{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:XKL4HPQZRZPSI7IJIPJETIX5UA","short_pith_number":"pith:XKL4HPQZ","schema_version":"1.0","canonical_sha256":"ba97c3be198e5f247d0943d249a2fda03c6e446b85f40f6022fd152fa397ed38","source":{"kind":"arxiv","id":"math/0702354","version":1},"attestation_state":"computed","paper":{"title":"Highly connected monochromatic subgraphs of multicoloured graphs","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henry Liu, Noah Prince, Robert Morris","submitted_at":"2007-02-13T04:18:16Z","abstract_excerpt":"We consider the following question of Bollobas: given an r-colouring of the edges of the complete graph on n vertices, how large a k-connected subgraph can we find using only one colour? We solve this problem asymptotically when r-1 is a prime power, and exactly for 2- and 3-colourings."},"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":"math/0702354","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2007-02-13T04:18:16Z","cross_cats_sorted":[],"title_canon_sha256":"af0df3319c66b4937d87cd3b2bdb32e372c7c0af44387923fd3012a8332bf6c4","abstract_canon_sha256":"5712f17c03f330843812b04fc97e337039f42fd5eee494e9d413d0c535fbbad0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:59:31.105303Z","signature_b64":"cl/0f+CHjxVz2abgEUzMbY5OzAzQUR+Xgxb44qMe1zp7nocOiZRadYNPYHy73IWwNsGCjI9kII5Yrkt5fM5UBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba97c3be198e5f247d0943d249a2fda03c6e446b85f40f6022fd152fa397ed38","last_reissued_at":"2026-07-04T14:59:31.104971Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:59:31.104971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Highly connected monochromatic subgraphs of multicoloured graphs","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henry Liu, Noah Prince, Robert Morris","submitted_at":"2007-02-13T04:18:16Z","abstract_excerpt":"We consider the following question of Bollobas: given an r-colouring of the edges of the complete graph on n vertices, how large a k-connected subgraph can we find using only one colour? We solve this problem asymptotically when r-1 is a prime power, and exactly for 2- and 3-colourings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702354","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/math/0702354/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":"math/0702354","created_at":"2026-07-04T14:59:31.105027+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0702354v1","created_at":"2026-07-04T14:59:31.105027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702354","created_at":"2026-07-04T14:59:31.105027+00:00"},{"alias_kind":"pith_short_12","alias_value":"XKL4HPQZRZPS","created_at":"2026-07-04T14:59:31.105027+00:00"},{"alias_kind":"pith_short_16","alias_value":"XKL4HPQZRZPSI7IJ","created_at":"2026-07-04T14:59:31.105027+00:00"},{"alias_kind":"pith_short_8","alias_value":"XKL4HPQZ","created_at":"2026-07-04T14:59:31.105027+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/XKL4HPQZRZPSI7IJIPJETIX5UA","json":"https://pith.science/pith/XKL4HPQZRZPSI7IJIPJETIX5UA.json","graph_json":"https://pith.science/api/pith-number/XKL4HPQZRZPSI7IJIPJETIX5UA/graph.json","events_json":"https://pith.science/api/pith-number/XKL4HPQZRZPSI7IJIPJETIX5UA/events.json","paper":"https://pith.science/paper/XKL4HPQZ"},"agent_actions":{"view_html":"https://pith.science/pith/XKL4HPQZRZPSI7IJIPJETIX5UA","download_json":"https://pith.science/pith/XKL4HPQZRZPSI7IJIPJETIX5UA.json","view_paper":"https://pith.science/paper/XKL4HPQZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0702354&json=true","fetch_graph":"https://pith.science/api/pith-number/XKL4HPQZRZPSI7IJIPJETIX5UA/graph.json","fetch_events":"https://pith.science/api/pith-number/XKL4HPQZRZPSI7IJIPJETIX5UA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XKL4HPQZRZPSI7IJIPJETIX5UA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XKL4HPQZRZPSI7IJIPJETIX5UA/action/storage_attestation","attest_author":"https://pith.science/pith/XKL4HPQZRZPSI7IJIPJETIX5UA/action/author_attestation","sign_citation":"https://pith.science/pith/XKL4HPQZRZPSI7IJIPJETIX5UA/action/citation_signature","submit_replication":"https://pith.science/pith/XKL4HPQZRZPSI7IJIPJETIX5UA/action/replication_record"}},"created_at":"2026-07-04T14:59:31.105027+00:00","updated_at":"2026-07-04T14:59:31.105027+00:00"}