{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:O7XLXV76YT5SYSKKMEBQW7NQ2D","short_pith_number":"pith:O7XLXV76","canonical_record":{"source":{"id":"1503.05420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-18T14:05:41Z","cross_cats_sorted":[],"title_canon_sha256":"b0fea907d3f4fd302b6226e56ffd140e5ddd245811122b74438ef59469d2f019","abstract_canon_sha256":"cedf8a4cfbb4f66d38c686d2f37c1d8e1aa67578a8e383131ad6d3859fbb073e"},"schema_version":"1.0"},"canonical_sha256":"77eebbd7fec4fb2c494a61030b7db0d0eba13f681006c5391a989a80a195483f","source":{"kind":"arxiv","id":"1503.05420","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05420","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05420v1","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05420","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"O7XLXV76YT5S","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7XLXV76YT5SYSKK","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7XLXV76","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:O7XLXV76YT5SYSKKMEBQW7NQ2D","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-18T14:05:41Z","cross_cats_sorted":[],"title_canon_sha256":"b0fea907d3f4fd302b6226e56ffd140e5ddd245811122b74438ef59469d2f019","abstract_canon_sha256":"cedf8a4cfbb4f66d38c686d2f37c1d8e1aa67578a8e383131ad6d3859fbb073e"},"schema_version":"1.0"},"canonical_sha256":"77eebbd7fec4fb2c494a61030b7db0d0eba13f681006c5391a989a80a195483f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:50.448984Z","signature_b64":"q8UrQJWH4Te1PlQJAJYa85j97RxaUKsCe4QjoBWnazrP6z1WRD2MkjA5KDzE9tuIH81GugrbEDcODtz6Ek2dDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77eebbd7fec4fb2c494a61030b7db0d0eba13f681006c5391a989a80a195483f","last_reissued_at":"2026-05-18T02:21:50.448584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:50.448584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05420","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":"2026-05-18T02:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9pcEFkbJte+WcBHa4vZtPOATROVkuHCxPacjLS62wuQVcKb0h9UXXwXUqwRtBVf++ezxLgik0x/UsQfh7/tkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:37:34.774656Z"},"content_sha256":"267e6727d64db4b323e7b33fdd5fddf139f40246e425bb493f1fbe18a0031e50","schema_version":"1.0","event_id":"sha256:267e6727d64db4b323e7b33fdd5fddf139f40246e425bb493f1fbe18a0031e50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:O7XLXV76YT5SYSKKMEBQW7NQ2D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nodal complete intersection threefold with defect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Remke Kloosterman","submitted_at":"2015-03-18T14:05:41Z","abstract_excerpt":"In this paper we show that a nodal complete intersection threefold $X$ in $\\mathbb{P}^{3+c}$ with defect, but without induced defect, has at least $\\sum_{i\\leq j} (d_i-1)(d_j-1)$ nodes, provided either $c=2$ or $d_c>\\sum_{i=1}^{c-1} d_i$ holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05420","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":"2026-05-18T02:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8pwxuUhhlFQnEXiiQqqLdacTPE1wvcudLaVH58lFr/FkeBS10NtQSx4O4iBEKfCSvErscl3TiYMxtG84AUE/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:37:34.775071Z"},"content_sha256":"0e292711d4fa32ca9f4c16db210c4c56dbf6a270801148445e58bf785068e243","schema_version":"1.0","event_id":"sha256:0e292711d4fa32ca9f4c16db210c4c56dbf6a270801148445e58bf785068e243"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7XLXV76YT5SYSKKMEBQW7NQ2D/bundle.json","state_url":"https://pith.science/pith/O7XLXV76YT5SYSKKMEBQW7NQ2D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7XLXV76YT5SYSKKMEBQW7NQ2D/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":"2026-06-09T02:37:34Z","links":{"resolver":"https://pith.science/pith/O7XLXV76YT5SYSKKMEBQW7NQ2D","bundle":"https://pith.science/pith/O7XLXV76YT5SYSKKMEBQW7NQ2D/bundle.json","state":"https://pith.science/pith/O7XLXV76YT5SYSKKMEBQW7NQ2D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7XLXV76YT5SYSKKMEBQW7NQ2D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:O7XLXV76YT5SYSKKMEBQW7NQ2D","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":"cedf8a4cfbb4f66d38c686d2f37c1d8e1aa67578a8e383131ad6d3859fbb073e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-18T14:05:41Z","title_canon_sha256":"b0fea907d3f4fd302b6226e56ffd140e5ddd245811122b74438ef59469d2f019"},"schema_version":"1.0","source":{"id":"1503.05420","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05420","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05420v1","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05420","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"O7XLXV76YT5S","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7XLXV76YT5SYSKK","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7XLXV76","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:0e292711d4fa32ca9f4c16db210c4c56dbf6a270801148445e58bf785068e243","target":"graph","created_at":"2026-05-18T02:21:50Z","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":"In this paper we show that a nodal complete intersection threefold $X$ in $\\mathbb{P}^{3+c}$ with defect, but without induced defect, has at least $\\sum_{i\\leq j} (d_i-1)(d_j-1)$ nodes, provided either $c=2$ or $d_c>\\sum_{i=1}^{c-1} d_i$ holds.","authors_text":"Remke Kloosterman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-18T14:05:41Z","title":"Nodal complete intersection threefold with defect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05420","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":"sha256:267e6727d64db4b323e7b33fdd5fddf139f40246e425bb493f1fbe18a0031e50","target":"record","created_at":"2026-05-18T02:21:50Z","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":"cedf8a4cfbb4f66d38c686d2f37c1d8e1aa67578a8e383131ad6d3859fbb073e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-18T14:05:41Z","title_canon_sha256":"b0fea907d3f4fd302b6226e56ffd140e5ddd245811122b74438ef59469d2f019"},"schema_version":"1.0","source":{"id":"1503.05420","kind":"arxiv","version":1}},"canonical_sha256":"77eebbd7fec4fb2c494a61030b7db0d0eba13f681006c5391a989a80a195483f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77eebbd7fec4fb2c494a61030b7db0d0eba13f681006c5391a989a80a195483f","first_computed_at":"2026-05-18T02:21:50.448584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:50.448584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q8UrQJWH4Te1PlQJAJYa85j97RxaUKsCe4QjoBWnazrP6z1WRD2MkjA5KDzE9tuIH81GugrbEDcODtz6Ek2dDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:50.448984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05420","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:267e6727d64db4b323e7b33fdd5fddf139f40246e425bb493f1fbe18a0031e50","sha256:0e292711d4fa32ca9f4c16db210c4c56dbf6a270801148445e58bf785068e243"],"state_sha256":"64beb0c6198f9f306c225f811224180fd6ad63aadeca03c2b74b2afb5c9a7a8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w+8vQ4dJ2iSF5buGcgg5cINGyQypkemi16fJSqNQxQlMfBCUKz3lXBL1KWWAOtpdVJmPk8JSr3q4/SbO2laKBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:37:34.778591Z","bundle_sha256":"3c61bbb946769167f9c0e3978ac9e12426a20cc468d134461bb05e8ba1de0fb8"}}