{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DMHOLY4MWS4CXXQTVJUOJSL7JP","short_pith_number":"pith:DMHOLY4M","canonical_record":{"source":{"id":"1408.1973","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-08T20:29:41Z","cross_cats_sorted":[],"title_canon_sha256":"6c99dcfca8e323055b3f4b2d4ecacbddac288569f803bdb101e8ba46542d50fe","abstract_canon_sha256":"4cba2988a0fef7cdc6afe6c098a4fb9824510fb64be6f12855d59149894a6a2c"},"schema_version":"1.0"},"canonical_sha256":"1b0ee5e38cb4b82bde13aa68e4c97f4bf162183c76bc1ceccecb1c3c54bf65a4","source":{"kind":"arxiv","id":"1408.1973","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1973","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1973v3","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1973","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"DMHOLY4MWS4C","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DMHOLY4MWS4CXXQT","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DMHOLY4M","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DMHOLY4MWS4CXXQTVJUOJSL7JP","target":"record","payload":{"canonical_record":{"source":{"id":"1408.1973","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-08T20:29:41Z","cross_cats_sorted":[],"title_canon_sha256":"6c99dcfca8e323055b3f4b2d4ecacbddac288569f803bdb101e8ba46542d50fe","abstract_canon_sha256":"4cba2988a0fef7cdc6afe6c098a4fb9824510fb64be6f12855d59149894a6a2c"},"schema_version":"1.0"},"canonical_sha256":"1b0ee5e38cb4b82bde13aa68e4c97f4bf162183c76bc1ceccecb1c3c54bf65a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:27.514568Z","signature_b64":"aG9MsPCxYJv6EjqoTDxCGOTg/eMGoBaaAxoYOGHFGK+pnrXeb7zYC1vQMA6Sjy8Ff8fvHJtn5bZ9ilwkIJvxCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b0ee5e38cb4b82bde13aa68e4c97f4bf162183c76bc1ceccecb1c3c54bf65a4","last_reissued_at":"2026-05-18T01:08:27.514153Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:27.514153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.1973","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MEIcIg1mdlIiYD4VHNIvxTWVNynB0I/m28ScoPIjNPXE6Stvmkkd0InCyyKVb7cbp/4A6GxZ9nKdQ0wvO5vuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:02:00.403594Z"},"content_sha256":"2ae37244fe5a50f95588f18373cdc572e9743b9c7ea495061eeab8c1af8a0816","schema_version":"1.0","event_id":"sha256:2ae37244fe5a50f95588f18373cdc572e9743b9c7ea495061eeab8c1af8a0816"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DMHOLY4MWS4CXXQTVJUOJSL7JP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K\\H{o}nig's Line Coloring and Vizing's Theorems for Graphings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Endre Cs\\'oka, Gabor Lippner, Oleg Pikhurko","submitted_at":"2014-08-08T20:29:41Z","abstract_excerpt":"The classical theorem of Vizing states that every graph of maximum degree $d$ admits an edge-coloring with at most $d+1$ colors. Furthermore, as it was earlier shown by K\\H{o}nig, $d$ colors suffice if the graph is bipartite.\n  We investigate the existence of measurable edge-colorings for graphings. A graphing is an analytic generalization of a bounded-degree graph that appears in various areas, such as sparse graph limits, orbit equivalence theory and measurable group theory. We show that every graphing of maximum degree $d$ admits a measurable edge-coloring with $d + O(\\sqrt{d})$ colors; fur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1973","kind":"arxiv","version":3},"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":"2026-05-18T01:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O2ZbqZfh9HBssnrs6UVJ5dlwfw18A/w1lvQ+AjUO2G54kVQWZ+s5KDGTcXtb8GSCSLb13OoN8uAi5nZ4XqOhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:02:00.404062Z"},"content_sha256":"9f3ff590f7bc5de9b72fbe7fba7bc895c944675566e202bd54efc32d69682379","schema_version":"1.0","event_id":"sha256:9f3ff590f7bc5de9b72fbe7fba7bc895c944675566e202bd54efc32d69682379"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DMHOLY4MWS4CXXQTVJUOJSL7JP/bundle.json","state_url":"https://pith.science/pith/DMHOLY4MWS4CXXQTVJUOJSL7JP