{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZMIHZHXKXZ2FMYXK6FANUGR4Z6","short_pith_number":"pith:ZMIHZHXK","canonical_record":{"source":{"id":"1608.05321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-18T16:29:57Z","cross_cats_sorted":[],"title_canon_sha256":"4a593ec4594ef98aac9aa6e2b070c7646252ce46b3b465ec39baa70f36e38025","abstract_canon_sha256":"7208cc78f154a72ce2b6e784120f308eb3c000b2c11b0a667baf662a284b1ac8"},"schema_version":"1.0"},"canonical_sha256":"cb107c9eeabe745662eaf140da1a3ccfb401faed52738953bb4dfe4b361e32fd","source":{"kind":"arxiv","id":"1608.05321","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05321","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05321v1","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05321","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZMIHZHXKXZ2F","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZMIHZHXKXZ2FMYXK","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZMIHZHXK","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZMIHZHXKXZ2FMYXK6FANUGR4Z6","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-18T16:29:57Z","cross_cats_sorted":[],"title_canon_sha256":"4a593ec4594ef98aac9aa6e2b070c7646252ce46b3b465ec39baa70f36e38025","abstract_canon_sha256":"7208cc78f154a72ce2b6e784120f308eb3c000b2c11b0a667baf662a284b1ac8"},"schema_version":"1.0"},"canonical_sha256":"cb107c9eeabe745662eaf140da1a3ccfb401faed52738953bb4dfe4b361e32fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:31.379637Z","signature_b64":"TQhfsm8vdjarRbhOjUaeLqi2UjXpU7CZiAmrsskx5UIvDnd+zLO4WLt0ZNNQC7SW6c2hJOfxHq+lG7Ppm8TuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb107c9eeabe745662eaf140da1a3ccfb401faed52738953bb4dfe4b361e32fd","last_reissued_at":"2026-05-18T01:08:31.379047Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:31.379047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05321","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":"2026-05-18T01:08:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D2MYQcDeXxt6Gs8jEB5AdfYb6I8dhk4EsatY2TorcwNjE+wmJcTSeTZI9iURAPEYiFch/d1gcbAIpD/TiYvuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:44:24.896412Z"},"content_sha256":"50b2002f0f760df202128cdcb0b67a2ac628ac78a9750c5dc8b11a101c1605b4","schema_version":"1.0","event_id":"sha256:50b2002f0f760df202128cdcb0b67a2ac628ac78a9750c5dc8b11a101c1605b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZMIHZHXKXZ2FMYXK6FANUGR4Z6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Woods Hole trace formula and indices for vector fields and foliations on $\\mathbb{C}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Valente Ram\\'irez","submitted_at":"2016-08-18T16:29:57Z","abstract_excerpt":"The purpose of this work is to introduce the reader to the Woods Hole trace formula and to show how several well-known index theorems for foliations, vector fields and endomorphisms can be rephrased as particular cases of such formula. The main objective in doing this is to use the Woods Hole formula in the future to produce new index theorems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05321","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":""},"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":"2026-05-18T01:08:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZKkokTJNSpC3OvVD18lqYAFOsdxAFcFucKSe/EJC67Vgqt2OuOJf7R+aVZjswu2ydE3hdJc/NHldsxhFVquCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:44:24.896758Z"},"content_sha256":"f0ab3cf149357f0b3f72c6fbc453604a86b2df51446e0abb0abd566ce7285093","schema_version":"1.0","event_id":"sha256:f0ab3cf149357f0b3f72c6fbc453604a86b2df51446e0abb0abd566ce7285093"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZMIHZHXKXZ2FMYXK6FANUGR4Z6/bundle.json","state_url":"https://pith.science/pith/ZMIHZHXKXZ2FMYXK6FANUGR4Z6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZMIHZHXKXZ2FMYXK6FANUGR4Z6/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":"2026-06-12T01:44:24Z","links":{"resolver":"https://pith.science/pith/ZMIHZHXKXZ2FMYXK6FANUGR4Z6","bundle":"https://pith.science/pith/ZMIHZHXKXZ2FMYXK6FANUGR4Z6/bundle.json","state":"https://pith.science/pith/ZMIHZHXKXZ2FMYXK6FANUGR4Z6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZMIHZHXKXZ2FMYXK6FANUGR4Z6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZMIHZHXKXZ2FMYXK6FANUGR4Z6","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":"7208cc78f154a72ce2b6e784120f308eb3c000b2c11b0a667baf662a284b1ac8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-18T16:29:57Z","title_canon_sha256":"4a593ec4594ef98aac9aa6e2b070c7646252ce46b3b465ec39baa70f36e38025"},"schema_version":"1.0","source":{"id":"1608.05321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05321","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05321v1","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05321","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZMIHZHXKXZ2F","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZMIHZHXKXZ2FMYXK","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZMIHZHXK","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:f0ab3cf149357f0b3f72c6fbc453604a86b2df51446e0abb0abd566ce7285093","target":"graph","created_at":"2026-05-18T01:08:31Z","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":"The purpose of this work is to introduce the reader to the Woods Hole trace formula and to show how several well-known index theorems for foliations, vector fields and endomorphisms can be rephrased as particular cases of such formula. The main objective in doing this is to use the Woods Hole formula in the future to produce new index theorems.","authors_text":"Valente Ram\\'irez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-18T16:29:57Z","title":"The Woods Hole trace formula and indices for vector fields and foliations on $\\mathbb{C}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05321","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":"sha256:50b2002f0f760df202128cdcb0b67a2ac628ac78a9750c5dc8b11a101c1605b4","target":"record","created_at":"2026-05-18T01:08:31Z","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":"7208cc78f154a72ce2b6e784120f308eb3c000b2c11b0a667baf662a284b1ac8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-18T16:29:57Z","title_canon_sha256":"4a593ec4594ef98aac9aa6e2b070c7646252ce46b3b465ec39baa70f36e38025"},"schema_version":"1.0","source":{"id":"1608.05321","kind":"arxiv","version":1}},"canonical_sha256":"cb107c9eeabe745662eaf140da1a3ccfb401faed52738953bb4dfe4b361e32fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb107c9eeabe745662eaf140da1a3ccfb401faed52738953bb4dfe4b361e32fd","first_computed_at":"2026-05-18T01:08:31.379047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:31.379047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TQhfsm8vdjarRbhOjUaeLqi2UjXpU7CZiAmrsskx5UIvDnd+zLO4WLt0ZNNQC7SW6c2hJOfxHq+lG7Ppm8TuDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:31.379637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50b2002f0f760df202128cdcb0b67a2ac628ac78a9750c5dc8b11a101c1605b4","sha256:f0ab3cf149357f0b3f72c6fbc453604a86b2df51446e0abb0abd566ce7285093"],"state_sha256":"e0d80733f86db102e76017cd963b07edc842143dbe65588a0496e7957f54f8e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cN5XEcAaY833CCY5mvO9piYjOXpyUKowTi20Pe/ztTdiG/+Lk5VUfnKIWo4xYIqFhtvgD3F3Sa0rXYjtn0qmDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:44:24.898670Z","bundle_sha256":"15e988cd20c8d7aa4d0723ed7aa7423b08fcc08d13d8b52c3b04a9ef768374c8"}}