{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OYMGXDT6H5A557MJSLCDKPGCF6","short_pith_number":"pith:OYMGXDT6","canonical_record":{"source":{"id":"1401.4710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-01-19T18:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"71d8f6413459ac307c72ede05aa0d5ce11f383a24c0a2a7e333cb8d0a5621de4","abstract_canon_sha256":"3578317031865b3904bbf0497b5e7042dce67b626b72327c6e13870a41497bfc"},"schema_version":"1.0"},"canonical_sha256":"76186b8e7e3f41defd8992c4353cc22fb9c572817abd20384c373e62918fe1df","source":{"kind":"arxiv","id":"1401.4710","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4710","created_at":"2026-05-18T03:01:44Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4710v1","created_at":"2026-05-18T03:01:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4710","created_at":"2026-05-18T03:01:44Z"},{"alias_kind":"pith_short_12","alias_value":"OYMGXDT6H5A5","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OYMGXDT6H5A557MJ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OYMGXDT6","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OYMGXDT6H5A557MJSLCDKPGCF6","target":"record","payload":{"canonical_record":{"source":{"id":"1401.4710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-01-19T18:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"71d8f6413459ac307c72ede05aa0d5ce11f383a24c0a2a7e333cb8d0a5621de4","abstract_canon_sha256":"3578317031865b3904bbf0497b5e7042dce67b626b72327c6e13870a41497bfc"},"schema_version":"1.0"},"canonical_sha256":"76186b8e7e3f41defd8992c4353cc22fb9c572817abd20384c373e62918fe1df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:44.863947Z","signature_b64":"IO/V1MjDGrspCDFmn9iKu8nR8JBm6lnuWq2MI4pdmYdRBWq4SL8pUidyded+UTTBoQQF8JSd9NgZ59wjudgGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76186b8e7e3f41defd8992c4353cc22fb9c572817abd20384c373e62918fe1df","last_reissued_at":"2026-05-18T03:01:44.863263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:44.863263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.4710","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":"2026-05-18T03:01:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mu6nZ1jwVJ6bd09gp81k1TV37vC+Ugi7xLoNFBRkmnsIdyHyI4KWa0zGue7hn8RZDkhG6v6DEy+sabbDjwgPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:00:02.210562Z"},"content_sha256":"d7b20126e082c3d0c125f3b89c80ffca03d51a9ebe925c7fcd9960ffcecdd292","schema_version":"1.0","event_id":"sha256:d7b20126e082c3d0c125f3b89c80ffca03d51a9ebe925c7fcd9960ffcecdd292"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OYMGXDT6H5A557MJSLCDKPGCF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ideals generated by quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Aron Simis, Jooyoun Hong, Wolmer V. Vasconcelos","submitted_at":"2014-01-19T18:13:52Z","abstract_excerpt":"Our purpose is to study the cohomological properties of the Rees algebras of a class of ideals generated by quadrics. For all such ideals $I\\subset R = K[x,y,z]$ we give the precise value of depth $R[It]$ and decide whether the corresponding rational maps are birational. In the case of dimension $d \\geq 3$, when $K=\\mathbb{R}$, we give structure theorems for all ideals of codimension $d$ minimally generated by ${{d+1}\\choose{2}}-1$ quadrics. For arbitrary fields $K$, we prove a polarized version."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4710","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":"2026-05-18T03:01:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jgrPNuh0nrujS15tfDHH1VTeWf+HgWo8MZcYIfceYqTc3WRWicX4+v38SukAlUWKdTB+2H1Tu+CFOKJnrGjpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:00:02.210912Z"},"content_sha256":"18a602e4a190182389aae30fc5456408bbaa2460d6ab4253fe2278b899daf536","schema_version":"1.0","event_id":"sha256:18a602e4a190182389aae30fc5456408bbaa2460d6ab4253fe2278b899daf536"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYMGXDT6H5A557MJSLCDKPGCF6/bundle.json","state_url":"https://pith.science