{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QVJETXLDBNQUL23AN75YYVT3A5","short_pith_number":"pith:QVJETXLD","canonical_record":{"source":{"id":"2506.11866","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-13T15:14:19Z","cross_cats_sorted":[],"title_canon_sha256":"283c2f37e714372405450eac174995d12775fd4cf76168d140945055009c5854","abstract_canon_sha256":"783b25b8331a930d20b76907face84f709dc3bd4717d1ba82786987774688ea0"},"schema_version":"1.0"},"canonical_sha256":"855249dd630b6145eb606ffb8c567b076b90903977ec54e59d80a088ab7ade4d","source":{"kind":"arxiv","id":"2506.11866","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11866","created_at":"2026-07-05T11:21:11Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11866v1","created_at":"2026-07-05T11:21:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11866","created_at":"2026-07-05T11:21:11Z"},{"alias_kind":"pith_short_12","alias_value":"QVJETXLDBNQU","created_at":"2026-07-05T11:21:11Z"},{"alias_kind":"pith_short_16","alias_value":"QVJETXLDBNQUL23A","created_at":"2026-07-05T11:21:11Z"},{"alias_kind":"pith_short_8","alias_value":"QVJETXLD","created_at":"2026-07-05T11:21:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QVJETXLDBNQUL23AN75YYVT3A5","target":"record","payload":{"canonical_record":{"source":{"id":"2506.11866","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-13T15:14:19Z","cross_cats_sorted":[],"title_canon_sha256":"283c2f37e714372405450eac174995d12775fd4cf76168d140945055009c5854","abstract_canon_sha256":"783b25b8331a930d20b76907face84f709dc3bd4717d1ba82786987774688ea0"},"schema_version":"1.0"},"canonical_sha256":"855249dd630b6145eb606ffb8c567b076b90903977ec54e59d80a088ab7ade4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:21:11.957968Z","signature_b64":"E4d7Cjc9Sov/oWT2si+ni+wPYq6V+7rJ4dRDhNM9PC68vVNxKk3TgLkhGsfbWeQu0xFZrJq5p9fIj8iZl1IRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"855249dd630b6145eb606ffb8c567b076b90903977ec54e59d80a088ab7ade4d","last_reissued_at":"2026-07-05T11:21:11.957525Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:21:11.957525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.11866","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":"2026-07-05T11:21:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wtw99qKP/tOxP5NlBhtA7PoXtw6YzHbrKPp2qFls/yHJ2c2hZVooWybbd7ANkqTv7MkiTZMKSbL8W7vb74J/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T19:50:56.527210Z"},"content_sha256":"8fd10e572e3831864310841edecc9a576b9dd6c42a008be7a5b04f84377679da","schema_version":"1.0","event_id":"sha256:8fd10e572e3831864310841edecc9a576b9dd6c42a008be7a5b04f84377679da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QVJETXLDBNQUL23AN75YYVT3A5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Antidirected paths in oriented graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Grzesik, Marek Skrzypczyk","submitted_at":"2025-06-13T15:14:19Z","abstract_excerpt":"We show that for any integer $k \\ge 4$, every oriented graph with minimum semidegree bigger than $\\frac{1}{2}(k-1+\\sqrt{k-3})$ contains an antidirected path of length $k$. Consequently, every oriented graph on $n$ vertices with more than $(k-1+\\sqrt{k-3})n$ edges contains an antidirected path of length $k$. This asymptotically proves the antidirected path version of a conjecture of Stein and of a conjecture of Addario-Berry, Havet, Linhares Sales, Reed and Thomass\\'e, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11866","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/2506.11866/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":"2026-07-05T11:21:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TZBLuHP5arU/xd+GPXmM39MwZuIMuBT9Gq2v209RXW57dxkla0lHpOSyYPHD7vvvyxdaPE1ba3VFje3D8fiZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T19:50:56.527854Z"},"content_sha256":"6e535cad7c0473eaf68e09602d3cbecd05b94f2a60b14f84c6027f6de953bc27","schema_version":"1.0","event_id":"sha256:6e535cad7c0473eaf68e09602d3cbecd05b94f2a60b14f84c6027f6de953bc27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVJETXLDBNQUL23AN75YYVT3A5/bundle.json","state_url":"https://pith.science