{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:K5SQJ7W6B5XUMB2HVFZ3GVJYGB","short_pith_number":"pith:K5SQJ7W6","canonical_record":{"source":{"id":"1407.0650","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-02T17:09:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"93334e855094589deca78e281cbacc9001c910e817fe56a0d9e09ee7d3996df7","abstract_canon_sha256":"d320a7e9663cee24ffade05c97399065fb931aeaca72f7532cdc3caca8985d61"},"schema_version":"1.0"},"canonical_sha256":"576504fede0f6f460747a973b355383074fe19cb4f4502fc2ec5ca3b49799c8f","source":{"kind":"arxiv","id":"1407.0650","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0650","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0650v2","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0650","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"pith_short_12","alias_value":"K5SQJ7W6B5XU","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K5SQJ7W6B5XUMB2H","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K5SQJ7W6","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:K5SQJ7W6B5XUMB2HVFZ3GVJYGB","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0650","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-02T17:09:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"93334e855094589deca78e281cbacc9001c910e817fe56a0d9e09ee7d3996df7","abstract_canon_sha256":"d320a7e9663cee24ffade05c97399065fb931aeaca72f7532cdc3caca8985d61"},"schema_version":"1.0"},"canonical_sha256":"576504fede0f6f460747a973b355383074fe19cb4f4502fc2ec5ca3b49799c8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:37.572175Z","signature_b64":"23aaPrSuwKvCVBxpKV0t/MimpKQS+t5vk4SDi1Tr0d7s3oitZFlq4rGdkh8bTuA9HJT7FrxsiLX3pxThmZGaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"576504fede0f6f460747a973b355383074fe19cb4f4502fc2ec5ca3b49799c8f","last_reissued_at":"2026-05-18T02:03:37.571516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:37.571516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0650","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":"2026-05-18T02:03:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JqcG/LtNbR7cScnpYo0jWIc640dXjU/pgwvQDtfaX9WbloP+bTkCJ+4aOXZsE+nHnmEuhHPvak2xJHT2BYfZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:14:45.934277Z"},"content_sha256":"51e0ad8e612e9e0b644d24e947299dd7ac15e8d0212450b77b5fa63787b3bb3b","schema_version":"1.0","event_id":"sha256:51e0ad8e612e9e0b644d24e947299dd7ac15e8d0212450b77b5fa63787b3bb3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:K5SQJ7W6B5XUMB2HVFZ3GVJYGB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Hilbert functions of sets of points in P^1 x P^1 x P^1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Adam Van Tuyl, Elena Guardo","submitted_at":"2014-07-02T17:09:02Z","abstract_excerpt":"Let H_X be the trigraded Hilbert function of a set X of reduced points in P^1 x P^1 x P^1. We show how to extract some geometric information about X from H_X. This note generalizes a similar result of Giuffrida, Maggioni, and Ragusa about sets of points in P^1 x P^1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0650","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":"2026-05-18T02:03:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pFslsOgK/GJUuOmlbetpDKcuZxCQV/dSjDWeLzjR82ftEkrL2fMyJUQHMYS0mbWG1dWT9iqygRoPuy1Ar98BCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:14:45.934659Z"},"content_sha256":"683a6563ddb89e8b4339433a3da99220406924edd15c098c7e547acb334d45cc","schema_version":"1.0","event_id":"sha256:683a6563ddb89e8b4339433a3da99220406924edd15c098c7e547acb334d45cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K5SQJ7W6B5XUMB2HVFZ3GVJYGB/bundle.json","state_url":"https://pith.science/pith/K5SQJ7W6B5XUMB2HVFZ3GVJYGB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K5SQJ7W6B5XUMB2HVFZ3GVJYGB/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":"2026-06-04T13:14:45Z","links":{"resolver":"https://pith.science/pith/K5SQJ7W6B5XUMB2HVFZ3GVJYGB","bundle":"https://pith.science/pith/K5SQJ7W6B5XUMB2HVFZ3GVJYGB/bundle.json","state":"https://pith.science/pith/K5SQJ7W6B5XUMB2HVFZ3GVJYGB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K5SQJ7W6B5XUMB2HVFZ3GVJYGB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:K5SQJ7W6B5XUMB2HVFZ3GVJYGB","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":"d320a7e9663cee24ffade05c97399065fb931aeaca72f7532cdc3caca8985d61","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-02T17:09:02Z","title_canon_sha256":"93334e855094589deca78e281cbacc9001c910e817fe56a0d9e09ee7d3996df7"},"schema_version":"1.0","source":{"id":"1407.0650","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0650","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0650v2","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0650","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"pith_short_12","alias_value":"K5SQJ7W6B5XU","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K5SQJ7W6B5XUMB2H","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K5SQJ7W6","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:683a6563ddb89e8b4339433a3da99220406924edd15c098c7e547acb334d45cc","target":"graph","created_at":"2026-05-18T02:03:37Z","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 H_X be the trigraded Hilbert function of a set X of reduced points in P^1 x P^1 x P^1. We show how to extract some geometric information about X from H_X. This note generalizes a similar result of Giuffrida, Maggioni, and Ragusa about sets of points in P^1 x P^1.","authors_text":"Adam Van Tuyl, Elena Guardo","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-02T17:09:02Z","title":"On the Hilbert functions of sets of points in P^1 x P^1 x P^1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0650","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":"sha256:51e0ad8e612e9e0b644d24e947299dd7ac15e8d0212450b77b5fa63787b3bb3b","target":"record","created_at":"2026-05-18T02:03:37Z","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":"d320a7e9663cee24ffade05c97399065fb931aeaca72f7532cdc3caca8985d61","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-02T17:09:02Z","title_canon_sha256":"93334e855094589deca78e281cbacc9001c910e817fe56a0d9e09ee7d3996df7"},"schema_version":"1.0","source":{"id":"1407.0650","kind":"arxiv","version":2}},"canonical_sha256":"576504fede0f6f460747a973b355383074fe19cb4f4502fc2ec5ca3b49799c8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"576504fede0f6f460747a973b355383074fe19cb4f4502fc2ec5ca3b49799c8f","first_computed_at":"2026-05-18T02:03:37.571516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:37.571516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"23aaPrSuwKvCVBxpKV0t/MimpKQS+t5vk4SDi1Tr0d7s3oitZFlq4rGdkh8bTuA9HJT7FrxsiLX3pxThmZGaCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:37.572175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0650","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51e0ad8e612e9e0b644d24e947299dd7ac15e8d0212450b77b5fa63787b3bb3b","sha256:683a6563ddb89e8b4339433a3da99220406924edd15c098c7e547acb334d45cc"],"state_sha256":"14416214074797bf915845959a6056d3196142b3e86b0c1984a85201aa503946"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xmPA2rR9xGm9n0k78JFHZuf4J6m3tqpq/njfaXHrH9Oz9IK8ne9HPiUUgYahG+Iv1d4jlgpxLiY0g4n8MesWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T13:14:45.936960Z","bundle_sha256":"fc40d0aa35320e40901dff5119811d140d42f42616406b091a886928d4bbf875"}}