{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HY3VIVPKX6FOF43AE4VBREXDXP","short_pith_number":"pith:HY3VIVPK","canonical_record":{"source":{"id":"1412.6978","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-22T13:52:35Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"13209aa5a65512c181d66af972f2d7788f347384a3b20470c4c389a5af1385c7","abstract_canon_sha256":"c72569e8e23c4a7ae5703ab3265775986a3daf6d52211147616f95e88e013e9e"},"schema_version":"1.0"},"canonical_sha256":"3e375455eabf8ae2f360272a1892e3bbf3a3629d8086feeea9d2707ec85e084d","source":{"kind":"arxiv","id":"1412.6978","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6978","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6978v3","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6978","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"HY3VIVPKX6FO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HY3VIVPKX6FOF43A","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HY3VIVPK","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HY3VIVPKX6FOF43AE4VBREXDXP","target":"record","payload":{"canonical_record":{"source":{"id":"1412.6978","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-22T13:52:35Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"13209aa5a65512c181d66af972f2d7788f347384a3b20470c4c389a5af1385c7","abstract_canon_sha256":"c72569e8e23c4a7ae5703ab3265775986a3daf6d52211147616f95e88e013e9e"},"schema_version":"1.0"},"canonical_sha256":"3e375455eabf8ae2f360272a1892e3bbf3a3629d8086feeea9d2707ec85e084d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:01.119311Z","signature_b64":"VTd0meg5VtesgJ46990v2WOaw3uxPLbmTsbgsRwxNteCD1B76liix+Rj2m8LpeQvkB3MtD/QF6/mJxQqxkbQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e375455eabf8ae2f360272a1892e3bbf3a3629d8086feeea9d2707ec85e084d","last_reissued_at":"2026-05-18T02:29:01.118926Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:01.118926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.6978","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W6CmU1EgxbWyZmz8NRyxl4dNd9OWLvqoD3q60AiSzOFHhfPTALrMEGJvcKt+a87uq+KIiIrXimqwLQIejoa9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T03:18:41.131369Z"},"content_sha256":"bfb33a8927dbe4aca160fce26aae753d781d775448b9a2d9bd18ed8167d37553","schema_version":"1.0","event_id":"sha256:bfb33a8927dbe4aca160fce26aae753d781d775448b9a2d9bd18ed8167d37553"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HY3VIVPKX6FOF43AE4VBREXDXP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orbit parametrizations of theta characteristics on hypersurfaces over arbitrary fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yasuhiro Ishitsuka","submitted_at":"2014-12-22T13:52:35Z","abstract_excerpt":"It is well-known that theta characteristics on smooth plane curves over a field of characteristic different from two are in bijection with certain smooth complete intersections of three quadrics. We generalize this bijection to possibly singular hypersurfaces of any dimension over arbitrary fields including those of characteristic two. It is accomplished in terms of linear orbits of tuples of symmetric matrices instead of smooth complete intersections of quadrics. As an application of our methods, we give a description of the projective automorphism groups of complete intersections of quadrics"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6978","kind":"arxiv","version":3},"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":"2026-05-18T02:29:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nwoRA8XAm4TLnP/GLQfUezx5uK0KXEUT022dC+IIUQ9BqyKbtTFbLrX85yuW6WRaKeyutQF9/FprU+4lCBMnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T03:18:41.131711Z"},"content_sha256":"d7e5b5c498b4c1f98d2f84e6d5a3ea854cef06e9868044a355147c2bbc5b9a14","schema_version":"1.0","event_id":"sha256:d7e5b5c498b4c1f98d2f84e6d5a3ea854cef06e9868044a355147c2bbc5b9a14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HY3VIVPKX6FOF43AE4VBREXDXP/bundle.json","state_url":"https://pith.science/pith/HY3VIVPKX6FOF43AE4VBREXDXP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HY3VIVPKX6FOF43AE4VBREXDXP/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":"2026-06-29T03:18:41Z","links":{"resolver":"https://pith.science/pith/HY3VIVPKX6FOF43AE4VBREXDXP","bundle":"https://pith.science/pith/HY3VIVPKX6FOF43AE4VBREXDXP/bundle.json","state":"https://pith.science/pith/HY3VIVPKX6FOF43AE4VBREXDXP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HY3VIVPKX6FOF43AE4VBREXDXP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HY3VIVPKX6FOF43AE4VBREXDXP","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":"c72569e8e23c4a7ae5703ab3265775986a3daf6d52211147616f95e88e013e9e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-22T13:52:35Z","title_canon_sha256":"13209aa5a65512c181d66af972f2d7788f347384a3b20470c4c389a5af1385c7"},"schema_version":"1.0","source":{"id":"1412.6978","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6978","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6978v3","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6978","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"HY3VIVPKX6FO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HY3VIVPKX6FOF43A","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HY3VIVPK","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:d7e5b5c498b4c1f98d2f84e6d5a3ea854cef06e9868044a355147c2bbc5b9a14","target":"graph","created_at":"2026-05-18T02:29:01Z","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":"It is well-known that theta characteristics on smooth plane curves over a field of characteristic different from two are in bijection with certain smooth complete intersections of three quadrics. We generalize this bijection to possibly singular hypersurfaces of any dimension over arbitrary fields including those of characteristic two. It is accomplished in terms of linear orbits of tuples of symmetric matrices instead of smooth complete intersections of quadrics. As an application of our methods, we give a description of the projective automorphism groups of complete intersections of quadrics","authors_text":"Yasuhiro Ishitsuka","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-22T13:52:35Z","title":"Orbit parametrizations of theta characteristics on hypersurfaces over arbitrary fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6978","kind":"arxiv","version":3},"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:bfb33a8927dbe4aca160fce26aae753d781d775448b9a2d9bd18ed8167d37553","target":"record","created_at":"2026-05-18T02:29:01Z","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":"c72569e8e23c4a7ae5703ab3265775986a3daf6d52211147616f95e88e013e9e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-22T13:52:35Z","title_canon_sha256":"13209aa5a65512c181d66af972f2d7788f347384a3b20470c4c389a5af1385c7"},"schema_version":"1.0","source":{"id":"1412.6978","kind":"arxiv","version":3}},"canonical_sha256":"3e375455eabf8ae2f360272a1892e3bbf3a3629d8086feeea9d2707ec85e084d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e375455eabf8ae2f360272a1892e3bbf3a3629d8086feeea9d2707ec85e084d","first_computed_at":"2026-05-18T02:29:01.118926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:01.118926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VTd0meg5VtesgJ46990v2WOaw3uxPLbmTsbgsRwxNteCD1B76liix+Rj2m8LpeQvkB3MtD/QF6/mJxQqxkbQBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:01.119311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6978","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfb33a8927dbe4aca160fce26aae753d781d775448b9a2d9bd18ed8167d37553","sha256:d7e5b5c498b4c1f98d2f84e6d5a3ea854cef06e9868044a355147c2bbc5b9a14"],"state_sha256":"6218a71207f9f2212b153ab0853eb0cea0dc4c19a8fa081162f83a23c70c714b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2VzeiEchy6PNzNmURzGvestO/8RcQ3FjuAvUI2OQhxNfmIy129TIMncHG/2c0dt22KUrZWhr/0NbYGyvNJdcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T03:18:41.133567Z","bundle_sha256":"e640ad28d5fd7646fcafddd1d9b38d9c840a20710b2ab020344ba488e9517f3a"}}