Established in scope
Absolute thermal sea regularization retains central phase
In the question: Automated construction of operator maps and sources
Conditional absolute extension of the supplied single chiral source. Regularization is input; neither subtraction nor bulk/eta cancellation of the central phase is proved from P1/P2. Angular determinant and thermal partition sum are different functionals. The finite excitation-product control already retains the full regularized sea term. The response is twist-conjugate spectral charge, not a new physical event law.
Read the exact result, assumptions and evidence
Result
The declared Abel/zeta subtraction gives E_sea=-1/96. At beta=2ell=8log4, q_beta=1/65536 and Z_beta[0]=exp(-beta E_sea) times the complete particle/hole product. Its two-mode factor is2^(1/6)69649/65536. Adjoint field action stays i/-i; the absolute time-loop operator additionally carries exp(-i pi/48). Existing tail bounds apply at the same beta. Under the same Hurwitz prescription E_sea=eta(0)^2/8-1/24 and d_alpha E_sea=-eta(0)/2. The logarithmic alpha derivative of the unnormalized thermal partition sum agrees with the occupation response including the sea term, checked by an independent Fock trace and explicit derivative tail bound. The resulting actual reference amplitude2^(1/12) passes the existing CLI moment search with206 source moments; the same data with reference amplitude1 are infeasible. This is a numerical software control under the same supplied regularization.
Required assumptions
- Given chiral source in both quarter domains
D_alpha=-i∂theta on f(theta+2pi)=exp(2pi i alpha)f(theta), filled negative spectrum and relative particle/hole excitation time; alpha=1/4,3/4. This compares two conjugate domains, not opposite charges in one fixed domain or all P1 sources.
- Charged CAR algebra and original negative sea
Assume the actual field algebra is charged CAR(H) and its reference state is the pure quasifree sea with occupation 1−C. Relative charge and positive excitation time are normal ordered against this sea. This physical identification is an additional premise.
- Explicit Abel subtraction of chiral sea
For the already given single chiral particle/hole source, use the exponential Abel sum of negative sea energies and subtract only its -1/epsilon² term. This is a declared absolute regularization; its selection and compensation of the central loop phase by an original eta/bulk contribution are not presumed consequences of P1/P2.
- 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 368–411
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-collar-multifield-20261016/PROOF.txt
3537a2b080df0bb8b5d30c73da7dd83dc8e1ae5a6cfea4bb48a8b99f0080dfce
- PROOF.txt lines 431–445
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-collar-multifield-20261016/PROOF.txt
3537a2b080df0bb8b5d30c73da7dd83dc8e1ae5a6cfea4bb48a8b99f0080dfce
finding:quarter-sea-absolute-thermal-central-phase