{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:X6IK3CH7YFZGCELYNECTWH6ACK","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":"31c35830fa22fffb839f20fded317672795393b51539671aee2f0af0d819907e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-02-19T05:48:12Z","title_canon_sha256":"30b2f921b52a73c77d277c7ce83b273db84ff20b827c65678fa8e42e9900aa75"},"schema_version":"1.0","source":{"id":"2402.11854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.11854","created_at":"2026-07-05T07:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"2402.11854v1","created_at":"2026-07-05T07:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.11854","created_at":"2026-07-05T07:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"X6IK3CH7YFZG","created_at":"2026-07-05T07:46:45Z"},{"alias_kind":"pith_short_16","alias_value":"X6IK3CH7YFZGCELY","created_at":"2026-07-05T07:46:45Z"},{"alias_kind":"pith_short_8","alias_value":"X6IK3CH7","created_at":"2026-07-05T07:46:45Z"}],"graph_snapshots":[{"event_id":"sha256:e00b9e6d2736f11bd2e20ffd855f88ae8e86d0346048318061e676e397c35214","target":"graph","created_at":"2026-07-05T07:46:45Z","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/2402.11854/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a special family of distributional alpha-densities and give a transversality criterion stating when their product is defined, closely related to Hormander's criterion for general distributions. Moreover, we show that for the subspace of distributional half-densities in this family the distribution product naturally yields a pairing that extends the usual one on smooth half-densities.","authors_text":"Alan Weinstein, Benoit Dherin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-02-19T05:48:12Z","title":"Geometric States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.11854","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":"sha256:2a8ac09c2dcded4cbce2d6dcd7d082e9f8a59217ffe4ba1798028cb2d55b9270","target":"record","created_at":"2026-07-05T07:46:45Z","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":"31c35830fa22fffb839f20fded317672795393b51539671aee2f0af0d819907e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-02-19T05:48:12Z","title_canon_sha256":"30b2f921b52a73c77d277c7ce83b273db84ff20b827c65678fa8e42e9900aa75"},"schema_version":"1.0","source":{"id":"2402.11854","kind":"arxiv","version":1}},"canonical_sha256":"bf90ad88ffc17261117869053b1fc012b3466a44ec83e865e44a1a4414925a5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf90ad88ffc17261117869053b1fc012b3466a44ec83e865e44a1a4414925a5b","first_computed_at":"2026-07-05T07:46:45.364018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:46:45.364018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fl8+rq3sPo+/tQdkQvw7ornGGO/eBcxedo7vyD7C04jVPGBW8f4Dhb5pdVFCqWY9gOnbxpwpdQBQzOQtnavGAg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:46:45.364625Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.11854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a8ac09c2dcded4cbce2d6dcd7d082e9f8a59217ffe4ba1798028cb2d55b9270","sha256:e00b9e6d2736f11bd2e20ffd855f88ae8e86d0346048318061e676e397c35214"],"state_sha256":"eb6d62a7983d98d34127c51162209801a0c24eba38b3dfc2c5365d2aca0f4481"}