{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KTIX75QAD5WJUUJ5Q7MNJ6JWBC","short_pith_number":"pith:KTIX75QA","canonical_record":{"source":{"id":"2509.07760","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-09-09T13:58:07Z","cross_cats_sorted":[],"title_canon_sha256":"45eef8e539d5114d01c796e6de2ee3a66d89681427fa800c7eae615c85daeade","abstract_canon_sha256":"6d70822a42f9b2d035bc742930fe47a0ad9922a48e4d92a86301494c883d5cf9"},"schema_version":"1.0"},"canonical_sha256":"54d17ff6001f6c9a513d87d8d4f93608a9a23c220a18490a757be29703c69c4e","source":{"kind":"arxiv","id":"2509.07760","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.07760","created_at":"2026-07-05T12:07:27Z"},{"alias_kind":"arxiv_version","alias_value":"2509.07760v1","created_at":"2026-07-05T12:07:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07760","created_at":"2026-07-05T12:07:27Z"},{"alias_kind":"pith_short_12","alias_value":"KTIX75QAD5WJ","created_at":"2026-07-05T12:07:27Z"},{"alias_kind":"pith_short_16","alias_value":"KTIX75QAD5WJUUJ5","created_at":"2026-07-05T12:07:27Z"},{"alias_kind":"pith_short_8","alias_value":"KTIX75QA","created_at":"2026-07-05T12:07:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KTIX75QAD5WJUUJ5Q7MNJ6JWBC","target":"record","payload":{"canonical_record":{"source":{"id":"2509.07760","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-09-09T13:58:07Z","cross_cats_sorted":[],"title_canon_sha256":"45eef8e539d5114d01c796e6de2ee3a66d89681427fa800c7eae615c85daeade","abstract_canon_sha256":"6d70822a42f9b2d035bc742930fe47a0ad9922a48e4d92a86301494c883d5cf9"},"schema_version":"1.0"},"canonical_sha256":"54d17ff6001f6c9a513d87d8d4f93608a9a23c220a18490a757be29703c69c4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:07:27.634230Z","signature_b64":"kmLZ+uc25DJ2KM/qimeAS1SMu6Q7j7+hwxTadyeJrlYIjviobiRWXQbp0Mjey+lRcB5abqQ8ohfHfeuFR29BAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54d17ff6001f6c9a513d87d8d4f93608a9a23c220a18490a757be29703c69c4e","last_reissued_at":"2026-07-05T12:07:27.633692Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:07:27.633692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.07760","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":"2026-07-05T12:07:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hx0nO6pOXKxAfx6qHv5O3+fwCzOK5sRprlC0paeyPN4/5FwlM9LSyd4JQaqvu4zInZl10PetLUpu6PT33a/VAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T00:18:11.369343Z"},"content_sha256":"4c1897d192ae8cfd88baa069ad466f31aed9392d7171dc012a38b860e9978678","schema_version":"1.0","event_id":"sha256:4c1897d192ae8cfd88baa069ad466f31aed9392d7171dc012a38b860e9978678"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KTIX75QAD5WJUUJ5Q7MNJ6JWBC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A directed Andr\\'asfai-Erd\\H{o}s-S\\'os theorem and chromatic profiles of oriented cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yisai Xue","submitted_at":"2025-09-09T13:58:07Z","abstract_excerpt":"The chromatic profile of a digraph $H$, denoted by $\\delta_{\\chi}^{+}(H,k)$, is the infimum $d$ such that any $H$-free digraph $D$ on $n$ vertices with minimum out-degree $\\delta^{+}(D) \\ge dn$ must be $k$-colorable. We determine the exact chromatic profile for several fundamental classes of digraphs. Our main result is a directed analogue of the Andr\\'asfai-Erd\\H{o}s-S\\'os theorem, stating that $\\delta_\\chi^{+}(T_r, r-1)=\\frac{3 r-7}{3 r-4}$, where $T_r$ is the transitive tournament on $r$ vertices. We then determine the chromatic profile for directed odd cycles, showing that $\\delta^+_\\chi(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07760","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/2509.07760/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":"2026-07-05T12:07:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R27OnHJ4kvXzouOXd/jjGqQ0ewnDe1watBxOdclHRyXDJJVDBmmTldHUJQexuP99tVNu44i/Px3jVOBmS276CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T00:18:11.369846Z"},"content_sha256":"fdf8d90095ee7989619c570ab1f27f5984b0e592b14e1aef72d6838812a56e8b","schema_version":"1.0","event_id":"sha256:fdf8d90095ee7989619c570ab1f27f5984b0e592b14e1aef72d6838812a56e8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KTIX75QAD5WJUUJ5Q7MNJ6JWBC/bundle.json","state_url":"https://pith.science/pith/KTIX75QAD5WJUUJ5Q7MNJ6JWBC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KTIX75QAD5WJUUJ5Q7MNJ6JWBC/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":"2026-08-06T00:18:11Z","links":{"resolver":"https://pith.science/pith/KTIX75QAD5WJUUJ5Q7MNJ6JWBC","bundle":"https://pith.science/pith/KTIX75QAD5WJUUJ5Q7MNJ6JWBC/bundle.json","state":"https://pith.science/pith/KTIX75QAD5WJUUJ5Q7MNJ6JWBC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KTIX75QAD5WJUUJ5Q7MNJ6JWBC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KTIX75QAD5WJUUJ5Q7MNJ6JWBC","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":"6d70822a42f9b2d035bc742930fe47a0ad9922a48e4d92a86301494c883d5cf9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-09-09T13:58:07Z","title_canon_sha256":"45eef8e539d5114d01c796e6de2ee3a66d89681427fa800c7eae615c85daeade"},"schema_version":"1.0","source":{"id":"2509.07760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.07760","created_at":"2026-07-05T12:07:27Z"},{"alias_kind":"arxiv_version","alias_value":"2509.07760v1","created_at":"2026-07-05T12:07:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07760","created_at":"2026-07-05T12:07:27Z"},{"alias_kind":"pith_short_12","alias_value":"KTIX75QAD5WJ","created_at":"2026-07-05T12:07:27Z"},{"alias_kind":"pith_short_16","alias_value":"KTIX75QAD5WJUUJ5","created_at":"2026-07-05T12:07:27Z"},{"alias_kind":"pith_short_8","alias_value":"KTIX75QA","created_at":"2026-07-05T12:07:27Z"}],"graph_snapshots":[{"event_id":"sha256:fdf8d90095ee7989619c570ab1f27f5984b0e592b14e1aef72d6838812a56e8b","target":"graph","created_at":"2026-07-05T12:07:27Z","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/2509.07760/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The chromatic profile of a digraph $H$, denoted by $\\delta_{\\chi}^{+}(H,k)$, is the infimum $d$ such that any $H$-free digraph $D$ on $n$ vertices with minimum out-degree $\\delta^{+}(D) \\ge dn$ must be $k$-colorable. We determine the exact chromatic profile for several fundamental classes of digraphs. Our main result is a directed analogue of the Andr\\'asfai-Erd\\H{o}s-S\\'os theorem, stating that $\\delta_\\chi^{+}(T_r, r-1)=\\frac{3 r-7}{3 r-4}$, where $T_r$ is the transitive tournament on $r$ vertices. We then determine the chromatic profile for directed odd cycles, showing that $\\delta^+_\\chi(\\","authors_text":"Yisai Xue","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-09-09T13:58:07Z","title":"A directed Andr\\'asfai-Erd\\H{o}s-S\\'os theorem and chromatic profiles of oriented cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07760","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":"sha256:4c1897d192ae8cfd88baa069ad466f31aed9392d7171dc012a38b860e9978678","target":"record","created_at":"2026-07-05T12:07:27Z","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":"6d70822a42f9b2d035bc742930fe47a0ad9922a48e4d92a86301494c883d5cf9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-09-09T13:58:07Z","title_canon_sha256":"45eef8e539d5114d01c796e6de2ee3a66d89681427fa800c7eae615c85daeade"},"schema_version":"1.0","source":{"id":"2509.07760","kind":"arxiv","version":1}},"canonical_sha256":"54d17ff6001f6c9a513d87d8d4f93608a9a23c220a18490a757be29703c69c4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54d17ff6001f6c9a513d87d8d4f93608a9a23c220a18490a757be29703c69c4e","first_computed_at":"2026-07-05T12:07:27.633692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:07:27.633692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kmLZ+uc25DJ2KM/qimeAS1SMu6Q7j7+hwxTadyeJrlYIjviobiRWXQbp0Mjey+lRcB5abqQ8ohfHfeuFR29BAA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:07:27.634230Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.07760","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c1897d192ae8cfd88baa069ad466f31aed9392d7171dc012a38b860e9978678","sha256:fdf8d90095ee7989619c570ab1f27f5984b0e592b14e1aef72d6838812a56e8b"],"state_sha256":"d15ee2e6a3b45473b2448117b7306634f03df810cd4f2c9fa11a79cf1071e5fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LrKM8D3CsZA5bO6vCFeQjX6axFaXfnOw6dvPo87GAjPyMwLQlBdzTu0+6MsHfcENQQGOUQ5plxbqPHjd5otOCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T00:18:11.374083Z","bundle_sha256":"2081eb1094e287526ab05ce08eb82072693d9c6c181a1b5f7202fae31d4b1893"}}