{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4XNUIF5XUKRV3Q2QTZWQNJ7CKE","short_pith_number":"pith:4XNUIF5X","canonical_record":{"source":{"id":"1312.0445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-12-02T13:26:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9cb8a4c00fc67db51ad4197afafbc4752d6d331dba31c04a44e4addf800a8279","abstract_canon_sha256":"1ebeff47d91bcdbf0b0907ba3411c90f4e96f733cfdca9b34d678920ca4019f1"},"schema_version":"1.0"},"canonical_sha256":"e5db4417b7a2a35dc3509e6d06a7e251233519d3156f626528b257fde4e6570b","source":{"kind":"arxiv","id":"1312.0445","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0445","created_at":"2026-05-18T00:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0445v1","created_at":"2026-05-18T00:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0445","created_at":"2026-05-18T00:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"4XNUIF5XUKRV","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4XNUIF5XUKRV3Q2Q","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4XNUIF5X","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4XNUIF5XUKRV3Q2QTZWQNJ7CKE","target":"record","payload":{"canonical_record":{"source":{"id":"1312.0445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-12-02T13:26:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9cb8a4c00fc67db51ad4197afafbc4752d6d331dba31c04a44e4addf800a8279","abstract_canon_sha256":"1ebeff47d91bcdbf0b0907ba3411c90f4e96f733cfdca9b34d678920ca4019f1"},"schema_version":"1.0"},"canonical_sha256":"e5db4417b7a2a35dc3509e6d06a7e251233519d3156f626528b257fde4e6570b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:54.142851Z","signature_b64":"415f0M6yK+3EWVxg9C5jwZnfxe9F7QWRqL6fYFEuUZDZg80x0I3N3i/oanvQRM7KPlCYoPLZzSC/AdMRybGfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5db4417b7a2a35dc3509e6d06a7e251233519d3156f626528b257fde4e6570b","last_reissued_at":"2026-05-18T00:29:54.142245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:54.142245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.0445","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":"2026-05-18T00:29:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UKQE3GApYX5eWaVY9h927PQjJFpb727SfYbI5lwQzpjdUuAjTaDxUNSkeS4RukakOktQ57FVskKm/NIuMTtDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T12:49:32.054530Z"},"content_sha256":"2561fa98fcfd171a2ce02c3e6318a8661527f463603372df5663cef56c0d62f7","schema_version":"1.0","event_id":"sha256:2561fa98fcfd171a2ce02c3e6318a8661527f463603372df5663cef56c0d62f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4XNUIF5XUKRV3Q2QTZWQNJ7CKE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Image of Abel-Jacobi map for hyperelliptic genus 3 and 4 curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Andrei Bogatyrev","submitted_at":"2013-12-02T13:26:49Z","abstract_excerpt":"For the evaluation and inversion of abelian integrals we show that the image of the Abel-Jacobi map of genus less than 5 hyperelliptic curve in its Jacobian is the intersection of shifted theta divisors with specified shifts. Therefore the image is a solution of a (slightly overdetermined) set of equations in the Jacobian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0445","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":"2026-05-18T00:29:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B918qnVzRQVaSzGYpqo9Qv8WYgt1kT1Y2/V0wlZRNq8PogKTvOUA5Nrq+X9hl+NKtw9jivH5WUfe5iQVLLNYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T12:49:32.054876Z"},"content_sha256":"3b7d8620b257f28316a7bedc7c775f1d1a9fe98004ed70f6fdaa92495f28d7ed","schema_version":"1.0","event_id":"sha256:3b7d8620b257f28316a7bedc7c775f1d1a9fe98004ed70f6fdaa92495f28d7ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XNUIF5XUKRV3Q2QTZWQNJ7CKE/bundle.json","state_url":"https://pith.science/pith/4XNUIF5XUKRV3Q2QTZWQNJ7CKE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XNUIF5XUKRV3Q2QTZWQNJ7CKE/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":"2026-06-21T12:49:32Z","links":{"resolver":"https://pith.science/pith/4XNUIF5XUKRV3Q2QTZWQNJ7CKE","bundle":"https://pith.science/pith/4XNUIF5XUKRV3Q2QTZWQNJ7CKE/bundle.json","state":"https://pith.science/pith/4XNUIF5XUKRV3Q2QTZWQNJ7CKE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XNUIF5XUKRV3Q2QTZWQNJ7CKE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4XNUIF5XUKRV3Q2QTZWQNJ7CKE","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":"1ebeff47d91bcdbf0b0907ba3411c90f4e96f733cfdca9b34d678920ca4019f1","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-12-02T13:26:49Z","title_canon_sha256":"9cb8a4c00fc67db51ad4197afafbc4752d6d331dba31c04a44e4addf800a8279"},"schema_version":"1.0","source":{"id":"1312.0445","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0445","created_at":"2026-05-18T00:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0445v1","created_at":"2026-05-18T00:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0445","created_at":"2026-05-18T00:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"4XNUIF5XUKRV","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4XNUIF5XUKRV3Q2Q","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4XNUIF5X","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:3b7d8620b257f28316a7bedc7c775f1d1a9fe98004ed70f6fdaa92495f28d7ed","target":"graph","created_at":"2026-05-18T00:29:54Z","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":"For the evaluation and inversion of abelian integrals we show that the image of the Abel-Jacobi map of genus less than 5 hyperelliptic curve in its Jacobian is the intersection of shifted theta divisors with specified shifts. Therefore the image is a solution of a (slightly overdetermined) set of equations in the Jacobian.","authors_text":"Andrei Bogatyrev","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-12-02T13:26:49Z","title":"Image of Abel-Jacobi map for hyperelliptic genus 3 and 4 curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0445","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":"sha256:2561fa98fcfd171a2ce02c3e6318a8661527f463603372df5663cef56c0d62f7","target":"record","created_at":"2026-05-18T00:29:54Z","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":"1ebeff47d91bcdbf0b0907ba3411c90f4e96f733cfdca9b34d678920ca4019f1","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-12-02T13:26:49Z","title_canon_sha256":"9cb8a4c00fc67db51ad4197afafbc4752d6d331dba31c04a44e4addf800a8279"},"schema_version":"1.0","source":{"id":"1312.0445","kind":"arxiv","version":1}},"canonical_sha256":"e5db4417b7a2a35dc3509e6d06a7e251233519d3156f626528b257fde4e6570b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5db4417b7a2a35dc3509e6d06a7e251233519d3156f626528b257fde4e6570b","first_computed_at":"2026-05-18T00:29:54.142245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:54.142245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"415f0M6yK+3EWVxg9C5jwZnfxe9F7QWRqL6fYFEuUZDZg80x0I3N3i/oanvQRM7KPlCYoPLZzSC/AdMRybGfCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:54.142851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0445","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2561fa98fcfd171a2ce02c3e6318a8661527f463603372df5663cef56c0d62f7","sha256:3b7d8620b257f28316a7bedc7c775f1d1a9fe98004ed70f6fdaa92495f28d7ed"],"state_sha256":"274199670b1413d662c32582f54021c225786d27dcbcf720aa9a8a4e5355fd94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9q6H7+DMEH6d7co59cBIOl2xnCW8mParRGuwz2gGRyFbMLT0JtkhUhBO3oI6IA9oTa90sdnx+R3p8AeBWjCPAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T12:49:32.056808Z","bundle_sha256":"555417f079eeec8d7d433c1dae207a6f4827ea6893264a7f77878ab8604cab3c"}}