{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TXG6Q4QCMRCLM5WYWOIMAFODZV","short_pith_number":"pith:TXG6Q4QC","canonical_record":{"source":{"id":"1307.3050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-07-11T10:52:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"621cdb7e29d308397034564ea91e917089f6cb2493d164f61e8d54ed031607a5","abstract_canon_sha256":"a177e15616f3f3db782adeaf8179fee277a4ec23438c1c310ad741b6ac54f7a1"},"schema_version":"1.0"},"canonical_sha256":"9dcde872026444b676d8b390c015c3cd7bcd434277612a406d56c3d9aa748961","source":{"kind":"arxiv","id":"1307.3050","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3050","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3050v1","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3050","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"TXG6Q4QCMRCL","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TXG6Q4QCMRCLM5WY","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TXG6Q4QC","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TXG6Q4QCMRCLM5WYWOIMAFODZV","target":"record","payload":{"canonical_record":{"source":{"id":"1307.3050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-07-11T10:52:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"621cdb7e29d308397034564ea91e917089f6cb2493d164f61e8d54ed031607a5","abstract_canon_sha256":"a177e15616f3f3db782adeaf8179fee277a4ec23438c1c310ad741b6ac54f7a1"},"schema_version":"1.0"},"canonical_sha256":"9dcde872026444b676d8b390c015c3cd7bcd434277612a406d56c3d9aa748961","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:41.410043Z","signature_b64":"+nSkZdxDCrsOqQwcOAjzJhl8snOiiCOy5nZGebAjLxb/+EDCaB7f+/yF1/9c5ChcuSZtveTASYpAN6/HgogrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dcde872026444b676d8b390c015c3cd7bcd434277612a406d56c3d9aa748961","last_reissued_at":"2026-05-18T03:18:41.409330Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:41.409330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.3050","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":"2026-05-18T03:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lPjtq/b2DUuQfkgbHCkvrdvNR/MgtZQKKG4zQvbqf4LVnW1XfCa1prImPhoV05q58xFIOXQlpBiVsu7n7T2kBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:27:31.065952Z"},"content_sha256":"091a2023b4fc165ab5edaf06ad6d7fa5e09e79b5b4aaf59d8e90201342c7850c","schema_version":"1.0","event_id":"sha256:091a2023b4fc165ab5edaf06ad6d7fa5e09e79b5b4aaf59d8e90201342c7850c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TXG6Q4QCMRCLM5WYWOIMAFODZV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The monomial ideal of independent sets associated to a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Oana Olteanu","submitted_at":"2013-07-11T10:52:13Z","abstract_excerpt":"Independent sets play a key role into the study of graphs and important problems arising in graph theory reduce to them. We define the monomial ideal of independent sets associated to a finite simple graph and describe its homological and algebraic invariants in terms of the combinatorics of the graph. We compute the minimal primary decomposition and characterize the Cohen--Macaulay ideals. Moreover, we provide a formula for computing the Betti numbers, which depends only on the coefficients of the independence polynomial of the graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3050","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":"2026-05-18T03:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LDVLfDnoV9sOJznjPtsww81xzZCZhbpnPZpJdJUnhasp8j0+rcV6/aZtTXuvvR515o8cQu7ASa4ke6MzPwszDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:27:31.066303Z"},"content_sha256":"a6206d733a085fca3e726a94fa3f45223196596b51315952d70a6d8e188927b4","schema_version":"1.0","event_id":"sha256:a6206d733a085fca3e726a94fa3f45223196596b51315952d70a6d8e188927b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TXG6Q4QCMRCLM5WYWOIMAFODZV/bundle.json","state_url":"https://pith.science/pith/TXG6Q4QCMRCLM5WYWOIMAFODZV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TXG6Q4QCMRCLM5WYWOIMAFODZV/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":"2026-06-01T10:27:31Z","links":{"resolver":"https://pith.science/pith/TXG6Q4QCMRCLM5WYWOIMAFODZV","bundle":"https://pith.science/pith/TXG6Q4QCMRCLM5WYWOIMAFODZV/bundle.json","state":"https://pith.science/pith/TXG6Q4QCMRCLM5WYWOIMAFODZV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TXG6Q4QCMRCLM5WYWOIMAFODZV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TXG6Q4QCMRCLM5WYWOIMAFODZV","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":"a177e15616f3f3db782adeaf8179fee277a4ec23438c1c310ad741b6ac54f7a1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-07-11T10:52:13Z","title_canon_sha256":"621cdb7e29d308397034564ea91e917089f6cb2493d164f61e8d54ed031607a5"},"schema_version":"1.0","source":{"id":"1307.3050","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3050","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3050v1","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3050","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"TXG6Q4QCMRCL","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TXG6Q4QCMRCLM5WY","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TXG6Q4QC","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:a6206d733a085fca3e726a94fa3f45223196596b51315952d70a6d8e188927b4","target":"graph","created_at":"2026-05-18T03:18:41Z","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":"Independent sets play a key role into the study of graphs and important problems arising in graph theory reduce to them. We define the monomial ideal of independent sets associated to a finite simple graph and describe its homological and algebraic invariants in terms of the combinatorics of the graph. We compute the minimal primary decomposition and characterize the Cohen--Macaulay ideals. Moreover, we provide a formula for computing the Betti numbers, which depends only on the coefficients of the independence polynomial of the graph.","authors_text":"Oana Olteanu","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-07-11T10:52:13Z","title":"The monomial ideal of independent sets associated to a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3050","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":"sha256:091a2023b4fc165ab5edaf06ad6d7fa5e09e79b5b4aaf59d8e90201342c7850c","target":"record","created_at":"2026-05-18T03:18:41Z","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":"a177e15616f3f3db782adeaf8179fee277a4ec23438c1c310ad741b6ac54f7a1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-07-11T10:52:13Z","title_canon_sha256":"621cdb7e29d308397034564ea91e917089f6cb2493d164f61e8d54ed031607a5"},"schema_version":"1.0","source":{"id":"1307.3050","kind":"arxiv","version":1}},"canonical_sha256":"9dcde872026444b676d8b390c015c3cd7bcd434277612a406d56c3d9aa748961","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dcde872026444b676d8b390c015c3cd7bcd434277612a406d56c3d9aa748961","first_computed_at":"2026-05-18T03:18:41.409330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:41.409330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+nSkZdxDCrsOqQwcOAjzJhl8snOiiCOy5nZGebAjLxb/+EDCaB7f+/yF1/9c5ChcuSZtveTASYpAN6/HgogrAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:41.410043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3050","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:091a2023b4fc165ab5edaf06ad6d7fa5e09e79b5b4aaf59d8e90201342c7850c","sha256:a6206d733a085fca3e726a94fa3f45223196596b51315952d70a6d8e188927b4"],"state_sha256":"1bb4c850ca084e99581d0eb47af1c1b37e7d2be75235136a24ef8a5eec92e890"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NVrg3pUHH6Sn2dpAq3+rRctoEaG8NUb2Em5wPYeNY4dmZOz0k6Oy8a1MeXzOp21D1ecAHVYY5NxO174DJKu4Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:27:31.068298Z","bundle_sha256":"231b60c3fb1dadc609d3a55ce17ab5c721a3df4f678d3fbf5c01ab4e813ebba6"}}