{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QFORT6VTAVXURACDE5KQB4KX5F","short_pith_number":"pith:QFORT6VT","canonical_record":{"source":{"id":"1608.04153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-14T23:19:57Z","cross_cats_sorted":[],"title_canon_sha256":"dd88a4ae37a9f5f4b91ebd9cd1da90af8b28689c1957bbc52688b632e86ecc3c","abstract_canon_sha256":"4d19d1f2df5087924696c1036e549986579ae8e55cdc537dafa0a60a0f67b03b"},"schema_version":"1.0"},"canonical_sha256":"815d19fab3056f488043275500f157e96a0a695e58302d5d8628cade465fbefe","source":{"kind":"arxiv","id":"1608.04153","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04153","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04153v2","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04153","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"QFORT6VTAVXU","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QFORT6VTAVXURACD","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QFORT6VT","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QFORT6VTAVXURACDE5KQB4KX5F","target":"record","payload":{"canonical_record":{"source":{"id":"1608.04153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-14T23:19:57Z","cross_cats_sorted":[],"title_canon_sha256":"dd88a4ae37a9f5f4b91ebd9cd1da90af8b28689c1957bbc52688b632e86ecc3c","abstract_canon_sha256":"4d19d1f2df5087924696c1036e549986579ae8e55cdc537dafa0a60a0f67b03b"},"schema_version":"1.0"},"canonical_sha256":"815d19fab3056f488043275500f157e96a0a695e58302d5d8628cade465fbefe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:02.287220Z","signature_b64":"rONm9GSewn63JmrfyqWXlcBHbtm0Ufj2WihFQc5CotSZI1VRVMO389XhLOLyL+Ec3SrsAwKV2rLQqXjXmSArDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"815d19fab3056f488043275500f157e96a0a695e58302d5d8628cade465fbefe","last_reissued_at":"2026-05-18T01:04:02.286529Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:02.286529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.04153","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ktg5VaK8RbHJuwNuA9LyqoFzDlK3WygRsRTWGTic+a4FDub9B464pVOIQBN//OvdPCXHF9Yr8LvfOJZARMIjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:45:08.738164Z"},"content_sha256":"6bc837e09e98718de1f2c182060fd9163331e4272259954592b86c18a870df58","schema_version":"1.0","event_id":"sha256:6bc837e09e98718de1f2c182060fd9163331e4272259954592b86c18a870df58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QFORT6VTAVXURACDE5KQB4KX5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"1-color-avoiding paths, special tournaments, and incidence geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Yang, Jonathan Tidor, Victor Y. Wang","submitted_at":"2016-08-14T23:19:57Z","abstract_excerpt":"We discuss two approaches to a recent question of Loh: must a 3-colored transitive tournament on $N$ vertices have a 1-color-\\emph{avoiding} path of vertex-length at least $N^{2/3}$? This question generalizes the Erd\\H{o}s--Szekeres theorem on monotone subsequences.\n  First, we define three canonical transformations on these tournaments called Color, Record, and Dual. We use these to establish a reduction to special tournaments with natural geometric and combinatorial properties. In many cases (including all known tight examples), these tournaments have recursive Gallai decompositions. Not all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04153","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:04:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owjCdJaIq+n7drx5gD6E16hzS/6+ruZCopVuFK6RBqS7b19qxSHyki+fEP6WVjEhKBLvvkUi5aFmJPZv2QZiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:45:08.738537Z"},"content_sha256":"30801b19e2acb24c71d5c6dcdda274d15ac18d25d09bb837fbe5b2cb93a11c9a","schema_version":"1.0","event_id":"sha256:30801b19e2acb24c71d5c6dcdda274d15ac18d25d09bb837fbe5b2cb93a11c9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QFORT6VTAVXURACDE5KQB4KX5F/bundle.json","state_url":"https://pith.science/pith/QFORT6VTAVXURACDE5KQB4KX5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QFORT6VTAVXURACDE5KQB4KX5F/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":"2026-06-11T03:45:08Z","links":{"resolver":"https://pith.science/pith/QFORT6VTAVXURACDE5KQB4KX5F","bundle":"https://pith.science/pith/QFORT6VTAVXURACDE5KQB4KX5F/bundle.json","state":"https://pith.science/pith/QFORT6VTAVXURACDE5KQB4KX5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QFORT6VTAVXURACDE5KQB4KX5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QFORT6VTAVXURACDE5KQB4KX5F","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":"4d19d1f2df5087924696c1036e549986579ae8e55cdc537dafa0a60a0f67b03b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-14T23:19:57Z","title_canon_sha256":"dd88a4ae37a9f5f4b91ebd9cd1da90af8b28689c1957bbc52688b632e86ecc3c"},"schema_version":"1.0","source":{"id":"1608.04153","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04153","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04153v2","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04153","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"QFORT6VTAVXU","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QFORT6VTAVXURACD","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QFORT6VT","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:30801b19e2acb24c71d5c6dcdda274d15ac18d25d09bb837fbe5b2cb93a11c9a","target":"graph","created_at":"2026-05-18T01:04:02Z","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"},"paper":{"abstract_excerpt":"We discuss two approaches to a recent question of Loh: must a 3-colored transitive tournament on $N$ vertices have a 1-color-\\emph{avoiding} path of vertex-length at least $N^{2/3}$? This question generalizes the Erd\\H{o}s--Szekeres theorem on monotone subsequences.\n  First, we define three canonical transformations on these tournaments called Color, Record, and Dual. We use these to establish a reduction to special tournaments with natural geometric and combinatorial properties. In many cases (including all known tight examples), these tournaments have recursive Gallai decompositions. Not all","authors_text":"Ben Yang, Jonathan Tidor, Victor Y. Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-14T23:19:57Z","title":"1-color-avoiding paths, special tournaments, and incidence geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04153","kind":"arxiv","version":2},"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":"sha256:6bc837e09e98718de1f2c182060fd9163331e4272259954592b86c18a870df58","target":"record","created_at":"2026-05-18T01:04:02Z","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":"4d19d1f2df5087924696c1036e549986579ae8e55cdc537dafa0a60a0f67b03b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-14T23:19:57Z","title_canon_sha256":"dd88a4ae37a9f5f4b91ebd9cd1da90af8b28689c1957bbc52688b632e86ecc3c"},"schema_version":"1.0","source":{"id":"1608.04153","kind":"arxiv","version":2}},"canonical_sha256":"815d19fab3056f488043275500f157e96a0a695e58302d5d8628cade465fbefe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"815d19fab3056f488043275500f157e96a0a695e58302d5d8628cade465fbefe","first_computed_at":"2026-05-18T01:04:02.286529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:02.286529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rONm9GSewn63JmrfyqWXlcBHbtm0Ufj2WihFQc5CotSZI1VRVMO389XhLOLyL+Ec3SrsAwKV2rLQqXjXmSArDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:02.287220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04153","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bc837e09e98718de1f2c182060fd9163331e4272259954592b86c18a870df58","sha256:30801b19e2acb24c71d5c6dcdda274d15ac18d25d09bb837fbe5b2cb93a11c9a"],"state_sha256":"9e4baf96072f879c18f8486f9b6a388d05b572ffef2c9b2543ca45fd35170414"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qNaJYxeitfPDoLNRGBW+QaOB4BHdOiTOiuSxJEKAOQLyMYWZ0eOyIDClimTkp8339u/2MqFflxqowZKY9ezYCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:45:08.740614Z","bundle_sha256":"48ccd7cbc676f7f80a2d2a14e8dc9aac014d5242968dff357fb77948ddafa4ce"}}