/pith/QVJETXLDBNQUL23AN75YYVT3A5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVJETXLDBNQUL23AN75YYVT3A5/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":"2026-08-13T19:50:56Z","links":{"resolver":"https://pith.science/pith/QVJETXLDBNQUL23AN75YYVT3A5","bundle":"https://pith.science/pith/QVJETXLDBNQUL23AN75YYVT3A5/bundle.json","state":"https://pith.science/pith/QVJETXLDBNQUL23AN75YYVT3A5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVJETXLDBNQUL23AN75YYVT3A5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QVJETXLDBNQUL23AN75YYVT3A5","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":"783b25b8331a930d20b76907face84f709dc3bd4717d1ba82786987774688ea0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-13T15:14:19Z","title_canon_sha256":"283c2f37e714372405450eac174995d12775fd4cf76168d140945055009c5854"},"schema_version":"1.0","source":{"id":"2506.11866","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11866","created_at":"2026-07-05T11:21:11Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11866v1","created_at":"2026-07-05T11:21:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11866","created_at":"2026-07-05T11:21:11Z"},{"alias_kind":"pith_short_12","alias_value":"QVJETXLDBNQU","created_at":"2026-07-05T11:21:11Z"},{"alias_kind":"pith_short_16","alias_value":"QVJETXLDBNQUL23A","created_at":"2026-07-05T11:21:11Z"},{"alias_kind":"pith_short_8","alias_value":"QVJETXLD","created_at":"2026-07-05T11:21:11Z"}],"graph_snapshots":[{"event_id":"sha256:6e535cad7c0473eaf68e09602d3cbecd05b94f2a60b14f84c6027f6de953bc27","target":"graph","created_at":"2026-07-05T11:21:11Z","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/2506.11866/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that for any integer $k \\ge 4$, every oriented graph with minimum semidegree bigger than $\\frac{1}{2}(k-1+\\sqrt{k-3})$ contains an antidirected path of length $k$. Consequently, every oriented graph on $n$ vertices with more than $(k-1+\\sqrt{k-3})n$ edges contains an antidirected path of length $k$. This asymptotically proves the antidirected path version of a conjecture of Stein and of a conjecture of Addario-Berry, Havet, Linhares Sales, Reed and Thomass\\'e, respectively.","authors_text":"Andrzej Grzesik, Marek Skrzypczyk","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-13T15:14:19Z","title":"Antidirected paths in oriented graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11866","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":"sha256:8fd10e572e3831864310841edecc9a576b9dd6c42a008be7a5b04f84377679da","target":"record","created_at":"2026-07-05T11:21:11Z","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":"783b25b8331a930d20b76907face84f709dc3bd4717d1ba82786987774688ea0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-13T15:14:19Z","title_canon_sha256":"283c2f37e714372405450eac174995d12775fd4cf76168d140945055009c5854"},"schema_version":"1.0","source":{"id":"2506.11866","kind":"arxiv","version":1}},"canonical_sha256":"855249dd630b6145eb606ffb8c567b076b90903977ec54e59d80a088ab7ade4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"855249dd630b6145eb606ffb8c567b076b90903977ec54e59d80a088ab7ade4d","first_computed_at":"2026-07-05T11:21:11.957525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:11.957525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E4d7Cjc9Sov/oWT2si+ni+wPYq6V+7rJ4dRDhNM9PC68vVNxKk3TgLkhGsfbWeQu0xFZrJq5p9fIj8iZl1IRAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:11.957968Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.11866","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fd10e572e3831864310841edecc9a576b9dd6c42a008be7a5b04f84377679da","sha256:6e535cad7c0473eaf68e09602d3cbecd05b94f2a60b14f84c6027f6de953bc27"],"state_sha256":"e48b2a835a6114424af441ab4d154d0a2a71c27eae59bda0f26b581eaa67ce3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l0XU3XWZyI29frQ8rJV+ft9S9W+Z9xsgzAaojznEFAxzFplkDIwPQkriMK3a2zI4ukGM+3/XFjKjoJsRohhnDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T19:50:56.598970Z","bundle_sha256":"4692caffd79c7c509697c2f3a929cbce9546873cf2de38e447fa48ea0565f0a4"}}