{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:REV7KYFWMIIIJA2H5C6E2WG2UH","short_pith_number":"pith:REV7KYFW","canonical_record":{"source":{"id":"2301.13607","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-01-31T13:07:38Z","cross_cats_sorted":[],"title_canon_sha256":"b2ab70c166e274344f07640785e47861b4d9f607b77646b531458583e0d95587","abstract_canon_sha256":"34bb7ad1a1bf5ee91a34ef8cd4d1fd2319535b8c85e9bd5428c6b2c55571990c"},"schema_version":"1.0"},"canonical_sha256":"892bf560b66210848347e8bc4d58daa1f6b308eaec95b830abf38f4e1de11068","source":{"kind":"arxiv","id":"2301.13607","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.13607","created_at":"2026-07-05T07:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"2301.13607v3","created_at":"2026-07-05T07:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.13607","created_at":"2026-07-05T07:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"REV7KYFWMIII","created_at":"2026-07-05T07:04:12Z"},{"alias_kind":"pith_short_16","alias_value":"REV7KYFWMIIIJA2H","created_at":"2026-07-05T07:04:12Z"},{"alias_kind":"pith_short_8","alias_value":"REV7KYFW","created_at":"2026-07-05T07:04:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:REV7KYFWMIIIJA2H5C6E2WG2UH","target":"record","payload":{"canonical_record":{"source":{"id":"2301.13607","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-01-31T13:07:38Z","cross_cats_sorted":[],"title_canon_sha256":"b2ab70c166e274344f07640785e47861b4d9f607b77646b531458583e0d95587","abstract_canon_sha256":"34bb7ad1a1bf5ee91a34ef8cd4d1fd2319535b8c85e9bd5428c6b2c55571990c"},"schema_version":"1.0"},"canonical_sha256":"892bf560b66210848347e8bc4d58daa1f6b308eaec95b830abf38f4e1de11068","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:04:12.487299Z","signature_b64":"mOj8wMsKj+66N9TBlL/9OqJV9pvoEI3MClOhyCgPVaiA5/s9+4Cg9zDyNPk12SAC1R/guEaTqCL2T7Y1HzxDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"892bf560b66210848347e8bc4d58daa1f6b308eaec95b830abf38f4e1de11068","last_reissued_at":"2026-07-05T07:04:12.486772Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:04:12.486772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.13607","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:04:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jdb7ZdDNUAIJ3Zs+UfbyUNNletHvKNvF+fd2B5DkdO2TkcKHf0EcRI7Izua/ce2EnoeYeoPjajfnjxc4tgFuDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:22:54.458033Z"},"content_sha256":"a16c5d12351eab333e325513d3cd14074697bd86900f9037a0bdddd2bb4b8812","schema_version":"1.0","event_id":"sha256:a16c5d12351eab333e325513d3cd14074697bd86900f9037a0bdddd2bb4b8812"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:REV7KYFWMIIIJA2H5C6E2WG2UH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph classes with few $P_4$'s: Universality and Brownian graphon limits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Th\\'eo Lenoir","submitted_at":"2023-01-31T13:07:38Z","abstract_excerpt":"We consider large uniform labeled random graphs in different classes with few induced $P_4$ ($P_4$ is the graph consisting of a single line of $4$ vertices) which generalize the case of cographs. Our main result is the convergence to a Brownian limit object in the space of graphons. As a by-product we obtain new asymptotic enumerative results for all these graph classes. We also obtain typical density results for a wide variety of induced subgraphs. These asymptotics hold at a smaller scale than what is observable through the graphon convergence. Our proofs rely on tree encoding of graphs. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.13607","kind":"arxiv","version":3},"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/2301.13607/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":"2026-07-05T07:04:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5pROUk3+Mgn9xN8Q8MYPItZ41/l9Yao3mciTWEXRadYQ3veJsxMrPF28Cs2NZ3+BFOevrP/cpP8st3ZiHY0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:22:54.458599Z"},"content_sha256":"1a0b05e9ed98d03a16342a8b875648066f4cfdb0573e5253b4e0e65663837eef","schema_version":"1.0","event_id":"sha256:1a0b05e9ed98d03a16342a8b875648066f4cfdb0573e5253b4e0e65663837eef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/REV7KYFWMIIIJA2H5C6E2WG2UH/bundle.json","state_url":"https://pith.science/