{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:DOTZV55DUEJLJ4DON7OERSTM3P","short_pith_number":"pith:DOTZV55D","canonical_record":{"source":{"id":"2302.08340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-16T14:50:20Z","cross_cats_sorted":["cs.DM","math.PR"],"title_canon_sha256":"cbb3c686715aa5df1128dbbbefeb17fedee7d22c8f6d46e5a79335957262feaa","abstract_canon_sha256":"667c20bdb86ddc055e54763c9f19b7ccfece2d77098798bc7c80db0e1cc31b0f"},"schema_version":"1.0"},"canonical_sha256":"1ba79af7a3a112b4f06e6fdc48ca6cdbd0ea9d777fc5c2e92edd2e981e5b2870","source":{"kind":"arxiv","id":"2302.08340","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08340","created_at":"2026-07-05T05:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08340v1","created_at":"2026-07-05T05:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08340","created_at":"2026-07-05T05:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"DOTZV55DUEJL","created_at":"2026-07-05T05:42:37Z"},{"alias_kind":"pith_short_16","alias_value":"DOTZV55DUEJLJ4DO","created_at":"2026-07-05T05:42:37Z"},{"alias_kind":"pith_short_8","alias_value":"DOTZV55D","created_at":"2026-07-05T05:42:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:DOTZV55DUEJLJ4DON7OERSTM3P","target":"record","payload":{"canonical_record":{"source":{"id":"2302.08340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-16T14:50:20Z","cross_cats_sorted":["cs.DM","math.PR"],"title_canon_sha256":"cbb3c686715aa5df1128dbbbefeb17fedee7d22c8f6d46e5a79335957262feaa","abstract_canon_sha256":"667c20bdb86ddc055e54763c9f19b7ccfece2d77098798bc7c80db0e1cc31b0f"},"schema_version":"1.0"},"canonical_sha256":"1ba79af7a3a112b4f06e6fdc48ca6cdbd0ea9d777fc5c2e92edd2e981e5b2870","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:42:37.027377Z","signature_b64":"BCFAEpx2aRuIVJswc9nmiyLOEx6uhOQrXrdf0F9CF7qn9OKgaEEZnVyJ9lGhQU04lHapHcceZs/1uSBkgqfFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ba79af7a3a112b4f06e6fdc48ca6cdbd0ea9d777fc5c2e92edd2e981e5b2870","last_reissued_at":"2026-07-05T05:42:37.027015Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:42:37.027015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.08340","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":"2026-07-05T05:42:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rqmKvii2MJNVqc0xQgJGFfkekJfUWSnwmTlVUarhTtwyw7XmBPgg5Qqdy1eAs/NoteWBiMO5kV7qV7YQ2aH1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:47:36.237714Z"},"content_sha256":"cc57c2a7d14ad1444804afe117c308e5a24b8035e60a6c9849b9de4b38f8981f","schema_version":"1.0","event_id":"sha256:cc57c2a7d14ad1444804afe117c308e5a24b8035e60a6c9849b9de4b38f8981f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:DOTZV55DUEJLJ4DON7OERSTM3P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The hitting time of clique factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.CO","authors_text":"Annika Heckel, Marc Kaufmann, Matija Pasch, Noela M\\\"uller","submitted_at":"2023-02-16T14:50:20Z","abstract_excerpt":"In a recent paper, Kahn gave the strongest possible, affirmative, answer to Shamir's problem, which had been open since the late 1970s: Let $r \\ge 3 $ and let $n$ be divisible by $r$. Then, in the random $r$-uniform hypergraph process on $n$ vertices, as soon as the last isolated vertex disappears, a perfect matching emerges. In the present work, we transfer this hitting time result to the setting of clique factors in the random graph process: At the time that the last vertex joins a copy of the complete graph $K_r$, the random graph process contains a $K_r$-factor. Our proof draws on a novel "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08340","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/2302.08340/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:42:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NpKQrdeZfkRptETnJaVj1ljcSOC2itNN+o9H1wtApJjk6/8EZdBCv7Gc12UedwaWDM7tqeJQiC6DThUpH5isBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:47:36.238090Z"},"content_sha256":"6360adde781ea92e1eccd9b68b66cfb2ed0f1bef989e5f1f068d630e96718d70","schema_version":"1.0","event_id":"sha256:6360adde781ea92e1eccd9b68b66cfb2ed0f1bef989e5f1f068d630e96718d70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOTZV55DUEJLJ4DON7OERSTM3P/bundle.json","state_url":