Established in scope
Quarter circle: absolute determinant1-i and joint Green/eta response
In the question: Automated construction of operator maps and sources
Supplied zero-mode-free angular circle operator with fixed spectral cut. Not the full physical TFPT source operator, not thermal occupation, and no identification of the diagnostic reference branch with D_ref. Transport periodic operator and source frames together when varying alpha.
Read the exact result, assumptions and evidence
Result
For supplied D_alpha, zeta quantization gives det D_alpha=1-exp(2pi i alpha), exactly1-i at alpha1/4 with eta(0)=1/2. The same operator gives G_-=i/(h-1), G_+=ih/(h-1), jumpi and retained holonomyh=i. The joint source derivative contains partial_alpha log det=pi cot(pi alpha)+i pi; the extra i pi is the eta contact term. The general determinant formula also retains zeta(K²;0).
Required assumptions
- Given angular quarter operator and zeta cut
Given a single circle operator D_alpha=-i partial_theta with f(2pi)=exp(2pi i alpha)f(0), 0<alpha<1, complex-fermion zeta quantization and negative eigenvalue argument +pi. The quarter source has alpha=1/4; alpha_ref=3/4 is a diagnostic comparison, not archival D_ref. Its angular Green propagation is not positive occupation covariance or already physical time evolution.
Original evidence
- PROOF.txt lines 327–366
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-collar-multifield-20261016/PROOF.txt
3537a2b080df0bb8b5d30c73da7dd83dc8e1ae5a6cfea4bb48a8b99f0080dfce
finding:quarter-circle-absolute-zeta-green-eta