{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:W53HAKZCWE7SEXVBEASVCS345P","short_pith_number":"pith:W53HAKZC","canonical_record":{"source":{"id":"1712.05886","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-16T01:00:27Z","cross_cats_sorted":[],"title_canon_sha256":"0cd218c358691b3eaa206966d5ec6f2837927d26e882681f1c4fa3fc9ffc9523","abstract_canon_sha256":"80a3a3c4fed3c693a41f8cd54e3e199482bc3cbc23301b0f0aae36e1b1910332"},"schema_version":"1.0"},"canonical_sha256":"b776702b22b13f225ea12025514b7cebe51d697ede2ea4853dc60a56c336e1df","source":{"kind":"arxiv","id":"1712.05886","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05886","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05886v2","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05886","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"W53HAKZCWE7S","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"W53HAKZCWE7SEXVB","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"W53HAKZC","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:W53HAKZCWE7SEXVBEASVCS345P","target":"record","payload":{"canonical_record":{"source":{"id":"1712.05886","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-16T01:00:27Z","cross_cats_sorted":[],"title_canon_sha256":"0cd218c358691b3eaa206966d5ec6f2837927d26e882681f1c4fa3fc9ffc9523","abstract_canon_sha256":"80a3a3c4fed3c693a41f8cd54e3e199482bc3cbc23301b0f0aae36e1b1910332"},"schema_version":"1.0"},"canonical_sha256":"b776702b22b13f225ea12025514b7cebe51d697ede2ea4853dc60a56c336e1df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:43.255225Z","signature_b64":"AJNwmaMYZ0/M52TS4JguVOqUatZdnq3hn+Xidebqe8DgWpjN0eO70v+KGxvOo/QPTxWoJ7Fz7KbFjRAHtjlkDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b776702b22b13f225ea12025514b7cebe51d697ede2ea4853dc60a56c336e1df","last_reissued_at":"2026-05-18T00:07:43.254586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:43.254586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.05886","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":"2026-05-18T00:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fsBDHieZw0jjn05xY2im3qXL6mS9LV7UJZXkfCNuwvZ2bf5KVRt7038OAllGc+qBNykE6Epx/b+CSD4kdc4gBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T07:47:15.985276Z"},"content_sha256":"c9355c525bf72fdeb1862811413e20e98c65b056874cb4acd1a14c49817782f2","schema_version":"1.0","event_id":"sha256:c9355c525bf72fdeb1862811413e20e98c65b056874cb4acd1a14c49817782f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:W53HAKZCWE7SEXVBEASVCS345P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete intersections with given Hilbert polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Christopher Eur, Sung Hyun Lim","submitted_at":"2017-12-16T01:00:27Z","abstract_excerpt":"The Hilbert polynomial of a homogeneous complete intersection is determined by the degrees of the generators of the defining ideal. The degrees of the generators are not, in general, determined by the Hilbert polynomial -- but sometimes they are. When? We give some general criteria and completely answer the question up to codimension 6."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05886","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":"2026-05-18T00:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EYI6z/VLBf5jkarekl4s0ChfY4tnEp3FDpMoYYk6epfZz0YrS/hSHNKAMsNncL9fpoYgUIWu+t+0EqZu80k9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T07:47:15.985654Z"},"content_sha256":"288c25fd08df0bdb4bc5a8b1c7110ad57b2cfea46a872be77a2bef7067c8431d","schema_version":"1.0","event_id":"sha256:288c25fd08df0bdb4bc5a8b1c7110ad57b2cfea46a872be77a2bef7067c8431d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W53HAKZCWE7SEXVBEASVCS345P/bundle.json","state_url":"https://pith.science/pith/W53HAKZCWE7SEXVBEASVCS345P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W53HAKZCWE7SEXVBEASVCS345P/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":"2026-07-11T07:47:15Z","links":{"resolver":"https://pith.science/pith/W53HAKZCWE7SEXVBEASVCS345P","bundle":"https://pith.science/pith/W53HAKZCWE7SEXVBEASVCS345P/bundle.json","state":"https://pith.science/pith/W53HAKZCWE7SEXVBEASVCS345P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W53HAKZCWE7SEXVBEASVCS345P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:W53HAKZCWE7SEXVBEASVCS345P","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":"80a3a3c4fed3c693a41f8cd54e3e199482bc3cbc23301b0f0aae36e1b1910332","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-16T01:00:27Z","title_canon_sha256":"0cd218c358691b3eaa206966d5ec6f2837927d26e882681f1c4fa3fc9ffc9523"},"schema_version":"1.0","source":{"id":"1712.05886","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05886","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05886v2","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05886","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"W53HAKZCWE7S","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"W53HAKZCWE7SEXVB","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"W53HAKZC","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:288c25fd08df0bdb4bc5a8b1c7110ad57b2cfea46a872be77a2bef7067c8431d","target":"graph","created_at":"2026-05-18T00:07:43Z","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":"The Hilbert polynomial of a homogeneous complete intersection is determined by the degrees of the generators of the defining ideal. The degrees of the generators are not, in general, determined by the Hilbert polynomial -- but sometimes they are. When? We give some general criteria and completely answer the question up to codimension 6.","authors_text":"Christopher Eur, Sung Hyun Lim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-16T01:00:27Z","title":"Complete intersections with given Hilbert polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05886","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:c9355c525bf72fdeb1862811413e20e98c65b056874cb4acd1a14c49817782f2","target":"record","created_at":"2026-05-18T00:07:43Z","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":"80a3a3c4fed3c693a41f8cd54e3e199482bc3cbc23301b0f0aae36e1b1910332","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-16T01:00:27Z","title_canon_sha256":"0cd218c358691b3eaa206966d5ec6f2837927d26e882681f1c4fa3fc9ffc9523"},"schema_version":"1.0","source":{"id":"1712.05886","kind":"arxiv","version":2}},"canonical_sha256":"b776702b22b13f225ea12025514b7cebe51d697ede2ea4853dc60a56c336e1df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b776702b22b13f225ea12025514b7cebe51d697ede2ea4853dc60a56c336e1df","first_computed_at":"2026-05-18T00:07:43.254586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:43.254586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AJNwmaMYZ0/M52TS4JguVOqUatZdnq3hn+Xidebqe8DgWpjN0eO70v+KGxvOo/QPTxWoJ7Fz7KbFjRAHtjlkDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:43.255225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05886","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9355c525bf72fdeb1862811413e20e98c65b056874cb4acd1a14c49817782f2","sha256:288c25fd08df0bdb4bc5a8b1c7110ad57b2cfea46a872be77a2bef7067c8431d"],"state_sha256":"a21b8544b452a0b8770097a077e3e6fca7fdba18d8b2deb68db7871cc72bdca4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xg1eELYHqSw4dJDqvnGoniM3IlXPS962qxvkMiNxUfvHTaOw7AF1Rhn9jkeU1jSifTYm0BycjpscFM2BIOK+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T07:47:15.987624Z","bundle_sha256":"cd5e009f35305118b98737d6a517b9126d5c67973627819d2e2858ed6f2fe6d4"}}