/pith/OYMGXDT6H5A557MJSLCDKPGCF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYMGXDT6H5A557MJSLCDKPGCF6/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":"2026-06-01T19:00:02Z","links":{"resolver":"https://pith.science/pith/OYMGXDT6H5A557MJSLCDKPGCF6","bundle":"https://pith.science/pith/OYMGXDT6H5A557MJSLCDKPGCF6/bundle.json","state":"https://pith.science/pith/OYMGXDT6H5A557MJSLCDKPGCF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYMGXDT6H5A557MJSLCDKPGCF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OYMGXDT6H5A557MJSLCDKPGCF6","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":"3578317031865b3904bbf0497b5e7042dce67b626b72327c6e13870a41497bfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-01-19T18:13:52Z","title_canon_sha256":"71d8f6413459ac307c72ede05aa0d5ce11f383a24c0a2a7e333cb8d0a5621de4"},"schema_version":"1.0","source":{"id":"1401.4710","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4710","created_at":"2026-05-18T03:01:44Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4710v1","created_at":"2026-05-18T03:01:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4710","created_at":"2026-05-18T03:01:44Z"},{"alias_kind":"pith_short_12","alias_value":"OYMGXDT6H5A5","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OYMGXDT6H5A557MJ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OYMGXDT6","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:18a602e4a190182389aae30fc5456408bbaa2460d6ab4253fe2278b899daf536","target":"graph","created_at":"2026-05-18T03:01:44Z","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":"Our purpose is to study the cohomological properties of the Rees algebras of a class of ideals generated by quadrics. For all such ideals $I\\subset R = K[x,y,z]$ we give the precise value of depth $R[It]$ and decide whether the corresponding rational maps are birational. In the case of dimension $d \\geq 3$, when $K=\\mathbb{R}$, we give structure theorems for all ideals of codimension $d$ minimally generated by ${{d+1}\\choose{2}}-1$ quadrics. For arbitrary fields $K$, we prove a polarized version.","authors_text":"Aron Simis, Jooyoun Hong, Wolmer V. Vasconcelos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-01-19T18:13:52Z","title":"Ideals generated by quadrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4710","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:d7b20126e082c3d0c125f3b89c80ffca03d51a9ebe925c7fcd9960ffcecdd292","target":"record","created_at":"2026-05-18T03:01:44Z","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":"3578317031865b3904bbf0497b5e7042dce67b626b72327c6e13870a41497bfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-01-19T18:13:52Z","title_canon_sha256":"71d8f6413459ac307c72ede05aa0d5ce11f383a24c0a2a7e333cb8d0a5621de4"},"schema_version":"1.0","source":{"id":"1401.4710","kind":"arxiv","version":1}},"canonical_sha256":"76186b8e7e3f41defd8992c4353cc22fb9c572817abd20384c373e62918fe1df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76186b8e7e3f41defd8992c4353cc22fb9c572817abd20384c373e62918fe1df","first_computed_at":"2026-05-18T03:01:44.863263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:44.863263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IO/V1MjDGrspCDFmn9iKu8nR8JBm6lnuWq2MI4pdmYdRBWq4SL8pUidyded+UTTBoQQF8JSd9NgZ59wjudgGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:44.863947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4710","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7b20126e082c3d0c125f3b89c80ffca03d51a9ebe925c7fcd9960ffcecdd292","sha256:18a602e4a190182389aae30fc5456408bbaa2460d6ab4253fe2278b899daf536"],"state_sha256":"65fa65c527cb7e0920106a6d24d1a878b76b510d17d2d6e0ce09e2ac069295d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c62r3m8wdF4MM0m/1+qF5RmyVoGAK6vmryEKNIM34vfJHZ27S9JVKa3uIlB+ddWhAcYmyjsmp8eCBNtOgOP2Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:00:02.212915Z","bundle_sha256":"3e05f8bd7978b9877c9952a0559efdeb507e2769900fa718f932d4501dd21e27"}}