{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MXJAKZZ7HFAFV56ZR5NVQTXFLA","short_pith_number":"pith:MXJAKZZ7","canonical_record":{"source":{"id":"1109.5834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-27T10:57:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6a340be1126e7581bbc9fb4ade8c49b62d19857fe5fff9698605e0a2306b3656","abstract_canon_sha256":"df841e7cbf9eed2c87e09a53514cbafe4e85470b03becc3d327689bc092be15d"},"schema_version":"1.0"},"canonical_sha256":"65d205673f39405af7d98f5b584ee55826d60673c95e891d880ff6eaa2dc2de3","source":{"kind":"arxiv","id":"1109.5834","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5834","created_at":"2026-05-18T04:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5834v2","created_at":"2026-05-18T04:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5834","created_at":"2026-05-18T04:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"MXJAKZZ7HFAF","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MXJAKZZ7HFAFV56Z","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MXJAKZZ7","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MXJAKZZ7HFAFV56ZR5NVQTXFLA","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-27T10:57:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6a340be1126e7581bbc9fb4ade8c49b62d19857fe5fff9698605e0a2306b3656","abstract_canon_sha256":"df841e7cbf9eed2c87e09a53514cbafe4e85470b03becc3d327689bc092be15d"},"schema_version":"1.0"},"canonical_sha256":"65d205673f39405af7d98f5b584ee55826d60673c95e891d880ff6eaa2dc2de3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:01.795001Z","signature_b64":"qCtIYVsa5Q/GbZJfjpJ3P4x1l0LVc8qiKRbQzVF61lsKAX0THJaCkEDnUGNYH7DHcv9GapCCjM53vfseIfs/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65d205673f39405af7d98f5b584ee55826d60673c95e891d880ff6eaa2dc2de3","last_reissued_at":"2026-05-18T04:12:01.794568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:01.794568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5834","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":"2026-05-18T04:12:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oQrecRMppjvypjuSey/CpbE/Z6tsDM1OgduyNB4Y4t81thEr0yfDh5X8nmnikjP//rxijj/IE3nCAkz+I/IrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:30:54.759760Z"},"content_sha256":"a710df1879aee018aaaefe98453ad3f39665a1823b5174311e431cf16e050492","schema_version":"1.0","event_id":"sha256:a710df1879aee018aaaefe98453ad3f39665a1823b5174311e431cf16e050492"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MXJAKZZ7HFAFV56ZR5NVQTXFLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The stable set of associated prime ideals of a polymatroidal ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Asia Rauf, J\\\"urgen Herzog, Marius Vladoiu","submitted_at":"2011-09-27T10:57:17Z","abstract_excerpt":"The associated prime ideals of powers of polymatroidal ideals are studied, including the stable set of associated prime ideals of this class of ideals. It is shown that polymatroidal ideals have the persistence property and for transversal polymatroids and polymatroidal ideals of Veronese type the index of stability and the stable set of associated ideals is determined explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5834","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":"2026-05-18T04:12:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ctm1u5/rJdl/CMsBb3FYLaTjbDBsAwpXnQOnishRbxGH0jnQQFWb4M5j5jjol0nKoGqw6UgmqXSGmJFPRWSRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:30:54.760437Z"},"content_sha256":"527e8a25e4d6af2bfd279446c2f00d6549dd8d2f5e918d0df9bf69e0b914ad8f","schema_version":"1.0","event_id":"sha256:527e8a25e4d6af2bfd279446c2f00d6549dd8d2f5e918d0df9bf69e0b914ad8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXJAKZZ7HFAFV56ZR5NVQTXFLA/bundle.json","state_url":"https://pith.science/pith/MXJAKZZ7HFAFV56ZR5NVQTXFLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXJAKZZ7HFAFV56ZR5NVQTXFLA/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":"2026-06-22T16:30:54Z","links":{"resolver":"https://pith.science/pith/MXJAKZZ7HFAFV56ZR5NVQTXFLA","bundle":"https://pith.science/pith/MXJAKZZ7HFAFV56ZR5NVQTXFLA/bundle.json","state":"https://pith.science/pith/MXJAKZZ7HFAFV56ZR5NVQTXFLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXJAKZZ7HFAFV56ZR5NVQTXFLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MXJAKZZ7HFAFV56ZR5NVQTXFLA","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":"df841e7cbf9eed2c87e09a53514cbafe4e85470b03becc3d327689bc092be15d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-27T10:57:17Z","title_canon_sha256":"6a340be1126e7581bbc9fb4ade8c49b62d19857fe5fff9698605e0a2306b3656"},"schema_version":"1.0","source":{"id":"1109.5834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5834","created_at":"2026-05-18T04:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5834v2","created_at":"2026-05-18T04:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5834","created_at":"2026-05-18T04:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"MXJAKZZ7HFAF","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MXJAKZZ7HFAFV56Z","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MXJAKZZ7","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:527e8a25e4d6af2bfd279446c2f00d6549dd8d2f5e918d0df9bf69e0b914ad8f","target":"graph","created_at":"2026-05-18T04:12:01Z","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":"The associated prime ideals of powers of polymatroidal ideals are studied, including the stable set of associated prime ideals of this class of ideals. It is shown that polymatroidal ideals have the persistence property and for transversal polymatroids and polymatroidal ideals of Veronese type the index of stability and the stable set of associated ideals is determined explicitly.","authors_text":"Asia Rauf, J\\\"urgen Herzog, Marius Vladoiu","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-27T10:57:17Z","title":"The stable set of associated prime ideals of a polymatroidal ideal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5834","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:a710df1879aee018aaaefe98453ad3f39665a1823b5174311e431cf16e050492","target":"record","created_at":"2026-05-18T04:12:01Z","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":"df841e7cbf9eed2c87e09a53514cbafe4e85470b03becc3d327689bc092be15d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-27T10:57:17Z","title_canon_sha256":"6a340be1126e7581bbc9fb4ade8c49b62d19857fe5fff9698605e0a2306b3656"},"schema_version":"1.0","source":{"id":"1109.5834","kind":"arxiv","version":2}},"canonical_sha256":"65d205673f39405af7d98f5b584ee55826d60673c95e891d880ff6eaa2dc2de3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65d205673f39405af7d98f5b584ee55826d60673c95e891d880ff6eaa2dc2de3","first_computed_at":"2026-05-18T04:12:01.794568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:01.794568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qCtIYVsa5Q/GbZJfjpJ3P4x1l0LVc8qiKRbQzVF61lsKAX0THJaCkEDnUGNYH7DHcv9GapCCjM53vfseIfs/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:01.795001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a710df1879aee018aaaefe98453ad3f39665a1823b5174311e431cf16e050492","sha256:527e8a25e4d6af2bfd279446c2f00d6549dd8d2f5e918d0df9bf69e0b914ad8f"],"state_sha256":"d635e8b767a2ab9580da95b0d46222cefe728aeb93cd1ac2f54fd49ffe1b5cb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ec1N4q3ibCnx/tSpuFOGZVy0ZwekfK0tb4lPbRwxuVMfL0tsf0C26muoQcVZP6v1Tws4nsbLl9PW+FzlDSoCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:30:54.764170Z","bundle_sha256":"dff6aff5f2df1b1037e91d8cd207347a635a0f30424800f313895f0e359e5e7b"}}