pith/REV7KYFWMIIIJA2H5C6E2WG2UH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/REV7KYFWMIIIJA2H5C6E2WG2UH/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":"2026-08-22T11:22:54Z","links":{"resolver":"https://pith.science/pith/REV7KYFWMIIIJA2H5C6E2WG2UH","bundle":"https://pith.science/pith/REV7KYFWMIIIJA2H5C6E2WG2UH/bundle.json","state":"https://pith.science/pith/REV7KYFWMIIIJA2H5C6E2WG2UH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/REV7KYFWMIIIJA2H5C6E2WG2UH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:REV7KYFWMIIIJA2H5C6E2WG2UH","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":"34bb7ad1a1bf5ee91a34ef8cd4d1fd2319535b8c85e9bd5428c6b2c55571990c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-01-31T13:07:38Z","title_canon_sha256":"b2ab70c166e274344f07640785e47861b4d9f607b77646b531458583e0d95587"},"schema_version":"1.0","source":{"id":"2301.13607","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.13607","created_at":"2026-07-05T07:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"2301.13607v3","created_at":"2026-07-05T07:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.13607","created_at":"2026-07-05T07:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"REV7KYFWMIII","created_at":"2026-07-05T07:04:12Z"},{"alias_kind":"pith_short_16","alias_value":"REV7KYFWMIIIJA2H","created_at":"2026-07-05T07:04:12Z"},{"alias_kind":"pith_short_8","alias_value":"REV7KYFW","created_at":"2026-07-05T07:04:12Z"}],"graph_snapshots":[{"event_id":"sha256:1a0b05e9ed98d03a16342a8b875648066f4cfdb0573e5253b4e0e65663837eef","target":"graph","created_at":"2026-07-05T07:04:12Z","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/2301.13607/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider large uniform labeled random graphs in different classes with few induced $P_4$ ($P_4$ is the graph consisting of a single line of $4$ vertices) which generalize the case of cographs. Our main result is the convergence to a Brownian limit object in the space of graphons. As a by-product we obtain new asymptotic enumerative results for all these graph classes. We also obtain typical density results for a wide variety of induced subgraphs. These asymptotics hold at a smaller scale than what is observable through the graphon convergence. Our proofs rely on tree encoding of graphs. We ","authors_text":"Th\\'eo Lenoir","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-01-31T13:07:38Z","title":"Graph classes with few $P_4$'s: Universality and Brownian graphon limits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.13607","kind":"arxiv","version":3},"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:a16c5d12351eab333e325513d3cd14074697bd86900f9037a0bdddd2bb4b8812","target":"record","created_at":"2026-07-05T07:04:12Z","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":"34bb7ad1a1bf5ee91a34ef8cd4d1fd2319535b8c85e9bd5428c6b2c55571990c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-01-31T13:07:38Z","title_canon_sha256":"b2ab70c166e274344f07640785e47861b4d9f607b77646b531458583e0d95587"},"schema_version":"1.0","source":{"id":"2301.13607","kind":"arxiv","version":3}},"canonical_sha256":"892bf560b66210848347e8bc4d58daa1f6b308eaec95b830abf38f4e1de11068","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"892bf560b66210848347e8bc4d58daa1f6b308eaec95b830abf38f4e1de11068","first_computed_at":"2026-07-05T07:04:12.486772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:04:12.486772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mOj8wMsKj+66N9TBlL/9OqJV9pvoEI3MClOhyCgPVaiA5/s9+4Cg9zDyNPk12SAC1R/guEaTqCL2T7Y1HzxDCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:04:12.487299Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.13607","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a16c5d12351eab333e325513d3cd14074697bd86900f9037a0bdddd2bb4b8812","sha256:1a0b05e9ed98d03a16342a8b875648066f4cfdb0573e5253b4e0e65663837eef"],"state_sha256":"762500e21b55a8c781465b30e90bfc9502f416ee981b9dd4b486d73f36fce1d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPwbnw56BNa5dZe2mFv3/wEiIRef8pliN94wZLgDQXqw4zW9442aA5sRrbnAEbEWmCVx6T3Q11TbvXgHkvKNAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T11:22:54.462537Z","bundle_sha256":"8959f0c71f5093a80b042175e92d172edee2d9a599098960260eaecdd6b5f47a"}}