"https://pith.science/pith/DOTZV55DUEJLJ4DON7OERSTM3P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOTZV55DUEJLJ4DON7OERSTM3P/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":"2026-07-06T10:47:36Z","links":{"resolver":"https://pith.science/pith/DOTZV55DUEJLJ4DON7OERSTM3P","bundle":"https://pith.science/pith/DOTZV55DUEJLJ4DON7OERSTM3P/bundle.json","state":"https://pith.science/pith/DOTZV55DUEJLJ4DON7OERSTM3P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOTZV55DUEJLJ4DON7OERSTM3P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:DOTZV55DUEJLJ4DON7OERSTM3P","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":"667c20bdb86ddc055e54763c9f19b7ccfece2d77098798bc7c80db0e1cc31b0f","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-16T14:50:20Z","title_canon_sha256":"cbb3c686715aa5df1128dbbbefeb17fedee7d22c8f6d46e5a79335957262feaa"},"schema_version":"1.0","source":{"id":"2302.08340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08340","created_at":"2026-07-05T05:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08340v1","created_at":"2026-07-05T05:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08340","created_at":"2026-07-05T05:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"DOTZV55DUEJL","created_at":"2026-07-05T05:42:37Z"},{"alias_kind":"pith_short_16","alias_value":"DOTZV55DUEJLJ4DO","created_at":"2026-07-05T05:42:37Z"},{"alias_kind":"pith_short_8","alias_value":"DOTZV55D","created_at":"2026-07-05T05:42:37Z"}],"graph_snapshots":[{"event_id":"sha256:6360adde781ea92e1eccd9b68b66cfb2ed0f1bef989e5f1f068d630e96718d70","target":"graph","created_at":"2026-07-05T05:42:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.08340/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a recent paper, Kahn gave the strongest possible, affirmative, answer to Shamir's problem, which had been open since the late 1970s: Let $r \\ge 3 $ and let $n$ be divisible by $r$. Then, in the random $r$-uniform hypergraph process on $n$ vertices, as soon as the last isolated vertex disappears, a perfect matching emerges. In the present work, we transfer this hitting time result to the setting of clique factors in the random graph process: At the time that the last vertex joins a copy of the complete graph $K_r$, the random graph process contains a $K_r$-factor. Our proof draws on a novel ","authors_text":"Annika Heckel, Marc Kaufmann, Matija Pasch, Noela M\\\"uller","cross_cats":["cs.DM","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-16T14:50:20Z","title":"The hitting time of clique factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08340","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:cc57c2a7d14ad1444804afe117c308e5a24b8035e60a6c9849b9de4b38f8981f","target":"record","created_at":"2026-07-05T05:42:37Z","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":"667c20bdb86ddc055e54763c9f19b7ccfece2d77098798bc7c80db0e1cc31b0f","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-16T14:50:20Z","title_canon_sha256":"cbb3c686715aa5df1128dbbbefeb17fedee7d22c8f6d46e5a79335957262feaa"},"schema_version":"1.0","source":{"id":"2302.08340","kind":"arxiv","version":1}},"canonical_sha256":"1ba79af7a3a112b4f06e6fdc48ca6cdbd0ea9d777fc5c2e92edd2e981e5b2870","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ba79af7a3a112b4f06e6fdc48ca6cdbd0ea9d777fc5c2e92edd2e981e5b2870","first_computed_at":"2026-07-05T05:42:37.027015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:42:37.027015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BCFAEpx2aRuIVJswc9nmiyLOEx6uhOQrXrdf0F9CF7qn9OKgaEEZnVyJ9lGhQU04lHapHcceZs/1uSBkgqfFDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:42:37.027377Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.08340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc57c2a7d14ad1444804afe117c308e5a24b8035e60a6c9849b9de4b38f8981f","sha256:6360adde781ea92e1eccd9b68b66cfb2ed0f1bef989e5f1f068d630e96718d70"],"state_sha256":"b1a87f2a3db7bcc2f91356d02e0141a27755b6fd08856054071905bfb5122721"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T87wjDvjyvC0ryd8TkezhH0f3D3Qcm2IXPHPDV6XnDh8Nl7l3d2EsUMCG5aw9TOBjqXvX25OBPSH2RWaZIbtBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T10:47:36.240064Z","bundle_sha256":"c4c36a09cde9ed33bfdb9e633694898f7c8e304cc7476e8ac3726a25fa3ba299"}}