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DMHOLY4MWS4CXXQTVJUOJSL7JP/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":"2026-06-07T06:02:00Z","links":{"resolver":"https://pith.science/pith/DMHOLY4MWS4CXXQTVJUOJSL7JP","bundle":"https://pith.science/pith/DMHOLY4MWS4CXXQTVJUOJSL7JP/bundle.json","state":"https://pith.science/pith/DMHOLY4MWS4CXXQTVJUOJSL7JP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DMHOLY4MWS4CXXQTVJUOJSL7JP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DMHOLY4MWS4CXXQTVJUOJSL7JP","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":"4cba2988a0fef7cdc6afe6c098a4fb9824510fb64be6f12855d59149894a6a2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-08T20:29:41Z","title_canon_sha256":"6c99dcfca8e323055b3f4b2d4ecacbddac288569f803bdb101e8ba46542d50fe"},"schema_version":"1.0","source":{"id":"1408.1973","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1973","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1973v3","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1973","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"DMHOLY4MWS4C","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DMHOLY4MWS4CXXQT","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DMHOLY4M","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:9f3ff590f7bc5de9b72fbe7fba7bc895c944675566e202bd54efc32d69682379","target":"graph","created_at":"2026-05-18T01:08:27Z","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"},"paper":{"abstract_excerpt":"The classical theorem of Vizing states that every graph of maximum degree $d$ admits an edge-coloring with at most $d+1$ colors. Furthermore, as it was earlier shown by K\\H{o}nig, $d$ colors suffice if the graph is bipartite.\n  We investigate the existence of measurable edge-colorings for graphings. A graphing is an analytic generalization of a bounded-degree graph that appears in various areas, such as sparse graph limits, orbit equivalence theory and measurable group theory. We show that every graphing of maximum degree $d$ admits a measurable edge-coloring with $d + O(\\sqrt{d})$ colors; fur","authors_text":"Endre Cs\\'oka, Gabor Lippner, Oleg Pikhurko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-08T20:29:41Z","title":"K\\H{o}nig's Line Coloring and Vizing's Theorems for Graphings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1973","kind":"arxiv","version":3},"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":"sha256:2ae37244fe5a50f95588f18373cdc572e9743b9c7ea495061eeab8c1af8a0816","target":"record","created_at":"2026-05-18T01:08:27Z","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":"4cba2988a0fef7cdc6afe6c098a4fb9824510fb64be6f12855d59149894a6a2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-08T20:29:41Z","title_canon_sha256":"6c99dcfca8e323055b3f4b2d4ecacbddac288569f803bdb101e8ba46542d50fe"},"schema_version":"1.0","source":{"id":"1408.1973","kind":"arxiv","version":3}},"canonical_sha256":"1b0ee5e38cb4b82bde13aa68e4c97f4bf162183c76bc1ceccecb1c3c54bf65a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b0ee5e38cb4b82bde13aa68e4c97f4bf162183c76bc1ceccecb1c3c54bf65a4","first_computed_at":"2026-05-18T01:08:27.514153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:27.514153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aG9MsPCxYJv6EjqoTDxCGOTg/eMGoBaaAxoYOGHFGK+pnrXeb7zYC1vQMA6Sjy8Ff8fvHJtn5bZ9ilwkIJvxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:27.514568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1973","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ae37244fe5a50f95588f18373cdc572e9743b9c7ea495061eeab8c1af8a0816","sha256:9f3ff590f7bc5de9b72fbe7fba7bc895c944675566e202bd54efc32d69682379"],"state_sha256":"a9a246165b23be3b7346b395f73d84c5aae84269343fc1fd0912420449dce116"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N3xkCwuYZUzFJQeSErqCDh03+dIXR898ds7FsJA5vVIbfdgWy+ygLIsn70qgJrq/xX4ZYqtZOC0DnwEeLxJ7Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:02:00.406960Z","bundle_sha256":"e4c754c33e7f9251de4442e57a1aed2d9baa142f0596fd9e51014e8ae0c2c4ae"}}