{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VPP47ZQ6HO6M4CNLNI64SXDHRE","short_pith_number":"pith:VPP47ZQ6","canonical_record":{"source":{"id":"1205.1490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-05-07T19:40:41Z","cross_cats_sorted":[],"title_canon_sha256":"0d6621acac6239bca41b7dbd2fcc7a1fa521bd98a7fa9f08cb62c0b20c05e179","abstract_canon_sha256":"279ac926207f729f29bef449ff195ce28eeffa8ad559077f04b946f897d6b6eb"},"schema_version":"1.0"},"canonical_sha256":"abdfcfe61e3bbcce09ab6a3dc95c67890b6622101d1ebe08ac855c3a2734fb09","source":{"kind":"arxiv","id":"1205.1490","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1490","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1490v1","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1490","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"VPP47ZQ6HO6M","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VPP47ZQ6HO6M4CNL","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VPP47ZQ6","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VPP47ZQ6HO6M4CNLNI64SXDHRE","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-05-07T19:40:41Z","cross_cats_sorted":[],"title_canon_sha256":"0d6621acac6239bca41b7dbd2fcc7a1fa521bd98a7fa9f08cb62c0b20c05e179","abstract_canon_sha256":"279ac926207f729f29bef449ff195ce28eeffa8ad559077f04b946f897d6b6eb"},"schema_version":"1.0"},"canonical_sha256":"abdfcfe61e3bbcce09ab6a3dc95c67890b6622101d1ebe08ac855c3a2734fb09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:11.052555Z","signature_b64":"vJfUqpf3UHJxUqMcslK7PVPnQz2LjfP/oqhaNAyRTICZchhYf1GJp8yEEXuf5OhZFTEsz6vo1sZvgmlvTbALAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abdfcfe61e3bbcce09ab6a3dc95c67890b6622101d1ebe08ac855c3a2734fb09","last_reissued_at":"2026-05-18T03:56:11.051737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:11.051737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1490","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":"2026-05-18T03:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"755mr3BOm0GnqTNTIZWyke99xOUCKwYV5Z7fkDHbqvol+OlI0k4ftmZFXiGfUVPE5YDZwkNK0Z9HYh87LVbvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:29:55.801095Z"},"content_sha256":"3389a74352f72800379ea1ab564a6b512d738c4fe69f9d4c740b87518259a0e9","schema_version":"1.0","event_id":"sha256:3389a74352f72800379ea1ab564a6b512d738c4fe69f9d4c740b87518259a0e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VPP47ZQ6HO6M4CNLNI64SXDHRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local GW Invariants of Elliptic Multiple Fibers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Junho Lee","submitted_at":"2012-05-07T19:40:41Z","abstract_excerpt":"We use simple geometric arguments to calculate the dimension zero local Gromov-Witten invariants of elliptic multiple fibers. This completes the calculation of all dimension zero GW invariants of elliptic surfaces with $p_g>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1490","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":"2026-05-18T03:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r6Xnsgwjj3cKOydir7vYaspFlIAxiT51Jgvzl3YU7IlnoNXbrIx+/lrIrrQZMuOOY+N+5D5VfFj3shT8HndGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:29:55.801441Z"},"content_sha256":"1eb6f3ce6cb3f3a043378e75364a41f32f3d09f73bb96eb6fc3c566146b5842e","schema_version":"1.0","event_id":"sha256:1eb6f3ce6cb3f3a043378e75364a41f32f3d09f73bb96eb6fc3c566146b5842e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VPP47ZQ6HO6M4CNLNI64SXDHRE/bundle.json","state_url":"https://pith.science/pith/VPP47ZQ6HO6M4CNLNI64SXDHRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VPP47ZQ6HO6M4CNLNI64SXDHRE/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":"2026-06-09T00:29:55Z","links":{"resolver":"https://pith.science/pith/VPP47ZQ6HO6M4CNLNI64SXDHRE","bundle":"https://pith.science/pith/VPP47ZQ6HO6M4CNLNI64SXDHRE/bundle.json","state":"https://pith.science/pith/VPP47ZQ6HO6M4CNLNI64SXDHRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VPP47ZQ6HO6M4CNLNI64SXDHRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VPP47ZQ6HO6M4CNLNI64SXDHRE","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":"279ac926207f729f29bef449ff195ce28eeffa8ad559077f04b946f897d6b6eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-05-07T19:40:41Z","title_canon_sha256":"0d6621acac6239bca41b7dbd2fcc7a1fa521bd98a7fa9f08cb62c0b20c05e179"},"schema_version":"1.0","source":{"id":"1205.1490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1490","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1490v1","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1490","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"VPP47ZQ6HO6M","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VPP47ZQ6HO6M4CNL","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VPP47ZQ6","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:1eb6f3ce6cb3f3a043378e75364a41f32f3d09f73bb96eb6fc3c566146b5842e","target":"graph","created_at":"2026-05-18T03:56:11Z","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 use simple geometric arguments to calculate the dimension zero local Gromov-Witten invariants of elliptic multiple fibers. This completes the calculation of all dimension zero GW invariants of elliptic surfaces with $p_g>0$.","authors_text":"Junho Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-05-07T19:40:41Z","title":"Local GW Invariants of Elliptic Multiple Fibers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1490","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":"sha256:3389a74352f72800379ea1ab564a6b512d738c4fe69f9d4c740b87518259a0e9","target":"record","created_at":"2026-05-18T03:56:11Z","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":"279ac926207f729f29bef449ff195ce28eeffa8ad559077f04b946f897d6b6eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-05-07T19:40:41Z","title_canon_sha256":"0d6621acac6239bca41b7dbd2fcc7a1fa521bd98a7fa9f08cb62c0b20c05e179"},"schema_version":"1.0","source":{"id":"1205.1490","kind":"arxiv","version":1}},"canonical_sha256":"abdfcfe61e3bbcce09ab6a3dc95c67890b6622101d1ebe08ac855c3a2734fb09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abdfcfe61e3bbcce09ab6a3dc95c67890b6622101d1ebe08ac855c3a2734fb09","first_computed_at":"2026-05-18T03:56:11.051737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:11.051737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vJfUqpf3UHJxUqMcslK7PVPnQz2LjfP/oqhaNAyRTICZchhYf1GJp8yEEXuf5OhZFTEsz6vo1sZvgmlvTbALAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:11.052555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3389a74352f72800379ea1ab564a6b512d738c4fe69f9d4c740b87518259a0e9","sha256:1eb6f3ce6cb3f3a043378e75364a41f32f3d09f73bb96eb6fc3c566146b5842e"],"state_sha256":"383dbef5a6848b40f6f4612dd979907292d227d47c46ef6256c483b3c4ea3977"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ot7Fo50ykcHzxtndZQPbimlAYX2VIRYh0GpAG9jIt+OqyxEa2tV7s1kZ0+sz8xkMTHqRA/kBAjaFP9lpi8SiDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T00:29:55.803252Z","bundle_sha256":"c666c5d506d5951b77c51392b7bc3eedaaca8dec44b6cbbd34c8df371f435cd8"}}