{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PZ5EJU2MKJ2JCPSHP7BN6NZ3YM","short_pith_number":"pith:PZ5EJU2M","canonical_record":{"source":{"id":"1304.4290","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-15T23:19:25Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"2d1adf2bed48efa6a8e63124b5680cc9eca2abc8487e18e7eeddbab11677cb4f","abstract_canon_sha256":"370effbd019ddf8d2af35a3d5321346633aae8c6fd3bb9fa9a8d887217410b18"},"schema_version":"1.0"},"canonical_sha256":"7e7a44d34c5274913e477fc2df373bc30e861fd5f753b7bbef447374372a6f57","source":{"kind":"arxiv","id":"1304.4290","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4290","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4290v3","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4290","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"PZ5EJU2MKJ2J","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PZ5EJU2MKJ2JCPSH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PZ5EJU2M","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PZ5EJU2MKJ2JCPSHP7BN6NZ3YM","target":"record","payload":{"canonical_record":{"source":{"id":"1304.4290","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-15T23:19:25Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"2d1adf2bed48efa6a8e63124b5680cc9eca2abc8487e18e7eeddbab11677cb4f","abstract_canon_sha256":"370effbd019ddf8d2af35a3d5321346633aae8c6fd3bb9fa9a8d887217410b18"},"schema_version":"1.0"},"canonical_sha256":"7e7a44d34c5274913e477fc2df373bc30e861fd5f753b7bbef447374372a6f57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:47.084917Z","signature_b64":"AHG/7JnBLIUp/IrcVUl1KmZ6/XV4/gtbCV2v9Qm9W6zyMDMt6xXv+1yRKwVy1AAv7wwUHGkUl+9iYqT7vzhZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e7a44d34c5274913e477fc2df373bc30e861fd5f753b7bbef447374372a6f57","last_reissued_at":"2026-05-18T02:54:47.084453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:47.084453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.4290","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4m/FCW1ujbk2WyUeyL5XX+S+s02zbn59NkyhQSWdIQcfxKo2c6mH7b2ixxc/hsaShnMKBvQBBqo0oVBvTZNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:01:02.501733Z"},"content_sha256":"e42e7b4af23d456f7272e275bda28695b2c2478861aac949192776034bac139c","schema_version":"1.0","event_id":"sha256:e42e7b4af23d456f7272e275bda28695b2c2478861aac949192776034bac139c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PZ5EJU2MKJ2JCPSHP7BN6NZ3YM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classes of complete intersection numerical semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AC","authors_text":"Alessio Sammartano, Marco D'Anna, Vincenzo Micale","submitted_at":"2013-04-15T23:19:25Z","abstract_excerpt":"We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the logical implications among these classes and provide examples. Most of these classes are shown to be well-behaved with respect to the operation of gluing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4290","kind":"arxiv","version":3},"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":"2026-05-18T02:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"20dM8vVqKsoJ1IAwQS7VxWp5DfjQeotorSx3kOyBjrPnmYCrfsdxzVldmXarQmH1dXPvA3T9Y0vi2vub/ljkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:01:02.502369Z"},"content_sha256":"2e241b76795eaca56b2633fec0234daba47a282e3cdbebcca4eb202d5183bcb6","schema_version":"1.0","event_id":"sha256:2e241b76795eaca56b2633fec0234daba47a282e3cdbebcca4eb202d5183bcb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZ5EJU2MKJ2JCPSHP7BN6NZ3YM/bundle.json","state_url":"https://pith.science/pith/PZ5EJU2MKJ2JCPSHP7BN6NZ3YM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZ5EJU2MKJ2JCPSHP7BN6NZ3YM/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":"2026-06-01T01:01:02Z","links":{"resolver":"https://pith.science/pith/PZ5EJU2MKJ2JCPSHP7BN6NZ3YM","bundle":"https://pith.science/pith/PZ5EJU2MKJ2JCPSHP7BN6NZ3YM/bundle.json","state":"https://pith.science/pith/PZ5EJU2MKJ2JCPSHP7BN6NZ3YM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZ5EJU2MKJ2JCPSHP7BN6NZ3YM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PZ5EJU2MKJ2JCPSHP7BN6NZ3YM","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":"370effbd019ddf8d2af35a3d5321346633aae8c6fd3bb9fa9a8d887217410b18","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-15T23:19:25Z","title_canon_sha256":"2d1adf2bed48efa6a8e63124b5680cc9eca2abc8487e18e7eeddbab11677cb4f"},"schema_version":"1.0","source":{"id":"1304.4290","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4290","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4290v3","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4290","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"PZ5EJU2MKJ2J","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PZ5EJU2MKJ2JCPSH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PZ5EJU2M","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:2e241b76795eaca56b2633fec0234daba47a282e3cdbebcca4eb202d5183bcb6","target":"graph","created_at":"2026-05-18T02:54:47Z","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 consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the logical implications among these classes and provide examples. Most of these classes are shown to be well-behaved with respect to the operation of gluing.","authors_text":"Alessio Sammartano, Marco D'Anna, Vincenzo Micale","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-15T23:19:25Z","title":"Classes of complete intersection numerical semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4290","kind":"arxiv","version":3},"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:e42e7b4af23d456f7272e275bda28695b2c2478861aac949192776034bac139c","target":"record","created_at":"2026-05-18T02:54:47Z","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":"370effbd019ddf8d2af35a3d5321346633aae8c6fd3bb9fa9a8d887217410b18","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-15T23:19:25Z","title_canon_sha256":"2d1adf2bed48efa6a8e63124b5680cc9eca2abc8487e18e7eeddbab11677cb4f"},"schema_version":"1.0","source":{"id":"1304.4290","kind":"arxiv","version":3}},"canonical_sha256":"7e7a44d34c5274913e477fc2df373bc30e861fd5f753b7bbef447374372a6f57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e7a44d34c5274913e477fc2df373bc30e861fd5f753b7bbef447374372a6f57","first_computed_at":"2026-05-18T02:54:47.084453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:47.084453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AHG/7JnBLIUp/IrcVUl1KmZ6/XV4/gtbCV2v9Qm9W6zyMDMt6xXv+1yRKwVy1AAv7wwUHGkUl+9iYqT7vzhZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:47.084917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4290","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e42e7b4af23d456f7272e275bda28695b2c2478861aac949192776034bac139c","sha256:2e241b76795eaca56b2633fec0234daba47a282e3cdbebcca4eb202d5183bcb6"],"state_sha256":"bd5e3f1426eedc6a8cac37d7a72d00eed8712551a8433d81a4ba0aab171389b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/XuiTrC1jSOCGlly+anjOArUzAJcD30my61hATk553cpPrtmgQh203q1PHPrVQJA52aYkmAalZj6QEbowb+VAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:01:02.505925Z","bundle_sha256":"eb7990a5d7584add08349285e9264b9fd579acf3cd91d35664ef4625f2ce6dc9"}}