{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HOBADRMQ6DLON4GPQMU6ATJHGG","short_pith_number":"pith:HOBADRMQ","canonical_record":{"source":{"id":"1703.08123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-23T16:07:08Z","cross_cats_sorted":[],"title_canon_sha256":"b82aab1135a4f57051b4b41f0cad3cfac9159772a95340a7bc06665366095661","abstract_canon_sha256":"ff211b52d95caa0b3bddf9903b0543d002a52006ba62085ac4cb802826126339"},"schema_version":"1.0"},"canonical_sha256":"3b8201c590f0d6e6f0cf8329e04d2731af13fcb80e7767882e579fa3681fd6cd","source":{"kind":"arxiv","id":"1703.08123","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08123","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08123v1","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08123","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"HOBADRMQ6DLO","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HOBADRMQ6DLON4GP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HOBADRMQ","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HOBADRMQ6DLON4GPQMU6ATJHGG","target":"record","payload":{"canonical_record":{"source":{"id":"1703.08123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-23T16:07:08Z","cross_cats_sorted":[],"title_canon_sha256":"b82aab1135a4f57051b4b41f0cad3cfac9159772a95340a7bc06665366095661","abstract_canon_sha256":"ff211b52d95caa0b3bddf9903b0543d002a52006ba62085ac4cb802826126339"},"schema_version":"1.0"},"canonical_sha256":"3b8201c590f0d6e6f0cf8329e04d2731af13fcb80e7767882e579fa3681fd6cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:03.819725Z","signature_b64":"7y8NVwIm4rrdmF75tJP0HBSlQ6mCejA9uEM1lmH8WhqY0R2vE/fzlhz4tA/UAzUdtr2c8MHF5o+gWhl5J5HWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b8201c590f0d6e6f0cf8329e04d2731af13fcb80e7767882e579fa3681fd6cd","last_reissued_at":"2026-05-18T00:48:03.819175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:03.819175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.08123","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":"2026-05-18T00:48:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EEP+ht4J5hHv5SDhUh+rIVH6qZes0js1JWHiToiVOaGGp+NyN+4sSM5QUj8J4N8elhpJeDxJ2Z+hnZmnxq2qBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:47:44.768873Z"},"content_sha256":"ba6620cace5400f76a055ac190599e968d09f9d2f9a500dc2636de41f39aa65f","schema_version":"1.0","event_id":"sha256:ba6620cace5400f76a055ac190599e968d09f9d2f9a500dc2636de41f39aa65f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HOBADRMQ6DLON4GPQMU6ATJHGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A proof of the Erd\\H{o}s-Sands-Sauer-Woodrow conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"N. Bousquet, S. Thomass\\'e, W. Lochet","submitted_at":"2017-03-23T16:07:08Z","abstract_excerpt":"A very nice result of B\\'ar\\'any and Lehel asserts that every finite subset $X$ or $\\mathbb R^d$ can be covered by $f(d)$ $X$-boxes (i.e. each box has two antipodal points in $X$). As shown by Gy\\'arf\\'as and P\\'alv\\H{o}lgyi this result would follow from the following conjecture : If a tournament admits a partition of its arc set into $k$ quasi orders, then its domination number is bounded in terms of $k$. This question is in turn implied by the Erd\\H{o}s-Sands-Sauer-Woodrow conjecture : If the arcs of a tournament $T$ are colored with $k$ colors, there is a set $X$ of at most $g(k)$ vertices "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08123","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":""},"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":"2026-05-18T00:48:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M4WqIbByIJCi4MO3Pq5x4yULkXYk44L+FwKclGJeD8KsUz82Lk2UUoqmAXRQqiDLtXH1nHaBhjLNFMyRCJPGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:47:44.769217Z"},"content_sha256":"5f7532925753dffe65e0965b7b2c46efa939324f9fba66c2d9709014285907c1","schema_version":"1.0","event_id":"sha256:5f7532925753dffe65e0965b7b2c46efa939324f9fba66c2d9709014285907c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HOBADRMQ6