{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:YTCRCK7YYFWBCQBTVFQD53AGAJ","short_pith_number":"pith:YTCRCK7Y","canonical_record":{"source":{"id":"2506.01067","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-01T16:12:34Z","cross_cats_sorted":[],"title_canon_sha256":"d59e80a7bdf0043545ca2e87207e1e12e3c59cbdac833adf6cd33b3b3c254e58","abstract_canon_sha256":"04e65536e1dd1ad2c7146b3cc777748286d015cf24dc95445c1d1d4e41943c12"},"schema_version":"1.0"},"canonical_sha256":"c4c5112bf8c16c114033a9603eec060266691b1c3b793490396f268e9cb67bd0","source":{"kind":"arxiv","id":"2506.01067","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01067","created_at":"2026-07-05T11:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01067v1","created_at":"2026-07-05T11:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01067","created_at":"2026-07-05T11:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"YTCRCK7YYFWB","created_at":"2026-07-05T11:13:45Z"},{"alias_kind":"pith_short_16","alias_value":"YTCRCK7YYFWBCQBT","created_at":"2026-07-05T11:13:45Z"},{"alias_kind":"pith_short_8","alias_value":"YTCRCK7Y","created_at":"2026-07-05T11:13:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:YTCRCK7YYFWBCQBTVFQD53AGAJ","target":"record","payload":{"canonical_record":{"source":{"id":"2506.01067","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-01T16:12:34Z","cross_cats_sorted":[],"title_canon_sha256":"d59e80a7bdf0043545ca2e87207e1e12e3c59cbdac833adf6cd33b3b3c254e58","abstract_canon_sha256":"04e65536e1dd1ad2c7146b3cc777748286d015cf24dc95445c1d1d4e41943c12"},"schema_version":"1.0"},"canonical_sha256":"c4c5112bf8c16c114033a9603eec060266691b1c3b793490396f268e9cb67bd0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:13:45.395343Z","signature_b64":"lSQCCYalhc36C6XQiIciePTiMm9DyKzjk/Nif6vkLy8Ed0EB/Gb3D7lo1a+3WlZ50oFanaIhezc+vUCoty8BDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4c5112bf8c16c114033a9603eec060266691b1c3b793490396f268e9cb67bd0","last_reissued_at":"2026-07-05T11:13:45.394688Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:13:45.394688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.01067","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":"2026-07-05T11:13:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fi+YqLPkbaGvGFIu0UpwEpzIkHPmnzx4ilvzX+q7tedHMOY3dOrW7DyjSWTs1DWOd7LZw/dsyxdZCambE5viCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:31:06.738755Z"},"content_sha256":"070afb27492bea79bd6387d0701cc770fdc7c64133ee35e2711e84fe0fcac35d","schema_version":"1.0","event_id":"sha256:070afb27492bea79bd6387d0701cc770fdc7c64133ee35e2711e84fe0fcac35d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:YTCRCK7YYFWBCQBTVFQD53AGAJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Typical $T$-free graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bruce Reed, Yelena Yuditsky","submitted_at":"2025-06-01T16:12:34Z","abstract_excerpt":"We prove that for every tree $T$ which is not an edge, for almost every graph $G$ which does not contain $T$ as an induced subgraph, $V(G)$ has a partition into $\\alpha(T)-1$ parts certifying this fact. Each part induces a graph which is $P_4$-free and has further properties which depend on $T$. As a consequence we obtain good bounds (often tight up to a constant factor) on the number of $T$-free graphs and show in a follow-up paper~\\cite{RY} that almost every $T$-free graph $G$ has chromatic number equal to the size of its largest clique."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01067","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/2506.01067/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":"2026-07-05T11:13:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lnx2v2Q11rSMAI9Rsp6DK6TpmkYpFIqG0d17rfHG5UFwGHgvQaJEM4A6PoUVywhOyLThTlczdze+HfLCCDjjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:31:06.739366Z"},"content_sha256":"4dd057f668c5bd36612e438a27b945369574add58c558ce38746b00eb15e468f","schema_version":"1.0","event_id":"sha256:4dd057f668c5bd36612e438a27b945369574add58c558ce38746b00eb15e468f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YTCRCK7YYFWBCQBTVFQD53AGAJ/bundle.json