{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:B733HOI6TNSV4YHQFDMLSMUZCO","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":"24fa20116822a98acde88aa39e43ce70810997aebe1865229835360844ff54b4","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-04-21T09:52:39Z","title_canon_sha256":"5c922b849cc722f4b604612a605af053c586f4d5f72a84f0b58849e9caa14f68"},"schema_version":"1.0","source":{"id":"0804.3258","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.3258","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"arxiv_version","alias_value":"0804.3258v7","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.3258","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"pith_short_12","alias_value":"B733HOI6TNSV","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"B733HOI6TNSV4YHQ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"B733HOI6","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:5de78347fcb9a40717dde0aed3f29bd134fe1fc8f432ab487c3e68002da087c8","target":"graph","created_at":"2026-05-18T04:41:35Z","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"},"paper":{"abstract_excerpt":"We define a local Riemann-Roch number for an open symplectic manifold when a complete integrable system without Bohr-Sommerfeld fiber is provided on its end. In particular when a structure of a singular Lagrangian fibration is given on a closed symplectic manifold, its Riemann-Roch number is described as the sum of the number of nonsingular Bohr-Sommerfeld fibers and a contribution of the singular fibers. A key step of the proof is formally explained as a version of Witten's deformation applied to a Hilbert bundle.","authors_text":"Hajime Fujita, Mikio Furuta, Takahiko Yoshida","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-04-21T09:52:39Z","title":"Torus fibrations and localization of index I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.3258","kind":"arxiv","version":7},"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":"sha256:3175cf8795a0cf8fa3f2fd9c99bf543293fb6b50adaea5cdae0f260234ffa91b","target":"record","created_at":"2026-05-18T04:41:35Z","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":"24fa20116822a98acde88aa39e43ce70810997aebe1865229835360844ff54b4","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-04-21T09:52:39Z","title_canon_sha256":"5c922b849cc722f4b604612a605af053c586f4d5f72a84f0b58849e9caa14f68"},"schema_version":"1.0","source":{"id":"0804.3258","kind":"arxiv","version":7}},"canonical_sha256":"0ff7b3b91e9b655e60f028d8b932991393af18ed99ff887572df340ad263f362","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ff7b3b91e9b655e60f028d8b932991393af18ed99ff887572df340ad263f362","first_computed_at":"2026-05-18T04:41:35.169863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:35.169863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u5grzLal1V3bZflqTTjWegwEQa8AyPrxSKvvIDRqZsv36DJQqu5QeznESgSEz7aM84DwNcdsDF90LkeqUePHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:35.170278Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.3258","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3175cf8795a0cf8fa3f2fd9c99bf543293fb6b50adaea5cdae0f260234ffa91b","sha256:5de78347fcb9a40717dde0aed3f29bd134fe1fc8f432ab487c3e68002da087c8"],"state_sha256":"419b16fdcc9a17ac8d8769d29e5d874eff5ca351a11647be85521c5253e8f77f"}