Established in scope
Exact moving-kernel reduction forces the off-diagonal Kato connection
In the question: Common clock sectors, quartic geometry and operational reconstruction
Complete classification at the explicitly fixed scalar principal symbol,not all P1 sources. Applies standard Kato structure;no general mathematical novelty. Neither the term nor its diagonal phases is physically selected. No adiabatic approximation is declared exact reduction;normal domains and field statistics remain separate prerequisites.
Read the exact result, assumptions and evidence
Result
For the entire given matrix first-order class,P reduces selfadjoint B_A iff -iP_prime+[A,P]=0,equivalently A=i[P_prime,P]+PAP+QAQ. Both Hermitian diagonal blocks remain free. For rankone and smooth periodic frame chi,V f=chi f gives the exact whole-H1 intertwiner with a_eff=chi* A chi-i chi*chi_prime,hence full Borel functional calculus. For unchanged scalar A=aI,reduction forces P_prime=0.
Required assumptions
- Smooth matrix circle source and moving projector at fixed scalar principal symbol
Given comparison class:H=L2(S1,C^r),B_A=-i partial_theta+A(theta),Dom=H1_per,A smooth periodic Hermitian,P(theta) smooth periodic orthogonal of fixed rank. P is a fiber family,not an executed measurement. Neither P nor A is selected from P1. A real normal operator family additionally needs its own common domains and field map.
- 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
- NORMAL-CONNECTION-MARKS-COVER.txt lines 1–76
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/NORMAL-CONNECTION-MARKS-COVER.txt
33448654daa781525df039173b862274036f8ef2c267865afec6555c12b4c9de
- NORMAL-INDEX-TRANSPORT.txt lines 49–132
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/NORMAL-INDEX-TRANSPORT.txt
f66b65fb9e23a2fe97c95ad924bd6ee39ea9c182111031392010cf4507620099
- check_normal_connection_marks.py lines 1–118
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/check_normal_connection_marks.py
9ab96cb0dc52bbc3e05b01ad4ab1ea6692cf574b86247226a2d18f7310ffbe5a
- normal-connection-marks-results.json lines 1–106
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/normal-connection-marks-results.json
f5f155dccfe808870db7c95fd650dc2aba34bdbf5752bb930a6220b703dcbf75
finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection