{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ONYWP6X6JL5IXIKVNIFTRUEVPR","short_pith_number":"pith:ONYWP6X6","schema_version":"1.0","canonical_sha256":"737167fafe4afa8ba1556a0b38d0957c74e01b470e759673a46fb211ccb264f4","source":{"kind":"arxiv","id":"2506.23794","version":1},"attestation_state":"computed","paper":{"title":"Sabotage the Mantel Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Debsoumya Chakraborti, Natalie Behague, Xizhi Liu","submitted_at":"2025-06-30T12:35:46Z","abstract_excerpt":"One of the earliest results in extremal graph theory, Mantel's theorem, states that the maximum number of edges in a triangle-free graph $G$ on $n$ vertices is $\\lfloor n^2/4 \\rfloor$. We investigate how this extremal bound is affected when $G$ is additionally required to contain a prescribed graph $\\mathbb{P}$ as a subgraph. We establish general upper and lower bounds for this problem, which are tight in the exponent for random triangle-free graphs and graphs generated by the triangle-free process, when the size of $\\mathbb{P}$ lies within certain ranges."},"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":"2506.23794","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-30T12:35:46Z","cross_cats_sorted":[],"title_canon_sha256":"1b5d90112a95fd654254f9cfc484184cf34710e2965bfe3feb5366709a34d8a2","abstract_canon_sha256":"829fb16e7dfbcfc7b9d2149717a33c49f4c19fa1da8084eb862a9a9b1600cd1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:28.076210Z","signature_b64":"Df1ompSSIC/D9ah8iS3q96dQkkLQSfsIb54Z3SWyK/70/60RjiTGM5e+RJKZ4q9OljPZb9HHLbzibXB5m4+1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"737167fafe4afa8ba1556a0b38d0957c74e01b470e759673a46fb211ccb264f4","last_reissued_at":"2026-07-05T11:29:28.075722Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:28.075722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sabotage the Mantel Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Debsoumya Chakraborti, Natalie Behague, Xizhi Liu","submitted_at":"2025-06-30T12:35:46Z","abstract_excerpt":"One of the earliest results in extremal graph theory, Mantel's theorem, states that the maximum number of edges in a triangle-free graph $G$ on $n$ vertices is $\\lfloor n^2/4 \\rfloor$. We investigate how this extremal bound is affected when $G$ is additionally required to contain a prescribed graph $\\mathbb{P}$ as a subgraph. We establish general upper and lower bounds for this problem, which are tight in the exponent for random triangle-free graphs and graphs generated by the triangle-free process, when the size of $\\mathbb{P}$ lies within certain ranges."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23794","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.23794/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.23794","created_at":"2026-07-05T11:29:28.075784+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.23794v1","created_at":"2026-07-05T11:29:28.075784+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23794","created_at":"2026-07-05T11:29:28.075784+00:00"},{"alias_kind":"pith_short_12","alias_value":"ONYWP6X6JL5I","created_at":"2026-07-05T11:29:28.075784+00:00"},{"alias_kind":"pith_short_16","alias_value":"ONYWP6X6JL5IXIKV","created_at":"2026-07-05T11:29:28.075784+00:00"},{"alias_kind":"pith_short_8","alias_value":"ONYWP6X6","created_at":"2026-07-05T11:29:28.075784+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/ONYWP6X6JL5IXIKVNIFTRUEVPR","json":"https://pith.science/pith/ONYWP6X6JL5IXIKVNIFTRUEVPR.json","graph_json":"https://pith.science/api/pith-number/ONYWP6X6JL5IXIKVNIFTRUEVPR/graph.json","events_json":"https://pith.science/api/pith-number/ONYWP6X6JL5IXIKVNIFTRUEVPR/events.json","paper":"https://pith.science/paper/ONYWP6X6"},"agent_actions":{"view_html":"https://pith.science/pith/ONYWP6X6JL5IXIKVNIFTRUEVPR","download_json":"https://pith.science/pith/ONYWP6X6JL5IXIKVNIFTRUEVPR.json","view_paper":"https://pith.science/paper/ONYWP6X6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.23794&json=true","fetch_graph":"https://pith.science/api/pith-number/ONYWP6X6JL5IXIKVNIFTRUEVPR/graph.json","fetch_events":"https://pith.science/api/pith-number/ONYWP6X6JL5IXIKVNIFTRUEVPR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ONYWP6X6JL5IXIKVNIFTRUEVPR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ONYWP6X6JL5IXIKVNIFTRUEVPR/action/storage_attestation","attest_author":"https://pith.science/pith/ONYWP6X6JL5IXIKVNIFTRUEVPR/action/author_attestation","sign_citation":"https://pith.science/pith/ONYWP6X6JL5IXIKVNIFTRUEVPR/action/citation_signature","submit_replication":"https://pith.science/pith/ONYWP6X6JL5IXIKVNIFTRUEVPR/action/replication_record"}},"created_at":"2026-07-05T11:29:28.075784+00:00","updated_at":"2026-07-05T11:29:28.075784+00:00"}