{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:QIPWLUO3HY4J6QGHWXKSKHW63W","short_pith_number":"pith:QIPWLUO3","canonical_record":{"source":{"id":"1003.3825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-03-19T16:00:56Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"375081b809593c3622d427893b9888fe19de772d91d6c558007fcf2ca43845f6","abstract_canon_sha256":"af8824880eda3bb405f56a916d311b297f602d6cc86a024ba5f070c51fca3193"},"schema_version":"1.0"},"canonical_sha256":"821f65d1db3e389f40c7b5d5251ededd9c0a04e8ba01a25d80221f2067e9547a","source":{"kind":"arxiv","id":"1003.3825","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3825","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3825v2","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3825","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"QIPWLUO3HY4J","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QIPWLUO3HY4J6QGH","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QIPWLUO3","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:QIPWLUO3HY4J6QGHWXKSKHW63W","target":"record","payload":{"canonical_record":{"source":{"id":"1003.3825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-03-19T16:00:56Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"375081b809593c3622d427893b9888fe19de772d91d6c558007fcf2ca43845f6","abstract_canon_sha256":"af8824880eda3bb405f56a916d311b297f602d6cc86a024ba5f070c51fca3193"},"schema_version":"1.0"},"canonical_sha256":"821f65d1db3e389f40c7b5d5251ededd9c0a04e8ba01a25d80221f2067e9547a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:23.419032Z","signature_b64":"LEIiXe9vnXlU80CpAuHDcHXJQ967/mz45KMRmJfXV5w2bsqwQ/ghpg4DpKqUU6kCT2NRDFKhGaUdTR49jCFNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"821f65d1db3e389f40c7b5d5251ededd9c0a04e8ba01a25d80221f2067e9547a","last_reissued_at":"2026-05-18T04:01:23.418196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:23.418196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.3825","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":"2026-05-18T04:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWb9fLhrsVVFhemybG9+bkWL2IEqqLYxZ9qGd5zULlZF5RxFRY435cRn9sqHASkTAu4n9XoeJj7uBz+SD1dbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:21:53.010538Z"},"content_sha256":"855cf0301465febb0465afed86811cded6c507e1ba834cce24cb13b23cb30b67","schema_version":"1.0","event_id":"sha256:855cf0301465febb0465afed86811cded6c507e1ba834cce24cb13b23cb30b67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:QIPWLUO3HY4J6QGHWXKSKHW63W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the shape of a pure O-sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CO","authors_text":"F. Zanello, J. Migliore, M. Boij, R. Miro'-Roig, U. Nagel","submitted_at":"2010-03-19T16:00:56Z","abstract_excerpt":"An order ideal is a finite poset X of (monic) monomials such that, whenever M is in X and N divides M, then N is in X. If all, say t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h=(1,h_1,...,h_e), counting the monomials of X in each degree. Equivalently, in the language of commutative algebra, pure O-sequences are the h-vectors of monomial Artinian level algebras. Pure O-sequences had their origin in one of Richard Stanley's early works in this area, and have since played a significant role in at least three disciplines: the study o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3825","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":"2026-05-18T04:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uHPNyC6G/cO3XB0jiAa+S6UOTw89yW6MVSlJFfymrh73+gabderhgXyr5Q31cXZm0Dxc6RFd8NWb0hM4gZy4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:21:53.010888Z"},"content_sha256":"7cddff702738b7941089194441ffe21c3915e1891a1b6fbb616fb34ed0d7d087","schema_version":"1.0","event_id":"sha256:7cddff702738b7941089194441ffe21c3915e1891a1b6fbb616fb34ed0d7d087"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QIPWLUO3HY4J6QGHWXKSKHW63W/bundle.json","state_url":"https://pith.science/pith/QIPWLUO3HY4J6QGHWXKSKHW63W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QIPWLUO3HY4J6QGHWXKSKHW63W/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":"2026-06-30T20:21:53Z","links":{"resolver":"https://pith.science/pith/QIPWLUO3HY4J6QGHWXKSKHW63W","bundle":"https://pith.science/pith/QIPWLUO3HY4J6QGHWXKSKHW63W/bundle.json","state":"https://pith.science/pith/QIPWLUO3HY4J6QGHWXKSKHW63W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QIPWLUO3HY4J6QGHWXKSKHW63W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QIPWLUO3HY4J6QGHWXKSKHW63W","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":"af8824880eda3bb405f56a916d311b297f602d6cc86a024ba5f070c51fca3193","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-03-19T16:00:56Z","title_canon_sha256":"375081b809593c3622d427893b9888fe19de772d91d6c558007fcf2ca43845f6"},"schema_version":"1.0","source":{"id":"1003.3825","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3825","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3825v2","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3825","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"QIPWLUO3HY4J","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QIPWLUO3HY4J6QGH","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QIPWLUO3","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:7cddff702738b7941089194441ffe21c3915e1891a1b6fbb616fb34ed0d7d087","target":"graph","created_at":"2026-05-18T04:01:23Z","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":"An order ideal is a finite poset X of (monic) monomials such that, whenever M is in X and N divides M, then N is in X. If all, say t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h=(1,h_1,...,h_e), counting the monomials of X in each degree. Equivalently, in the language of commutative algebra, pure O-sequences are the h-vectors of monomial Artinian level algebras. Pure O-sequences had their origin in one of Richard Stanley's early works in this area, and have since played a significant role in at least three disciplines: the study o","authors_text":"F. Zanello, J. Migliore, M. Boij, R. Miro'-Roig, U. Nagel","cross_cats":["math.AC","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-03-19T16:00:56Z","title":"On the shape of a pure O-sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3825","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":"sha256:855cf0301465febb0465afed86811cded6c507e1ba834cce24cb13b23cb30b67","target":"record","created_at":"2026-05-18T04:01:23Z","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":"af8824880eda3bb405f56a916d311b297f602d6cc86a024ba5f070c51fca3193","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-03-19T16:00:56Z","title_canon_sha256":"375081b809593c3622d427893b9888fe19de772d91d6c558007fcf2ca43845f6"},"schema_version":"1.0","source":{"id":"1003.3825","kind":"arxiv","version":2}},"canonical_sha256":"821f65d1db3e389f40c7b5d5251ededd9c0a04e8ba01a25d80221f2067e9547a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"821f65d1db3e389f40c7b5d5251ededd9c0a04e8ba01a25d80221f2067e9547a","first_computed_at":"2026-05-18T04:01:23.418196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:23.418196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LEIiXe9vnXlU80CpAuHDcHXJQ967/mz45KMRmJfXV5w2bsqwQ/ghpg4DpKqUU6kCT2NRDFKhGaUdTR49jCFNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:23.419032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3825","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:855cf0301465febb0465afed86811cded6c507e1ba834cce24cb13b23cb30b67","sha256:7cddff702738b7941089194441ffe21c3915e1891a1b6fbb616fb34ed0d7d087"],"state_sha256":"c995a7faa030c77ade04aea90bd36a1eb1b6b9b527cd89546a551a79d7889444"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZuP0pLKIZM/XJo6+BwSOwk5qRoPiI2FqzhtHOZpGvvK6ld9HCe2g3wA2H/1YcJ9fTf0/kVWD3tFSZ+cv+sulCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T20:21:53.012954Z","bundle_sha256":"d177dbbb838ffe905c4add64f10f5aa98ecf73b3ab04cc3c45947e9a37deebe1"}}