Established in scope
Massive transverse zero-index channels retain positive determinant response
In the question: Common clock sectors, quartic geometry and operational reconstruction
Explicit individual positive channel with actual two-dimensional block multiplicity. Spectral a is not electromagnetic alpha;not a refutation of the original alpha Ward identity. Full source must retain complement,measure,renormalization and Quillen connection,or prove cancellation. No supertrace replacing tr_adm or unjustified zeta multiplicativity.
Read the exact result, assumptions and evidence
Result
For lambda>0,det_zeta(B_a^2+lambda^2)/det_zeta(B_a0^2+lambda^2)=[cosh(2pi lambda)-cos(2pi a)]/[cosh(2pi lambda)-cos(2pi a0)]. Its logarithmic a derivative is2pi sin(2pi a)/[cosh(2pi lambda)-cos(2pi a)],strictly positive at a=1/4. Yet the corresponding +/-lambda block has zero spectral flow. Zero index therefore justifies neither constant positive response nor dropping the complement.
Required assumptions
- Positive determinant response of given transverse product channels
Compare positive scalar circle operators A_(a,lambda)=(-i partial_theta+a)^2+lambda^2,lambda>0,with common relative zeta normalization. a denotes spectral holonomy,not electromagnetic alpha. Actual two-dimensional block multiplicity is retained;separate infinite zeta factors require their own gluing/anomaly proof.
Original evidence
- NORMAL-INDEX-TRANSPORT.txt lines 174–224
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/NORMAL-INDEX-TRANSPORT.txt
f66b65fb9e23a2fe97c95ad924bd6ee39ea9c182111031392010cf4507620099
- TRANSVERSE-INDEX-EM-RESPONSE.txt lines 1–190
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/TRANSVERSE-INDEX-EM-RESPONSE.txt
1d8758b405532f5f1e31421be142bd2759bddc3e361072581f71945a56402036
- TRANSVERSE-INDEX-EM-RESPONSE.txt lines 191–390
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/TRANSVERSE-INDEX-EM-RESPONSE.txt
1d8758b405532f5f1e31421be142bd2759bddc3e361072581f71945a56402036
- check_normal_index_transport.py lines 1–95
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/check_normal_index_transport.py
c3335673ea0d790002b52f96b039b41a8758deed474b4477cb02c77e6bce81b8
- normal-index-transport-results.json lines 1–98
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/normal-index-transport-results.json
f895c5bf54a5a17b696feccb3134931e8ff1c6ece603495045e133f504cd60c8
finding:massive-transverse-zero-index-retains-positive-determinant-response