{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VNOPJSAIRJ65XHQJWCFUKKMN6J","short_pith_number":"pith:VNOPJSAI","canonical_record":{"source":{"id":"1010.0398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-03T12:48:56Z","cross_cats_sorted":[],"title_canon_sha256":"03b0397d3aadfb84c35125008cff86afdd93dae18c638c6b54039cfbecb3aa53","abstract_canon_sha256":"619e23a10df3aa321fcd388acf9cbff33ae87a3b80ad1db2952e221c4d1f8d5a"},"schema_version":"1.0"},"canonical_sha256":"ab5cf4c8088a7ddb9e09b08b45298df24b4dc1d4f358939006d5e801228811bb","source":{"kind":"arxiv","id":"1010.0398","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0398","created_at":"2026-05-18T04:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0398v2","created_at":"2026-05-18T04:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0398","created_at":"2026-05-18T04:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"VNOPJSAIRJ65","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VNOPJSAIRJ65XHQJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VNOPJSAI","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VNOPJSAIRJ65XHQJWCFUKKMN6J","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-03T12:48:56Z","cross_cats_sorted":[],"title_canon_sha256":"03b0397d3aadfb84c35125008cff86afdd93dae18c638c6b54039cfbecb3aa53","abstract_canon_sha256":"619e23a10df3aa321fcd388acf9cbff33ae87a3b80ad1db2952e221c4d1f8d5a"},"schema_version":"1.0"},"canonical_sha256":"ab5cf4c8088a7ddb9e09b08b45298df24b4dc1d4f358939006d5e801228811bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:40.874584Z","signature_b64":"ojoBkKlv9yX3A0MCC3ohCJmxQPUgD+a0847YLvsNGQSLIXrRYyIKkylaDqptXu7PojFftPKaFiB4iAVuKiXOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab5cf4c8088a7ddb9e09b08b45298df24b4dc1d4f358939006d5e801228811bb","last_reissued_at":"2026-05-18T04:16:40.873932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:40.873932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0398","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0HA0kEnNvt2ygotW3RDxLSvz1crCJiNhP0hBZjQEizlwNNv00ljuEkNL8vJQo8otIpnAkixRnBsPhasEVroAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:30:54.838422Z"},"content_sha256":"b3fe06687b6b9161418fcc049eaf0244e99179804955248cc77c938e6aea3579","schema_version":"1.0","event_id":"sha256:b3fe06687b6b9161418fcc049eaf0244e99179804955248cc77c938e6aea3579"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VNOPJSAIRJ65XHQJWCFUKKMN6J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theta-duality on Prym varieties and a Torelli Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Juan Carlos Naranjo, Mart\\'i Lahoz","submitted_at":"2010-10-03T12:48:56Z","abstract_excerpt":"Let p:C' -> C be an unramified double covering of irreducible smooth curves and let P be the attached Prym variety. We prove the schematic theta-dual equalities in the Prym variety T(C')=V^2 and T(V^2)=C', where V^2 is the Brill-Noether locus of P associated to p considered by Welters. As an application we prove a Torelli Theorem analogous to the fact that the g-th symmetric product of a curve D of genus g determines the curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0398","kind":"arxiv","version":2},"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":"2026-05-18T04:16:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WfhmaBg7bVjKL9L0egmMPkNsIiIsKezQLJHRHB1VysyTUmnFD8QcFjmibOS+3CuM7am1oApsABxabI1Dca6mDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:30:54.838823Z"},"content_sha256":"fc14469872a649afb0c7411f1db6338de62f9fe05b4eb057bcc439e9348d0636","schema_version":"1.0","event_id":"sha256:fc14469872a649afb0c7411f1db6338de62f9fe05b4eb057bcc439e9348d0636"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VNOPJSAIRJ65XHQJWCFUKKMN6J/bundle.json","state_url":"https://pith.science/pith/VNOPJSAIRJ65XHQJWCFUKKMN6J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VNOPJSAIRJ65XHQJWCFUKKMN6J/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":"2026-05-28T10:30:54Z","links":{"resolver":"https://pith.science/pith/VNOPJSAIRJ65XHQJWCFUKKMN6J","bundle":"https://pith.science/pith/VNOPJSAIRJ65XHQJWCFUKKMN6J/bundle.json","state":"https://pith.science/pith/VNOPJSAIRJ65XHQJWCFUKKMN6J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VNOPJSAIRJ65XHQJWCFUKKMN6J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VNOPJSAIRJ65XHQJWCFUKKMN6J","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":"619e23a10df3aa321fcd388acf9cbff33ae87a3b80ad1db2952e221c4d1f8d5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-03T12:48:56Z","title_canon_sha256":"03b0397d3aadfb84c35125008cff86afdd93dae18c638c6b54039cfbecb3aa53"},"schema_version":"1.0","source":{"id":"1010.0398","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0398","created_at":"2026-05-18T04:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0398v2","created_at":"2026-05-18T04:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0398","created_at":"2026-05-18T04:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"VNOPJSAIRJ65","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VNOPJSAIRJ65XHQJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VNOPJSAI","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:fc14469872a649afb0c7411f1db6338de62f9fe05b4eb057bcc439e9348d0636","target":"graph","created_at":"2026-05-18T04:16:40Z","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":"Let p:C' -> C be an unramified double covering of irreducible smooth curves and let P be the attached Prym variety. We prove the schematic theta-dual equalities in the Prym variety T(C')=V^2 and T(V^2)=C', where V^2 is the Brill-Noether locus of P associated to p considered by Welters. As an application we prove a Torelli Theorem analogous to the fact that the g-th symmetric product of a curve D of genus g determines the curve.","authors_text":"Juan Carlos Naranjo, Mart\\'i Lahoz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-03T12:48:56Z","title":"Theta-duality on Prym varieties and a Torelli Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0398","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:b3fe06687b6b9161418fcc049eaf0244e99179804955248cc77c938e6aea3579","target":"record","created_at":"2026-05-18T04:16:40Z","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":"619e23a10df3aa321fcd388acf9cbff33ae87a3b80ad1db2952e221c4d1f8d5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-03T12:48:56Z","title_canon_sha256":"03b0397d3aadfb84c35125008cff86afdd93dae18c638c6b54039cfbecb3aa53"},"schema_version":"1.0","source":{"id":"1010.0398","kind":"arxiv","version":2}},"canonical_sha256":"ab5cf4c8088a7ddb9e09b08b45298df24b4dc1d4f358939006d5e801228811bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab5cf4c8088a7ddb9e09b08b45298df24b4dc1d4f358939006d5e801228811bb","first_computed_at":"2026-05-18T04:16:40.873932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:40.873932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ojoBkKlv9yX3A0MCC3ohCJmxQPUgD+a0847YLvsNGQSLIXrRYyIKkylaDqptXu7PojFftPKaFiB4iAVuKiXOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:40.874584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0398","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3fe06687b6b9161418fcc049eaf0244e99179804955248cc77c938e6aea3579","sha256:fc14469872a649afb0c7411f1db6338de62f9fe05b4eb057bcc439e9348d0636"],"state_sha256":"8d555482e23fb2a0994773d96b453504a55c9c3ffc064545f894d28ed1963f47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Um9e4JSo+qwr01TsL9/ZPqsvXEza753NXLCcJ/daxL88C6/lcV/be33J2nop/FtxNMhZok8EPenNAiJL7ZASDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:30:54.840736Z","bundle_sha256":"eca371f03cb5d5a0c351e53c1f173b5f84a84d5e5a80bc84d852203a9fdbd036"}}