{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AH3CMO5EOM7EM6VZFM6BDO6ODR","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":"444ec4d511d1cf9e0a65845cf7f930a4686c7aed32c5cb27a6a4f1e1974fa856","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2023-12-19T11:24:43Z","title_canon_sha256":"6efaa3b2cce9436de37f2d22d0e83e94076c9b79ded4981b723069a0069a7d73"},"schema_version":"1.0","source":{"id":"2312.12061","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.12061","created_at":"2026-07-05T07:32:25Z"},{"alias_kind":"arxiv_version","alias_value":"2312.12061v2","created_at":"2026-07-05T07:32:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.12061","created_at":"2026-07-05T07:32:25Z"},{"alias_kind":"pith_short_12","alias_value":"AH3CMO5EOM7E","created_at":"2026-07-05T07:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"AH3CMO5EOM7EM6VZ","created_at":"2026-07-05T07:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"AH3CMO5E","created_at":"2026-07-05T07:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:bec9e5a58169b59dfc1281ca4176b38f0f0244f09b77fcc409e59c21b816ed9b","target":"graph","created_at":"2026-07-05T07:32:25Z","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/2312.12061/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Spectral flow was first studied by Atiyah and Lusztig, and first appeared in print in the work of Atiyah-Patodi-Singer (APS). For a norm-continuous path of self-adjoint Fredholm operators in the multiplier algebra $\\mathcal{M}(\\mathcal{B})$ with $\\mathcal{B}$ separable and stable, spectral flow roughly measures the ``net mass\" of spectrum that passes through zero in the positive direction, as we move along the continuous path. As the index of a Fredholm operator has had many fruitful and important generalizations to general operator algebras, generalizing the spectral flow of a path of self-ad","authors_text":"Arindam Sutradhar, Cangyuan Wang, Ping Wong Ng","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2023-12-19T11:24:43Z","title":"On spectral flow for operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.12061","kind":"arxiv","version":2},"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":"sha256:39cbb27f04be87ec8f767a9d33b1bba6d4c5eabb660e63961bb2dc664d195e1f","target":"record","created_at":"2026-07-05T07:32:25Z","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":"444ec4d511d1cf9e0a65845cf7f930a4686c7aed32c5cb27a6a4f1e1974fa856","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2023-12-19T11:24:43Z","title_canon_sha256":"6efaa3b2cce9436de37f2d22d0e83e94076c9b79ded4981b723069a0069a7d73"},"schema_version":"1.0","source":{"id":"2312.12061","kind":"arxiv","version":2}},"canonical_sha256":"01f6263ba4733e467ab92b3c11bbce1c45d91c7b4e81b9a5f97a22ba64222007","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01f6263ba4733e467ab92b3c11bbce1c45d91c7b4e81b9a5f97a22ba64222007","first_computed_at":"2026-07-05T07:32:25.946979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:32:25.946979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r90RaRm/idIfGvYIKG50FPPqDz1v46CVk8RDUTQb9SdtWyVC3Lc9nDTEAULl+j1j20DdUZWrJyLqqwM+gwutCA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:32:25.947465Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.12061","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39cbb27f04be87ec8f767a9d33b1bba6d4c5eabb660e63961bb2dc664d195e1f","sha256:bec9e5a58169b59dfc1281ca4176b38f0f0244f09b77fcc409e59c21b816ed9b"],"state_sha256":"b5dea9c90346e273a1a546fb8a10fb66b0744d3544ff5f342e505d9faf58212d"}