{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QNR7EN4JAPWDXB4QTLETBTQYCZ","short_pith_number":"pith:QNR7EN4J","canonical_record":{"source":{"id":"1304.3682","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-12T16:55:29Z","cross_cats_sorted":[],"title_canon_sha256":"57c1ddcfefa0a3174595da0712dc7db0c373e2fc8c67b01faf0aeabb1885cfdb","abstract_canon_sha256":"036856f21318af5a19b60f800e640be48bcd069044b7048b1c513614e031ec8a"},"schema_version":"1.0"},"canonical_sha256":"8363f2378903ec3b87909ac930ce181662051f735f37ddd9a0e81956f96ff163","source":{"kind":"arxiv","id":"1304.3682","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3682","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3682v4","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3682","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"pith_short_12","alias_value":"QNR7EN4JAPWD","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QNR7EN4JAPWDXB4Q","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QNR7EN4J","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QNR7EN4JAPWDXB4QTLETBTQYCZ","target":"record","payload":{"canonical_record":{"source":{"id":"1304.3682","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-12T16:55:29Z","cross_cats_sorted":[],"title_canon_sha256":"57c1ddcfefa0a3174595da0712dc7db0c373e2fc8c67b01faf0aeabb1885cfdb","abstract_canon_sha256":"036856f21318af5a19b60f800e640be48bcd069044b7048b1c513614e031ec8a"},"schema_version":"1.0"},"canonical_sha256":"8363f2378903ec3b87909ac930ce181662051f735f37ddd9a0e81956f96ff163","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:32.942371Z","signature_b64":"GB5y9yiogOhw7YLgO46I4092KAqR9MmndlByDTNbF7UEl1mDGPeus0K3Rbhdg61vpOwz5cqBpICwdbNEjYU2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8363f2378903ec3b87909ac930ce181662051f735f37ddd9a0e81956f96ff163","last_reissued_at":"2026-05-18T03:12:32.941613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:32.941613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.3682","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:12:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fSUH02ZtTO9XmYwCRlpeXCKDThIlxAs2tRF5iqRyPVA1Um9GKbQ9crsG3pOSk/+UOCnpu8wjQqqdHIeJr+dODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:27:58.049624Z"},"content_sha256":"39774155231344e56d35319026869ca09df04f8e35a23573509535cc5131e25c","schema_version":"1.0","event_id":"sha256:39774155231344e56d35319026869ca09df04f8e35a23573509535cc5131e25c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QNR7EN4JAPWDXB4QTLETBTQYCZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A properness result for degenerate Quadratic and Symplectic Bundles on a smooth projective curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yashonidhi Pandey","submitted_at":"2013-04-12T16:55:29Z","abstract_excerpt":"Let $(V,q)$ be a vector bundle on a smooth projective curve $X$ together with a quadratic form $q: \\mathrm{Sym}^2(V) \\ra \\mathcal{O}_X$ (respectively symplectic form $q: \\Lambda^2V \\ra \\mathcal{O}_X$). Fixing the degeneracy locus of the quadratic form induced on $V/\\ker(q)$, we construct a coarse moduli of such objects. Further, we prove semi-stable reduction theorem for equivalence classes of such objects. In particular, the case when degeneracies of $q$ are higher than one is that of principal interest. We also provide a proof of properness of polystable orthogonal bundles without appealing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3682","kind":"arxiv","version":4},"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":"2026-05-18T03:12:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6pH09FfPaAi3nwIOFHcbKqmGMEIs28w8PDlbyOykUjp6OXbMocDK4fMshZ4xtNQc7JqTX7QNTQyw2cHJlkFoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:27:58.049978Z"},"content_sha256":"bad7a0a06232a51a4f2ca6c55bc7c94545422ae0554504f163f691b3d4a27c0f","schema_version":"1.0","event_id":"sha256:bad7a0a06232a51a4f2ca6c55bc7c94545422ae0554504f163f691b3d4a27c0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNR7EN4JAPWDXB4QTLETBTQYCZ/bundle.json","state_url":"https://pith.science/pith