{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MSCCLJPP3TF5LM67NZJ23R65BY","short_pith_number":"pith:MSCCLJPP","schema_version":"1.0","canonical_sha256":"648425a5efdccbd5b3df6e53adc7dd0e16193fc28dc69d9f024a2ca933cae9bf","source":{"kind":"arxiv","id":"1802.09871","version":2},"attestation_state":"computed","paper":{"title":"On the random version of the Erd\\H{o}s matching conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ali Taherkhani, Meysam Alishahi","submitted_at":"2018-02-27T13:28:21Z","abstract_excerpt":"The Kneser hypergraph ${\\rm KG}^r_{n,k}$ is an $r$-uniform hypergraph with vertex set consisting of all $k$-subsets of $\\{1,\\ldots,n\\}$ and any collection of $r$ vertices forms an edge if their corresponding $k$-sets are pairwise disjoint. The random Kneser hypergraph ${\\rm KG}^r_{n,k}(p)$ is a spanning subhypergraph of ${\\rm KG}^r_{n,k}$ in which each edge of ${\\rm KG}^r_{n,k}$ is retained independently of each other with probability $p$. The independence number of random subgraphs of ${\\rm KG}^2_{n,k}$ was recently addressed in a series of works by Bollob{\\'a}s, Narayanan, and Raigorodskii ("},"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":"1802.09871","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-27T13:28:21Z","cross_cats_sorted":[],"title_canon_sha256":"a2024110ca08fc6896312f8bd5dece728c273f3d2b34072ae640a9f8b1cc484e","abstract_canon_sha256":"e3c0a2aa0bba43fefb8078c1ff49d2ba0bc8b8b0ca6000f040779b5964035780"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:32.114591Z","signature_b64":"jpxi7PE99BxJa4BUiArEMRkJ6mj4lSqt/ZsfyYjF+cUfUj9YYI9XsIF8Yix4xlCdnRxTstmo70f6PmZqXa2PDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"648425a5efdccbd5b3df6e53adc7dd0e16193fc28dc69d9f024a2ca933cae9bf","last_reissued_at":"2026-05-18T00:12:32.113952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:32.113952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the random version of the Erd\\H{o}s matching conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ali Taherkhani, Meysam Alishahi","submitted_at":"2018-02-27T13:28:21Z","abstract_excerpt":"The Kneser hypergraph ${\\rm KG}^r_{n,k}$ is an $r$-uniform hypergraph with vertex set consisting of all $k$-subsets of $\\{1,\\ldots,n\\}$ and any collection of $r$ vertices forms an edge if their corresponding $k$-sets are pairwise disjoint. The random Kneser hypergraph ${\\rm KG}^r_{n,k}(p)$ is a spanning subhypergraph of ${\\rm KG}^r_{n,k}$ in which each edge of ${\\rm KG}^r_{n,k}$ is retained independently of each other with probability $p$. The independence number of random subgraphs of ${\\rm KG}^2_{n,k}$ was recently addressed in a series of works by Bollob{\\'a}s, Narayanan, and Raigorodskii ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09871","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":"1802.09871","created_at":"2026-05-18T00:12:32.114085+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.09871v2","created_at":"2026-05-18T00:12:32.114085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09871","created_at":"2026-05-18T00:12:32.114085+00:00"},{"alias_kind":"pith_short_12","alias_value":"MSCCLJPP3TF5","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"MSCCLJPP3TF5LM67","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"MSCCLJPP","created_at":"2026-05-18T12:32:40.477152+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/MSCCLJPP3TF5LM67NZJ23R65BY","json":"https://pith.science/pith/MSCCLJPP3TF5LM67NZJ23R65BY.json","graph_json":"https://pith.science/api/pith-number/MSCCLJPP3TF5LM67NZJ23R65BY/graph.json","events_json":"https://pith.science/api/pith-number/MSCCLJPP3TF5LM67NZJ23R65BY/events.json","paper":"https://pith.science/paper/MSCCLJPP"},"agent_actions":{"view_html":"https://pith.science/pith/MSCCLJPP3TF5LM67NZJ23R65BY","download_json":"https://pith.science/pith/MSCCLJPP3TF5LM67NZJ23R65BY.json","view_paper":"https://pith.science/paper/MSCCLJPP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.09871&json=true","fetch_graph":"https://pith.science/api/pith-number/MSCCLJPP3TF5LM67NZJ23R65BY/graph.json","fetch_events":"https://pith.science/api/pith-number/MSCCLJPP3TF5LM67NZJ23R65BY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MSCCLJPP3TF5LM67NZJ23R65BY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MSCCLJPP3TF5LM67NZJ23R65BY/action/storage_attestation","attest_author":"https://pith.science/pith/MSCCLJPP3TF5LM67NZJ23R65BY/action/author_attestation","sign_citation":"https://pith.science/pith/MSCCLJPP3TF5LM67NZJ23R65BY/action/citation_signature","submit_replication":"https://pith.science/pith/MSCCLJPP3TF5LM67NZJ23R65BY/action/replication_record"}},"created_at":"2026-05-18T00:12:32.114085+00:00","updated_at":"2026-05-18T00:12:32.114085+00:00"}