pi/2,0,0,0),a1 the ordinary product gives K=i gamma1 pi/2, actual Craig D=1+i gamma1 and Cayley-required D(1-D/2)^-1=2i gamma1. The fixed Cayley identity fails. Nor can a two-sided unitary chiral map identify the distinct singular values pi/2 and sqrt2. A_-^dagger A_-=I2/2 yields Berezin Jacobian magnitude2 per two-dimensional Weyl fiber with unchanged anti-leg. This example and an independently formed product action do not compute the whole original TFPT measure identity.
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.
- 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.
Original evidence
- ACTUAL-PRODUCT-PAIRING.txt lines 1–169
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/craig-original-source-bridge-20261103/ACTUAL-PRODUCT-PAIRING.txt
e7200e2d30179214f0a63c856c3598cbffab7013d8747cc5b7f00f4beca96817
finding:craig-fixed-product-free-operator-equality-fails