/QNR7EN4JAPWDXB4QTLETBTQYCZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNR7EN4JAPWDXB4QTLETBTQYCZ/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":"2026-06-02T18:27:58Z","links":{"resolver":"https://pith.science/pith/QNR7EN4JAPWDXB4QTLETBTQYCZ","bundle":"https://pith.science/pith/QNR7EN4JAPWDXB4QTLETBTQYCZ/bundle.json","state":"https://pith.science/pith/QNR7EN4JAPWDXB4QTLETBTQYCZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNR7EN4JAPWDXB4QTLETBTQYCZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QNR7EN4JAPWDXB4QTLETBTQYCZ","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":"036856f21318af5a19b60f800e640be48bcd069044b7048b1c513614e031ec8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-12T16:55:29Z","title_canon_sha256":"57c1ddcfefa0a3174595da0712dc7db0c373e2fc8c67b01faf0aeabb1885cfdb"},"schema_version":"1.0","source":{"id":"1304.3682","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3682","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3682v4","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3682","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"pith_short_12","alias_value":"QNR7EN4JAPWD","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QNR7EN4JAPWDXB4Q","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QNR7EN4J","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:bad7a0a06232a51a4f2ca6c55bc7c94545422ae0554504f163f691b3d4a27c0f","target":"graph","created_at":"2026-05-18T03:12:32Z","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 $(V,q)$ be a vector bundle on a smooth projective curve $X$ together with a quadratic form $q: \\mathrm{Sym}^2(V) \\ra \\mathcal{O}_X$ (respectively symplectic form $q: \\Lambda^2V \\ra \\mathcal{O}_X$). Fixing the degeneracy locus of the quadratic form induced on $V/\\ker(q)$, we construct a coarse moduli of such objects. Further, we prove semi-stable reduction theorem for equivalence classes of such objects. In particular, the case when degeneracies of $q$ are higher than one is that of principal interest. We also provide a proof of properness of polystable orthogonal bundles without appealing ","authors_text":"Yashonidhi Pandey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-12T16:55:29Z","title":"A properness result for degenerate Quadratic and Symplectic Bundles on a smooth projective curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3682","kind":"arxiv","version":4},"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":"sha256:39774155231344e56d35319026869ca09df04f8e35a23573509535cc5131e25c","target":"record","created_at":"2026-05-18T03:12:32Z","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":"036856f21318af5a19b60f800e640be48bcd069044b7048b1c513614e031ec8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-12T16:55:29Z","title_canon_sha256":"57c1ddcfefa0a3174595da0712dc7db0c373e2fc8c67b01faf0aeabb1885cfdb"},"schema_version":"1.0","source":{"id":"1304.3682","kind":"arxiv","version":4}},"canonical_sha256":"8363f2378903ec3b87909ac930ce181662051f735f37ddd9a0e81956f96ff163","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8363f2378903ec3b87909ac930ce181662051f735f37ddd9a0e81956f96ff163","first_computed_at":"2026-05-18T03:12:32.941613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:32.941613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GB5y9yiogOhw7YLgO46I4092KAqR9MmndlByDTNbF7UEl1mDGPeus0K3Rbhdg61vpOwz5cqBpICwdbNEjYU2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:32.942371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.3682","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39774155231344e56d35319026869ca09df04f8e35a23573509535cc5131e25c","sha256:bad7a0a06232a51a4f2ca6c55bc7c94545422ae0554504f163f691b3d4a27c0f"],"state_sha256":"ffa8116c9814599b68d10fc896f62cdc08defe392479b040bb5eacdc302cbff4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYJuyEqJetClcKTgsKGc7Ea2+tuedym71EgoD6mMOZwAdQzKQq0cEsBI/4t4eJUi9R6TY52e1sfVJe9DzLTsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:27:58.051964Z","bundle_sha256":"ec9ef832efec7c59f64300bc591ba273a1c9d537f3b94f52d65b7bbf9c40d41f"}}