{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BRYDFHUXTBTZXOMXPPHHAKBYZ6","short_pith_number":"pith:BRYDFHUX","canonical_record":{"source":{"id":"1501.00207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-31T20:47:32Z","cross_cats_sorted":[],"title_canon_sha256":"fd280d1117ab4f06806107cf1ad4bb2d290df6841cf8595b6cee0a414524ee69","abstract_canon_sha256":"d9c04af8671495edeef42e00d75e41b2def82018f86a68ac969f11f44abd4b51"},"schema_version":"1.0"},"canonical_sha256":"0c70329e9798679bb9977bce702838cfabb3addbcb827f4cb5f164d18ba982ce","source":{"kind":"arxiv","id":"1501.00207","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00207","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00207v1","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00207","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"BRYDFHUXTBTZ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BRYDFHUXTBTZXOMX","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BRYDFHUX","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BRYDFHUXTBTZXOMXPPHHAKBYZ6","target":"record","payload":{"canonical_record":{"source":{"id":"1501.00207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-31T20:47:32Z","cross_cats_sorted":[],"title_canon_sha256":"fd280d1117ab4f06806107cf1ad4bb2d290df6841cf8595b6cee0a414524ee69","abstract_canon_sha256":"d9c04af8671495edeef42e00d75e41b2def82018f86a68ac969f11f44abd4b51"},"schema_version":"1.0"},"canonical_sha256":"0c70329e9798679bb9977bce702838cfabb3addbcb827f4cb5f164d18ba982ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:44.460600Z","signature_b64":"rVG6vyza5/rcrhapTHm2aMhq0caU89+RvNbEedWwxK0CRtbWcRWSdF5ZUqthcWmLgVWSJO7tbqzrE0Mt3ij4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c70329e9798679bb9977bce702838cfabb3addbcb827f4cb5f164d18ba982ce","last_reissued_at":"2026-05-18T00:57:44.460020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:44.460020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.00207","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":"2026-05-18T00:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2kTwcEwPNWe/3lBCbNFL1nKscrYeHV/uSZAy4AsYxsWhdnN5EcHYoN2jb0URwnHRVVrECwpno4A4CUJNd8HIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:01:30.062139Z"},"content_sha256":"134bf240acbbc587df1a7ffa1f3f3a01c5757c7804df293dcd2aff22644fb5cd","schema_version":"1.0","event_id":"sha256:134bf240acbbc587df1a7ffa1f3f3a01c5757c7804df293dcd2aff22644fb5cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BRYDFHUXTBTZXOMXPPHHAKBYZ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The cone of Betti tables over three non-collinear points in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Iulia Gheorghita, Steven V Sam","submitted_at":"2014-12-31T20:47:32Z","abstract_excerpt":"We describe the cone of Betti tables of all finitely generated graded modules over the homogeneous coordinate ring of three non-collinear points in the projective plane. We also describe the cone of Betti tables of all finite length modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00207","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":"2026-05-18T00:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tOn/MbaJGlnQVm2SrVEJ03qsu3eEplcKUI+pptx8XkH9/Z4EB1LRY2k02HrDn6yJjI/PsVdNv2t7Mp88e4LTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:01:30.062876Z"},"content_sha256":"9953e0a0e3249e7cd0a60f210680675ccd84b0c055a1a8147f856948f063e164","schema_version":"1.0","event_id":"sha256:9953e0a0e3249e7cd0a60f210680675ccd84b0c055a1a8147f856948f063e164"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BRYDFHUXTBTZXOMXPPHHAKBYZ6/bundle.json","state_url":"https://pith.science/pith/BRYDFHUXTBTZXOMXPPHHAKBYZ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BRYDFHUXTBTZXOMXPPHHAKBYZ6/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":"2026-06-09T03:01:30Z","links":{"resolver":"https://pith.science/pith/BRYDFHUXTBTZXOMXPPHHAKBYZ6","bundle":"https://pith.science/pith/BRYDFHUXTBTZXOMXPPHHAKBYZ6/bundle.json","state":"https://pith.science/pith/BRYDFHUXTBTZXOMXPPHHAKBYZ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BRYDFHUXTBTZXOMXPPHHAKBYZ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BRYDFHUXTBTZXOMXPPHHAKBYZ6","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":"d9c04af8671495edeef42e00d75e41b2def82018f86a68ac969f11f44abd4b51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-31T20:47:32Z","title_canon_sha256":"fd280d1117ab4f06806107cf1ad4bb2d290df6841cf8595b6cee0a414524ee69"},"schema_version":"1.0","source":{"id":"1501.00207","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00207","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00207v1","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00207","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"BRYDFHUXTBTZ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BRYDFHUXTBTZXOMX","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BRYDFHUX","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:9953e0a0e3249e7cd0a60f210680675ccd84b0c055a1a8147f856948f063e164","target":"graph","created_at":"2026-05-18T00:57:44Z","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":"We describe the cone of Betti tables of all finitely generated graded modules over the homogeneous coordinate ring of three non-collinear points in the projective plane. We also describe the cone of Betti tables of all finite length modules.","authors_text":"Iulia Gheorghita, Steven V Sam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-31T20:47:32Z","title":"The cone of Betti tables over three non-collinear points in the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00207","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":"sha256:134bf240acbbc587df1a7ffa1f3f3a01c5757c7804df293dcd2aff22644fb5cd","target":"record","created_at":"2026-05-18T00:57:44Z","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":"d9c04af8671495edeef42e00d75e41b2def82018f86a68ac969f11f44abd4b51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-31T20:47:32Z","title_canon_sha256":"fd280d1117ab4f06806107cf1ad4bb2d290df6841cf8595b6cee0a414524ee69"},"schema_version":"1.0","source":{"id":"1501.00207","kind":"arxiv","version":1}},"canonical_sha256":"0c70329e9798679bb9977bce702838cfabb3addbcb827f4cb5f164d18ba982ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c70329e9798679bb9977bce702838cfabb3addbcb827f4cb5f164d18ba982ce","first_computed_at":"2026-05-18T00:57:44.460020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:44.460020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rVG6vyza5/rcrhapTHm2aMhq0caU89+RvNbEedWwxK0CRtbWcRWSdF5ZUqthcWmLgVWSJO7tbqzrE0Mt3ij4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:44.460600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.00207","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:134bf240acbbc587df1a7ffa1f3f3a01c5757c7804df293dcd2aff22644fb5cd","sha256:9953e0a0e3249e7cd0a60f210680675ccd84b0c055a1a8147f856948f063e164"],"state_sha256":"281b0011af4b99907a98fa471d15ad4e45e89361dc3ffcf83a3346f5e7d2d554"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ahHQjgub6fCiVtG2NgJXrjTObMN93lVanEDjPmndK5pVUHPj5YA9vOgdn3yJaHEj+Q0xxwBHWecGJUitVaXlBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:01:30.067170Z","bundle_sha256":"92434528a214e55474e59afa2567d9e77461c253cf20615325b5dafd1b594778"}}