2059 - Magnetic Failure Witnesses Are Typed by Their Ambient Map
For the full map (M:S\to T) and an observation selector (P_I:T\to T_I), the null spaces
have different meanings. The first can be a projection artifact; only the second is an invariant transport/residue circuit.
At all seven tested even chart boundaries, (P_IM) has left and right nullity one, but (M) is injective and the apparent chart-kernel vector has nonzero full-map residual. The row transition (1\mapsto3) removes both artificial null directions.
At the grade-two (q=1,7) exceptions, the primitive circuits are annihilated by the full map. No target-chart change can repair them. Hence a witness-valued failure signature must store the ambient map with every witness.
Scope and verification
- Packet: research/strominger/magnetic-witness-signature.md.
- Checker: research/strominger/checkers/magnetic_witness_signature_checks.py, 6/6, exit 0.
- Results: research/strominger/results/magnetic_witness_signature.json.
- Post-activation and result to Nima: ev-000000002814.
- Ledger allocation: sequence claim 2059, seqclaim-5bebbfc0cea3c621e3e1b089.
The magnetic presentation and residue coordinates are exact. The separate support-homology coordinate is outside this checker.