Established in scope
Periodic zero modes distinguish original covariance and Slater choice
In the question: Origin reverse selection, field dictionary and original P1 kernel
Exact finite original case. No nonexistence of B_N, selected continuum state or E8 refutation. Previous energy test uses twist1 without zero modes and is unchanged. Numerical norm diagnostics normal and -OO byte-identical; independent proof review and rerun accepted.
Read the exact result, assumptions and evidence
Result
On unchanged v988 Nx16 Ny6 M1, explicit integral boundary zero vectors, modular ranks over F65537 and exact sign pairing prove ranks190/192/192/192. Periodic counts are95 negative,95 positive,2 zero; other twists96/96/0. Original covariance C=Pminus+Pi0/2 differs from pure occ_frame projector P=Pminus+Q with rankQ1 in the nullspace: norm(C-P)HS²=1/2 and norm(C-C²)HS²=1/8. Both original functions are valid and deliberately distinct. A state-preserving microscopic dictionary cannot silently exchange these periodic states.
Required assumptions
- Actual periodic v988 state and occupied frame
Keep unchanged qwz_cylinder, occ_frame and fermi_cov at Nx16 Ny6 M1 and original twists0,1,2,3. Compare their actual finite CAR covariances. Physical selection of either state or equality with the E8 vacuum is not assumed.
- 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
- MICROSCOPIC-STATE.txt lines 1–82
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-source-reconstruction-20261024/MICROSCOPIC-STATE.txt
40359e2205b27adcd96bdbcc61d8adcc1a2788562df85058c076b8aac2d3b209
- microscopic_state_audit.py lines 20–108
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-source-reconstruction-20261024/microscopic_state_audit.py
eb8dad78cc685d2951f9aec22966a622773c0d50e1ebd1706ef86a71320a9b6f
- v988_psi_lambda_reduction.py lines 75–106
Source checked at this snapshot
Original location and fingerprint
verification/v988_psi_lambda_reduction.py
eae02e79be5703ccec67f1f11470e3ffd99895b17575c9ce1d553720bd1752cd
finding:periodic-microscopic-zero-modes-distinguish-source-state