{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:XXIY5Z5K7HQGFCWLR6GPL2KP6O","short_pith_number":"pith:XXIY5Z5K","canonical_record":{"source":{"id":"2607.24238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-07-27T10:17:20Z","cross_cats_sorted":["math.AT","math.DG","math.MP"],"title_canon_sha256":"26a0bdeb1e8c03d2e4d06bb5aeb52a706d5b3eb35ad8cccc17327f8f45da015a","abstract_canon_sha256":"ed948f93f73ff78567eb04235e1ec964477b894fd9539743ef7f291f753be00e"},"schema_version":"1.0"},"canonical_sha256":"bdd18ee7aaf9e0628acb8f8cf5e94ff3b485c00f551dbd4a60a25c1bcba11dd5","source":{"kind":"arxiv","id":"2607.24238","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.24238","created_at":"2026-07-28T02:23:52Z"},{"alias_kind":"arxiv_version","alias_value":"2607.24238v1","created_at":"2026-07-28T02:23:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24238","created_at":"2026-07-28T02:23:52Z"},{"alias_kind":"pith_short_12","alias_value":"XXIY5Z5K7HQG","created_at":"2026-07-28T02:23:52Z"},{"alias_kind":"pith_short_16","alias_value":"XXIY5Z5K7HQGFCWL","created_at":"2026-07-28T02:23:52Z"},{"alias_kind":"pith_short_8","alias_value":"XXIY5Z5K","created_at":"2026-07-28T02:23:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:XXIY5Z5K7HQGFCWLR6GPL2KP6O","target":"record","payload":{"canonical_record":{"source":{"id":"2607.24238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-07-27T10:17:20Z","cross_cats_sorted":["math.AT","math.DG","math.MP"],"title_canon_sha256":"26a0bdeb1e8c03d2e4d06bb5aeb52a706d5b3eb35ad8cccc17327f8f45da015a","abstract_canon_sha256":"ed948f93f73ff78567eb04235e1ec964477b894fd9539743ef7f291f753be00e"},"schema_version":"1.0"},"canonical_sha256":"bdd18ee7aaf9e0628acb8f8cf5e94ff3b485c00f551dbd4a60a25c1bcba11dd5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T02:23:52.790175Z","signature_b64":"7KEINXV1wIkqDnFOsz1pVbfgkL1z6tMnwAZCxkZaS9t/4sVHemphMuCk0l/Lw5sx5hZfhvEAFpNeYHP0QYRdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdd18ee7aaf9e0628acb8f8cf5e94ff3b485c00f551dbd4a60a25c1bcba11dd5","last_reissued_at":"2026-07-28T02:23:52.789306Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T02:23:52.789306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.24238","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-28T02:23:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"boOMmqvQvZXYpLJBi+QomATsKF4VVSQWOj22cCH7yyNEOs8AaYI886lhNLTCVROhpao0ZUy76mEqWzRAkqJXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:07:51.474117Z"},"content_sha256":"8fe90aec2ee3ead4418ab372ff48a218d20bacd7d1f9101935e2d7af8bccda20","schema_version":"1.0","event_id":"sha256:8fe90aec2ee3ead4418ab372ff48a218d20bacd7d1f9101935e2d7af8bccda20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:XXIY5Z5K7HQGFCWLR6GPL2KP6O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Milnor metric for Morse--Smale flows from field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Giovanni Molinari, Michele Schiavina","submitted_at":"2026-07-27T10:17:20Z","abstract_excerpt":"We study the partition function of Abelian $BF$ theory with an axial gauge fixing condition given by a Morse--Smale vector field, and we show that it recovers the Milnor metric on the determinant line on the twisted cohomology of the manifold. To do this we use the Batalin--Vilkovisky formalism and, in particular, a BV pushforward to cohomology in two steps. In this context, the Milnor metric serves as the generalisation of the Ruelle dynamical zeta function evaluated at zero for systems containing both closed orbits and critical points. This, together with a classic result due to Schwarz on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24238","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24238/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-28T02:23:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/4em1V/52wdxZuQT2kKtUcWRmBYo/00vszq1N3ymMLZgi9Ju6p5AebR7RJuIB0cNd7ji5qi2Q6UaoyAc6CmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:07:51.474821Z"},"content_sha256":"d549432e8a8c63ae1bcf2e5f6d2c17fe13cbbdcd8acf0ea19218c16c8aa22f6c","schema_version":"1.0","event_id":"sha256:d549432e8a8c63ae1bcf2e5f6d2c17fe13cbbdcd8acf0ea19218c16c8aa22f6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XXIY5Z5K7HQGFCWLR6GPL2KP6O/bundle.json","state_url":"https://pith.science/pith/XXIY5