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For constant symmetric kinetic matrices, this condition reduces to a commutation relation with the Hessian of the potential, yielding an orthogonal spectral decomposition of the configuration space.","weakest_assumption":"The kinetic matrices are constant and symmetric, which is required for the compatibility condition to reduce to a commutation relation with the Hessian (as stated in the abstract for the constant symmetric case)."}},"verdict_id":"7abf0d83-831e-4ca1-8a6d-612be4cf2620"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1ac39cec6a5ee46a94d3877ced9f5899d80de9e7c25ff6f290de8a5ee921f296","target":"record","created_at":"2026-05-20T00:01:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"81631051bb8e8cb3ace28d925648991259f3e72c4e78f07f4baa195d87c6afe7","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-15T07:01:35Z","title_canon_sha256":"8edc86f27dcab524da00d6d9e40e454f493ce909bb6c46c4943c99cb45dc540f"},"schema_version":"1.0","source":{"id":"2605.15679","kind":"arxiv","version":1}},"canonical_sha256":"f220ee627887cedb357d78376119b3a5c550438830ac467ba7a9d82bafd128da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f220ee627887cedb357d78376119b3a5c550438830ac467ba7a9d82bafd128da","first_computed_at":"2026-05-20T00:01:11.984610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:11.984610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"anL5AfmhYLHgUSHRCOvW4idADlHJ60rGzFBYkbJkcfWzPmjb5IdXdTQacx4r48C1k157acMJQuZ3Huac5YO8Aw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:11.985441Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15679","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ac39cec6a5ee46a94d3877ced9f5899d80de9e7c25ff6f290de8a5ee921f296","sha256:25cb258481516eb9fa1e0912c04227b76694790d25fa865a21c6b426ac03e6e1"],"state_sha256":"bbde0356d6cc270ae0170bd073237c21951aff960d97b905d7eaa199473d4fd8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SqCxlCaYRV7mfbU/FVCBAHjETZXHjqVXVXDXlRfvjwSrmGTTQIoBjQUDbEy6fcioF5Y33bfheAhD7rKlOS3aAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:44:08.855401Z","bundle_sha256":"7531b42c89b9ceccf5a1ad6768089451d35474fa5413fe9bc16a4fb88488cdcf"}}