{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EIT73TL4J5ZW2PFXOMIG77YWGZ","short_pith_number":"pith:EIT73TL4","canonical_record":{"source":{"id":"2501.18238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-30T09:54:39Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"5f87037da93a212e8327671b286507d941ac940ce88f42bbb04188e9307c9b45","abstract_canon_sha256":"2f8bf4d3b925e2bbdd1dd98e1497e69a1e8e18364a4bab9d59c328f4145db80d"},"schema_version":"1.0"},"canonical_sha256":"2227fdcd7c4f736d3cb773106fff16364a4e59e0bd2bc6f7d0e491106181a774","source":{"kind":"arxiv","id":"2501.18238","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.18238","created_at":"2026-07-05T10:07:31Z"},{"alias_kind":"arxiv_version","alias_value":"2501.18238v1","created_at":"2026-07-05T10:07:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18238","created_at":"2026-07-05T10:07:31Z"},{"alias_kind":"pith_short_12","alias_value":"EIT73TL4J5ZW","created_at":"2026-07-05T10:07:31Z"},{"alias_kind":"pith_short_16","alias_value":"EIT73TL4J5ZW2PFX","created_at":"2026-07-05T10:07:31Z"},{"alias_kind":"pith_short_8","alias_value":"EIT73TL4","created_at":"2026-07-05T10:07:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EIT73TL4J5ZW2PFXOMIG77YWGZ","target":"record","payload":{"canonical_record":{"source":{"id":"2501.18238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-30T09:54:39Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"5f87037da93a212e8327671b286507d941ac940ce88f42bbb04188e9307c9b45","abstract_canon_sha256":"2f8bf4d3b925e2bbdd1dd98e1497e69a1e8e18364a4bab9d59c328f4145db80d"},"schema_version":"1.0"},"canonical_sha256":"2227fdcd7c4f736d3cb773106fff16364a4e59e0bd2bc6f7d0e491106181a774","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:31.514347Z","signature_b64":"6vwgU6whkrws92LdR7hU+3RZf/fW52DT3G5cSTWwrjyU5AKKhv0U8IDtBzqUPNkOA1LHeD15v7lPaQ0VZti3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2227fdcd7c4f736d3cb773106fff16364a4e59e0bd2bc6f7d0e491106181a774","last_reissued_at":"2026-07-05T10:07:31.513902Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:31.513902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.18238","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":"2026-07-05T10:07:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sJA8gs+6bKqtw6xxqMeSA2o4CsIzyHeznZLCZ6yIORDDK84nvpLyNnqeBXUOu8CW+bm8sgEeAUXvFLNdcxD2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:38:40.127073Z"},"content_sha256":"be5af91bad24213aeb22a83a9d3a30727632a0d6721c0e633f6b4c8e63097f78","schema_version":"1.0","event_id":"sha256:be5af91bad24213aeb22a83a9d3a30727632a0d6721c0e633f6b4c8e63097f78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EIT73TL4J5ZW2PFXOMIG77YWGZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triangle-free $d$-degenerate graphs have small fractional chromatic number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Anders Martinsson","submitted_at":"2025-01-30T09:54:39Z","abstract_excerpt":"A well-known conjecture by Harris states that any triangle-free $d$-degenerate graph has fractional chromatic number at most $O\\left(\\frac{d}{\\ln d}\\right)$. This conjecture has gained much attention in recent years, and is known to have many interesting implications, including a conjecture by Esperet, Kang and Thomass\\'e that any triangle-free graph with minimum degree $d$ contains a bipartite induced subgraph of minimum degree $\\Omega(\\log d)$. Despite this attention, Harris' conjecture has remained wide open with no known improvement on the trivial upper bound, until now.\n  In this article,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18238","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/2501.18238/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":"2026-07-05T10:07:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gg5TH6ZgKQ0kIxO0F8wzfCvr0FdCd+n4dBKI4YuWLxE/i8sEb/Ckv7lrfnsX7eZHrFx0M5fvhBaoGDjmM3LIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:38:40.128075Z"},"content_sha256":"3a9ccd7278df33b502f5c456355e0bb23c442cf33667064a4c44f7c3091b9f51","schema_version":"1.0","event_id":"sha256:3a9ccd7278df33b502f5c456355e0bb23c442cf33667064a4c44f7c3091b9f51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EIT73TL4J5ZW2PFXOMIG77YWGZ/bundle.json","state_url":"https://pith.