{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FP3KL6SO2XE6RLQXEJLKYGHU2Q","short_pith_number":"pith:FP3KL6SO","schema_version":"1.0","canonical_sha256":"2bf6a5fa4ed5c9e8ae172256ac18f4d41c5907a36d928afc52a75dc3002caa15","source":{"kind":"arxiv","id":"1205.3678","version":2},"attestation_state":"computed","paper":{"title":"Edge Ideals of Weighted Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Chelsey Paulsen, Sean Sather-Wagstaff","submitted_at":"2012-05-16T13:51:35Z","abstract_excerpt":"We study weighted graphs and their \"edge ideals\" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in terms of the combinatorics of \"weighted vertex covers\". We use these, for instance, to say when these ideals are m-unmixed. We explicitly describe which weighted cycles, suspensions, and trees are unmixed and which ones are Cohen-Macaulay, and we prove that all weighted complete graphs are Cohen-Macaulay."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.3678","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-05-16T13:51:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"00d3a24802a680e47c4246c39e3f7761dd823ff3de3c76d39d5223fe6e9770d7","abstract_canon_sha256":"24cd70f692f7be2675733b64e7c248562bf3bd7dfd54b590e25f7d7cdb86aacf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:45.239740Z","signature_b64":"7JcQ5uu1/2jqGQjvh3AC0TOrqLXjf6yDXlh7XQstsSrubDEHJrEOM3YT9znLkk+Iy27uyyXYLNZqXaSmDboxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bf6a5fa4ed5c9e8ae172256ac18f4d41c5907a36d928afc52a75dc3002caa15","last_reissued_at":"2026-05-18T03:32:45.238919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:45.238919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edge Ideals of Weighted Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Chelsey Paulsen, Sean Sather-Wagstaff","submitted_at":"2012-05-16T13:51:35Z","abstract_excerpt":"We study weighted graphs and their \"edge ideals\" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in terms of the combinatorics of \"weighted vertex covers\". We use these, for instance, to say when these ideals are m-unmixed. We explicitly describe which weighted cycles, suspensions, and trees are unmixed and which ones are Cohen-Macaulay, and we prove that all weighted complete graphs are Cohen-Macaulay."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3678","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.3678","created_at":"2026-05-18T03:32:45.239053+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.3678v2","created_at":"2026-05-18T03:32:45.239053+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3678","created_at":"2026-05-18T03:32:45.239053+00:00"},{"alias_kind":"pith_short_12","alias_value":"FP3KL6SO2XE6","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FP3KL6SO2XE6RLQX","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FP3KL6SO","created_at":"2026-05-18T12:27:06.952714+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FP3KL6SO2XE6RLQXEJLKYGHU2Q","json":"https://pith.science/pith/FP3KL6SO2XE6RLQXEJLKYGHU2Q.json","graph_json":"https://pith.science/api/pith-number/FP3KL6SO2XE6RLQXEJLKYGHU2Q/graph.json","events_json":"https://pith.science/api/pith-number/FP3KL6SO2XE6RLQXEJLKYGHU2Q/events.json","paper":"https://pith.science/paper/FP3KL6SO"},"agent_actions":{"view_html":"https://pith.science/pith/FP3KL6SO2XE6RLQXEJLKYGHU2Q","download_json":"https://pith.science/pith/FP3KL6SO2XE6RLQXEJLKYGHU2Q.json","view_paper":"https://pith.science/paper/FP3KL6SO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.3678&json=true","fetch_graph":"https://pith.science/api/pith-number/FP3KL6SO2XE6RLQXEJLKYGHU2Q/graph.json","fetch_events":"https://pith.science/api/pith-number/FP3KL6SO2XE6RLQXEJLKYGHU2Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FP3KL6SO2XE6RLQXEJLKYGHU2Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FP3KL6SO2XE6RLQXEJLKYGHU2Q/action/storage_attestation","attest_author":"https://pith.science/pith/FP3KL6SO2XE6RLQXEJLKYGHU2Q/action/author_attestation","sign_citation":"https://pith.science/pith/FP3KL6SO2XE6RLQXEJLKYGHU2Q/action/citation_signature","submit_replication":"https://pith.science/pith/FP3KL6SO2XE6RLQXEJLKYGHU2Q/action/replication_record"}},"created_at":"2026-05-18T03:32:45.239053+00:00","updated_at":"2026-05-18T03:32:45.239053+00:00"}