","state_url":"https://pith.science/pith/YTCRCK7YYFWBCQBTVFQD53AGAJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YTCRCK7YYFWBCQBTVFQD53AGAJ/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":"2026-08-08T12:31:06Z","links":{"resolver":"https://pith.science/pith/YTCRCK7YYFWBCQBTVFQD53AGAJ","bundle":"https://pith.science/pith/YTCRCK7YYFWBCQBTVFQD53AGAJ/bundle.json","state":"https://pith.science/pith/YTCRCK7YYFWBCQBTVFQD53AGAJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YTCRCK7YYFWBCQBTVFQD53AGAJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YTCRCK7YYFWBCQBTVFQD53AGAJ","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":"04e65536e1dd1ad2c7146b3cc777748286d015cf24dc95445c1d1d4e41943c12","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-01T16:12:34Z","title_canon_sha256":"d59e80a7bdf0043545ca2e87207e1e12e3c59cbdac833adf6cd33b3b3c254e58"},"schema_version":"1.0","source":{"id":"2506.01067","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01067","created_at":"2026-07-05T11:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01067v1","created_at":"2026-07-05T11:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01067","created_at":"2026-07-05T11:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"YTCRCK7YYFWB","created_at":"2026-07-05T11:13:45Z"},{"alias_kind":"pith_short_16","alias_value":"YTCRCK7YYFWBCQBT","created_at":"2026-07-05T11:13:45Z"},{"alias_kind":"pith_short_8","alias_value":"YTCRCK7Y","created_at":"2026-07-05T11:13:45Z"}],"graph_snapshots":[{"event_id":"sha256:4dd057f668c5bd36612e438a27b945369574add58c558ce38746b00eb15e468f","target":"graph","created_at":"2026-07-05T11:13:45Z","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/2506.01067/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that for every tree $T$ which is not an edge, for almost every graph $G$ which does not contain $T$ as an induced subgraph, $V(G)$ has a partition into $\\alpha(T)-1$ parts certifying this fact. Each part induces a graph which is $P_4$-free and has further properties which depend on $T$. As a consequence we obtain good bounds (often tight up to a constant factor) on the number of $T$-free graphs and show in a follow-up paper~\\cite{RY} that almost every $T$-free graph $G$ has chromatic number equal to the size of its largest clique.","authors_text":"Bruce Reed, Yelena Yuditsky","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-01T16:12:34Z","title":"Typical $T$-free graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01067","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":"sha256:070afb27492bea79bd6387d0701cc770fdc7c64133ee35e2711e84fe0fcac35d","target":"record","created_at":"2026-07-05T11:13:45Z","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":"04e65536e1dd1ad2c7146b3cc777748286d015cf24dc95445c1d1d4e41943c12","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-01T16:12:34Z","title_canon_sha256":"d59e80a7bdf0043545ca2e87207e1e12e3c59cbdac833adf6cd33b3b3c254e58"},"schema_version":"1.0","source":{"id":"2506.01067","kind":"arxiv","version":1}},"canonical_sha256":"c4c5112bf8c16c114033a9603eec060266691b1c3b793490396f268e9cb67bd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4c5112bf8c16c114033a9603eec060266691b1c3b793490396f268e9cb67bd0","first_computed_at":"2026-07-05T11:13:45.394688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:13:45.394688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lSQCCYalhc36C6XQiIciePTiMm9DyKzjk/Nif6vkLy8Ed0EB/Gb3D7lo1a+3WlZ50oFanaIhezc+vUCoty8BDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:13:45.395343Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:070afb27492bea79bd6387d0701cc770fdc7c64133ee35e2711e84fe0fcac35d","sha256:4dd057f668c5bd36612e438a27b945369574add58c558ce38746b00eb15e468f"],"state_sha256":"80b00eff90f140c5fd1be128ae384a40033df8af6ab20312d9455a2a1d456a24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t4fvCohuiYfNkuH+rvZChPcdepU8eyBetWt+yD6FRX98nd+CzIfU9Bu/TvZZvzcOJIlTidJ5g2PRKkrhJa6IAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T12:31:06.744386Z","bundle_sha256":"7e7a768b4f17acc43abb9897690c9d73458243bf2a470a46fbb091abad594fd6"}}