science/pith/EIT73TL4J5ZW2PFXOMIG77YWGZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EIT73TL4J5ZW2PFXOMIG77YWGZ/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":"2026-08-12T23:38:40Z","links":{"resolver":"https://pith.science/pith/EIT73TL4J5ZW2PFXOMIG77YWGZ","bundle":"https://pith.science/pith/EIT73TL4J5ZW2PFXOMIG77YWGZ/bundle.json","state":"https://pith.science/pith/EIT73TL4J5ZW2PFXOMIG77YWGZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EIT73TL4J5ZW2PFXOMIG77YWGZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EIT73TL4J5ZW2PFXOMIG77YWGZ","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":"2f8bf4d3b925e2bbdd1dd98e1497e69a1e8e18364a4bab9d59c328f4145db80d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-30T09:54:39Z","title_canon_sha256":"5f87037da93a212e8327671b286507d941ac940ce88f42bbb04188e9307c9b45"},"schema_version":"1.0","source":{"id":"2501.18238","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.18238","created_at":"2026-07-05T10:07:31Z"},{"alias_kind":"arxiv_version","alias_value":"2501.18238v1","created_at":"2026-07-05T10:07:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18238","created_at":"2026-07-05T10:07:31Z"},{"alias_kind":"pith_short_12","alias_value":"EIT73TL4J5ZW","created_at":"2026-07-05T10:07:31Z"},{"alias_kind":"pith_short_16","alias_value":"EIT73TL4J5ZW2PFX","created_at":"2026-07-05T10:07:31Z"},{"alias_kind":"pith_short_8","alias_value":"EIT73TL4","created_at":"2026-07-05T10:07:31Z"}],"graph_snapshots":[{"event_id":"sha256:3a9ccd7278df33b502f5c456355e0bb23c442cf33667064a4c44f7c3091b9f51","target":"graph","created_at":"2026-07-05T10:07:31Z","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/2501.18238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A well-known conjecture by Harris states that any triangle-free $d$-degenerate graph has fractional chromatic number at most $O\\left(\\frac{d}{\\ln d}\\right)$. This conjecture has gained much attention in recent years, and is known to have many interesting implications, including a conjecture by Esperet, Kang and Thomass\\'e that any triangle-free graph with minimum degree $d$ contains a bipartite induced subgraph of minimum degree $\\Omega(\\log d)$. Despite this attention, Harris' conjecture has remained wide open with no known improvement on the trivial upper bound, until now.\n  In this article,","authors_text":"Anders Martinsson","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-30T09:54:39Z","title":"Triangle-free $d$-degenerate graphs have small fractional chromatic number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18238","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:be5af91bad24213aeb22a83a9d3a30727632a0d6721c0e633f6b4c8e63097f78","target":"record","created_at":"2026-07-05T10:07:31Z","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":"2f8bf4d3b925e2bbdd1dd98e1497e69a1e8e18364a4bab9d59c328f4145db80d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-30T09:54:39Z","title_canon_sha256":"5f87037da93a212e8327671b286507d941ac940ce88f42bbb04188e9307c9b45"},"schema_version":"1.0","source":{"id":"2501.18238","kind":"arxiv","version":1}},"canonical_sha256":"2227fdcd7c4f736d3cb773106fff16364a4e59e0bd2bc6f7d0e491106181a774","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2227fdcd7c4f736d3cb773106fff16364a4e59e0bd2bc6f7d0e491106181a774","first_computed_at":"2026-07-05T10:07:31.513902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:07:31.513902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6vwgU6whkrws92LdR7hU+3RZf/fW52DT3G5cSTWwrjyU5AKKhv0U8IDtBzqUPNkOA1LHeD15v7lPaQ0VZti3Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:07:31.514347Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.18238","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be5af91bad24213aeb22a83a9d3a30727632a0d6721c0e633f6b4c8e63097f78","sha256:3a9ccd7278df33b502f5c456355e0bb23c442cf33667064a4c44f7c3091b9f51"],"state_sha256":"4af7bcb54a1744dd092f31d14b166d6ca0fd843a2b850ca136ff2e1b41695366"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9anl2q2Ebg3a/kkVVVtIu9S4yQt4wtmrip3EvHranAijtyjPGawcPxryCOeJBbdt9UkfQeLrTYvp8ME8hs16CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T23:38:40.135507Z","bundle_sha256":"05f87291850732a57a456e6299868a49aaaaa8751bbff5f1c9a0dbaafa3e8056"}}