Z5K7HQGFCWLR6GPL2KP6O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XXIY5Z5K7HQGFCWLR6GPL2KP6O/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T17:07:51Z","links":{"resolver":"https://pith.science/pith/XXIY5Z5K7HQGFCWLR6GPL2KP6O","bundle":"https://pith.science/pith/XXIY5Z5K7HQGFCWLR6GPL2KP6O/bundle.json","state":"https://pith.science/pith/XXIY5Z5K7HQGFCWLR6GPL2KP6O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XXIY5Z5K7HQGFCWLR6GPL2KP6O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XXIY5Z5K7HQGFCWLR6GPL2KP6O","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ed948f93f73ff78567eb04235e1ec964477b894fd9539743ef7f291f753be00e","cross_cats_sorted":["math.AT","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-07-27T10:17:20Z","title_canon_sha256":"26a0bdeb1e8c03d2e4d06bb5aeb52a706d5b3eb35ad8cccc17327f8f45da015a"},"schema_version":"1.0","source":{"id":"2607.24238","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.24238","created_at":"2026-07-28T02:23:52Z"},{"alias_kind":"arxiv_version","alias_value":"2607.24238v1","created_at":"2026-07-28T02:23:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24238","created_at":"2026-07-28T02:23:52Z"},{"alias_kind":"pith_short_12","alias_value":"XXIY5Z5K7HQG","created_at":"2026-07-28T02:23:52Z"},{"alias_kind":"pith_short_16","alias_value":"XXIY5Z5K7HQGFCWL","created_at":"2026-07-28T02:23:52Z"},{"alias_kind":"pith_short_8","alias_value":"XXIY5Z5K","created_at":"2026-07-28T02:23:52Z"}],"graph_snapshots":[{"event_id":"sha256:d549432e8a8c63ae1bcf2e5f6d2c17fe13cbbdcd8acf0ea19218c16c8aa22f6c","target":"graph","created_at":"2026-07-28T02:23:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.24238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the partition function of Abelian $BF$ theory with an axial gauge fixing condition given by a Morse--Smale vector field, and we show that it recovers the Milnor metric on the determinant line on the twisted cohomology of the manifold. To do this we use the Batalin--Vilkovisky formalism and, in particular, a BV pushforward to cohomology in two steps. In this context, the Milnor metric serves as the generalisation of the Ruelle dynamical zeta function evaluated at zero for systems containing both closed orbits and critical points. This, together with a classic result due to Schwarz on t","authors_text":"Giovanni Molinari, Michele Schiavina","cross_cats":["math.AT","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-07-27T10:17:20Z","title":"Milnor metric for Morse--Smale flows from field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24238","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8fe90aec2ee3ead4418ab372ff48a218d20bacd7d1f9101935e2d7af8bccda20","target":"record","created_at":"2026-07-28T02:23:52Z","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":"ed948f93f73ff78567eb04235e1ec964477b894fd9539743ef7f291f753be00e","cross_cats_sorted":["math.AT","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-07-27T10:17:20Z","title_canon_sha256":"26a0bdeb1e8c03d2e4d06bb5aeb52a706d5b3eb35ad8cccc17327f8f45da015a"},"schema_version":"1.0","source":{"id":"2607.24238","kind":"arxiv","version":1}},"canonical_sha256":"bdd18ee7aaf9e0628acb8f8cf5e94ff3b485c00f551dbd4a60a25c1bcba11dd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdd18ee7aaf9e0628acb8f8cf5e94ff3b485c00f551dbd4a60a25c1bcba11dd5","first_computed_at":"2026-07-28T02:23:52.789306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T02:23:52.789306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7KEINXV1wIkqDnFOsz1pVbfgkL1z6tMnwAZCxkZaS9t/4sVHemphMuCk0l/Lw5sx5hZfhvEAFpNeYHP0QYRdBg==","signature_status":"signed_v1","signed_at":"2026-07-28T02:23:52.790175Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.24238","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fe90aec2ee3ead4418ab372ff48a218d20bacd7d1f9101935e2d7af8bccda20","sha256:d549432e8a8c63ae1bcf2e5f6d2c17fe13cbbdcd8acf0ea19218c16c8aa22f6c"],"state_sha256":"01dcd1308d493a707272556afe5e97c1a9475b876308391487b09a0a4e7b4cd4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5qizx8PpoFxY2yxvhVEw0bqMkCOX1AF+b9vO8DuJM4FgJhVj5vleL7brpMzNk05NkEmQ0xJy29IRXoYE0OIjAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T17:07:51.480511Z","bundle_sha256":"7040ce398debdbfc14a0ed76f5a6c7682051c7508c8bc48c001070f91df146b8"}}