DLON4GPQMU6ATJHGG/bundle.json","state_url":"https://pith.science/pith/HOBADRMQ6DLON4GPQMU6ATJHGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HOBADRMQ6DLON4GPQMU6ATJHGG/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":"2026-06-26T16:47:44Z","links":{"resolver":"https://pith.science/pith/HOBADRMQ6DLON4GPQMU6ATJHGG","bundle":"https://pith.science/pith/HOBADRMQ6DLON4GPQMU6ATJHGG/bundle.json","state":"https://pith.science/pith/HOBADRMQ6DLON4GPQMU6ATJHGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HOBADRMQ6DLON4GPQMU6ATJHGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HOBADRMQ6DLON4GPQMU6ATJHGG","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":"ff211b52d95caa0b3bddf9903b0543d002a52006ba62085ac4cb802826126339","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-23T16:07:08Z","title_canon_sha256":"b82aab1135a4f57051b4b41f0cad3cfac9159772a95340a7bc06665366095661"},"schema_version":"1.0","source":{"id":"1703.08123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08123","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08123v1","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08123","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"HOBADRMQ6DLO","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HOBADRMQ6DLON4GP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HOBADRMQ","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:5f7532925753dffe65e0965b7b2c46efa939324f9fba66c2d9709014285907c1","target":"graph","created_at":"2026-05-18T00:48:03Z","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":"A very nice result of B\\'ar\\'any and Lehel asserts that every finite subset $X$ or $\\mathbb R^d$ can be covered by $f(d)$ $X$-boxes (i.e. each box has two antipodal points in $X$). As shown by Gy\\'arf\\'as and P\\'alv\\H{o}lgyi this result would follow from the following conjecture : If a tournament admits a partition of its arc set into $k$ quasi orders, then its domination number is bounded in terms of $k$. This question is in turn implied by the Erd\\H{o}s-Sands-Sauer-Woodrow conjecture : If the arcs of a tournament $T$ are colored with $k$ colors, there is a set $X$ of at most $g(k)$ vertices ","authors_text":"N. Bousquet, S. Thomass\\'e, W. Lochet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-23T16:07:08Z","title":"A proof of the Erd\\H{o}s-Sands-Sauer-Woodrow conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08123","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:ba6620cace5400f76a055ac190599e968d09f9d2f9a500dc2636de41f39aa65f","target":"record","created_at":"2026-05-18T00:48:03Z","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":"ff211b52d95caa0b3bddf9903b0543d002a52006ba62085ac4cb802826126339","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-23T16:07:08Z","title_canon_sha256":"b82aab1135a4f57051b4b41f0cad3cfac9159772a95340a7bc06665366095661"},"schema_version":"1.0","source":{"id":"1703.08123","kind":"arxiv","version":1}},"canonical_sha256":"3b8201c590f0d6e6f0cf8329e04d2731af13fcb80e7767882e579fa3681fd6cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b8201c590f0d6e6f0cf8329e04d2731af13fcb80e7767882e579fa3681fd6cd","first_computed_at":"2026-05-18T00:48:03.819175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:03.819175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7y8NVwIm4rrdmF75tJP0HBSlQ6mCejA9uEM1lmH8WhqY0R2vE/fzlhz4tA/UAzUdtr2c8MHF5o+gWhl5J5HWAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:03.819725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba6620cace5400f76a055ac190599e968d09f9d2f9a500dc2636de41f39aa65f","sha256:5f7532925753dffe65e0965b7b2c46efa939324f9fba66c2d9709014285907c1"],"state_sha256":"1de5cf7ad26ac2c41f19e66c6f7d17c54477475b586da31ab63baa8ca35856ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZAt3J8miYC+lgKvZ/4BuOHOkrF98oXHzRLfBSKsaHeR1R+pgga5GmR/Mna/FixRgi9qdB1i/xHJx/eaRxF8uCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:47:44.771236Z","bundle_sha256":"8de15cb5227e8734ae64515eabab7502d2a5a2172066d1a79578acf0172cb216"}}