{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UNYYZKKQFKLRHLXWQPWV4VWELC","short_pith_number":"pith:UNYYZKKQ","canonical_record":{"source":{"id":"1708.02370","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-08T04:51:01Z","cross_cats_sorted":[],"title_canon_sha256":"aa875aab6233678d21793c3deeee66649201cc78d92452032d487b803d61f326","abstract_canon_sha256":"4add6b6fd446424514acb4062f23b057341c7e09cb5101ffe7403bb010a5c0e7"},"schema_version":"1.0"},"canonical_sha256":"a3718ca9502a9713aef683ed5e56c4589dbc2a730c2daed54a8b74d643f40bef","source":{"kind":"arxiv","id":"1708.02370","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02370","created_at":"2026-07-05T00:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02370v2","created_at":"2026-07-05T00:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02370","created_at":"2026-07-05T00:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"UNYYZKKQFKLR","created_at":"2026-07-05T00:40:41Z"},{"alias_kind":"pith_short_16","alias_value":"UNYYZKKQFKLRHLXW","created_at":"2026-07-05T00:40:41Z"},{"alias_kind":"pith_short_8","alias_value":"UNYYZKKQ","created_at":"2026-07-05T00:40:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UNYYZKKQFKLRHLXWQPWV4VWELC","target":"record","payload":{"canonical_record":{"source":{"id":"1708.02370","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-08T04:51:01Z","cross_cats_sorted":[],"title_canon_sha256":"aa875aab6233678d21793c3deeee66649201cc78d92452032d487b803d61f326","abstract_canon_sha256":"4add6b6fd446424514acb4062f23b057341c7e09cb5101ffe7403bb010a5c0e7"},"schema_version":"1.0"},"canonical_sha256":"a3718ca9502a9713aef683ed5e56c4589dbc2a730c2daed54a8b74d643f40bef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:40:41.238536Z","signature_b64":"t+SqmHkpoutNxlnkK4FgDkINHh1/YdRkkYVxOtxGSSht3M8KPtKCJijC4pNgKCU+ABW/fZfWDNdrnn1A4SnLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3718ca9502a9713aef683ed5e56c4589dbc2a730c2daed54a8b74d643f40bef","last_reissued_at":"2026-07-05T00:40:41.238156Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:40:41.238156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.02370","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":"2026-07-05T00:40:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FfApd2M32NP5UrE0y1VNIsqkmP2MR9v+6b/dtq2QXIlpD+a0j8yjHZoHWI3Rr+vI7mF6+d4e1Bo5qRPC/MOVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T12:51:30.979267Z"},"content_sha256":"f511804012ec955fd6aeb67b21d6c72f7fe8dda8b8b35e53d7969ac12b3baba0","schema_version":"1.0","event_id":"sha256:f511804012ec955fd6aeb67b21d6c72f7fe8dda8b8b35e53d7969ac12b3baba0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UNYYZKKQFKLRHLXWQPWV4VWELC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Clustered Colouring in Minor-Closed Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, David R. Wood, Paul Seymour, Sergey Norin","submitted_at":"2017-08-08T04:51:01Z","abstract_excerpt":"The \"clustered chromatic number\" of a class of graphs is the minimum integer $k$ such that for some integer $c$ every graph in the class is $k$-colourable with monochromatic components of size at most $c$. We prove that for every graph $H$, the clustered chromatic number of the class of $H$-minor-free graphs is tied to the tree-depth of $H$. In particular, if $H$ is connected with tree-depth $t$ then every $H$-minor-free graph is $(2^{t+1}-4)$-colourable with monochromatic components of size at most $c(H)$. This provides the first evidence for a conjecture of Ossona de Mendez, Oum and Wood (20"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02370","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1708.02370/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":"2026-07-05T00:40:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d6jf58RjzLW5nKXkgsi8JjC1sTYt7IFOZ2R/UfSZuLBzweLVLxJqdKa32EvlHMQo7pKEl1OhXogHY/5Yw/wcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T12:51:30.980982Z"},"content_sha256":"6dd0c2907f2cf73f79ff0b69018e72f17d2fbf3fab8088c8ba5cd7f978f16f3c","schema_version":"1.0","event_id":"sha256:6dd0c2907f2cf73f79ff0b69018e72f17d2fbf3fab8088c8ba5cd7f978f16f3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNYYZKKQFKLRHLXWQPWV4VWELC/bundle.json","state_url":"https://pith.science/pith/UNYYZKKQFKLRHLXWQPWV4VWELC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNYYZKKQFKLRHLXWQPWV4VWELC/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":"2026-08-14T12:51:30Z","links":{"resolver":"https://pith.science/pith/UNYYZKKQFKLRHLXWQPWV4VWELC","bundle":"https://pith.science/pith/UNYYZKKQFKLRHLXWQPWV4VWELC/bundle.json","state":"https://pith.science/pith/UNYYZKKQFKLRHLXWQPWV4VWELC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNYYZKKQFKLRHLXWQPWV4VWELC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UNYYZKKQFKLRHLXWQPWV4VWELC","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":"4add6b6fd446424514acb4062f23b057341c7e09cb5101ffe7403bb010a5c0e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-08T04:51:01Z","title_canon_sha256":"aa875aab6233678d21793c3deeee66649201cc78d92452032d487b803d61f326"},"schema_version":"1.0","source":{"id":"1708.02370","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02370","created_at":"2026-07-05T00:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02370v2","created_at":"2026-07-05T00:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02370","created_at":"2026-07-05T00:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"UNYYZKKQFKLR","created_at":"2026-07-05T00:40:41Z"},{"alias_kind":"pith_short_16","alias_value":"UNYYZKKQFKLRHLXW","created_at":"2026-07-05T00:40:41Z"},{"alias_kind":"pith_short_8","alias_value":"UNYYZKKQ","created_at":"2026-07-05T00:40:41Z"}],"graph_snapshots":[{"event_id":"sha256:6dd0c2907f2cf73f79ff0b69018e72f17d2fbf3fab8088c8ba5cd7f978f16f3c","target":"graph","created_at":"2026-07-05T00:40:41Z","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/1708.02370/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The \"clustered chromatic number\" of a class of graphs is the minimum integer $k$ such that for some integer $c$ every graph in the class is $k$-colourable with monochromatic components of size at most $c$. We prove that for every graph $H$, the clustered chromatic number of the class of $H$-minor-free graphs is tied to the tree-depth of $H$. In particular, if $H$ is connected with tree-depth $t$ then every $H$-minor-free graph is $(2^{t+1}-4)$-colourable with monochromatic components of size at most $c(H)$. This provides the first evidence for a conjecture of Ossona de Mendez, Oum and Wood (20","authors_text":"Alex Scott, David R. Wood, Paul Seymour, Sergey Norin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-08T04:51:01Z","title":"Clustered Colouring in Minor-Closed Classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02370","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:f511804012ec955fd6aeb67b21d6c72f7fe8dda8b8b35e53d7969ac12b3baba0","target":"record","created_at":"2026-07-05T00:40:41Z","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":"4add6b6fd446424514acb4062f23b057341c7e09cb5101ffe7403bb010a5c0e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-08T04:51:01Z","title_canon_sha256":"aa875aab6233678d21793c3deeee66649201cc78d92452032d487b803d61f326"},"schema_version":"1.0","source":{"id":"1708.02370","kind":"arxiv","version":2}},"canonical_sha256":"a3718ca9502a9713aef683ed5e56c4589dbc2a730c2daed54a8b74d643f40bef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3718ca9502a9713aef683ed5e56c4589dbc2a730c2daed54a8b74d643f40bef","first_computed_at":"2026-07-05T00:40:41.238156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:40:41.238156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t+SqmHkpoutNxlnkK4FgDkINHh1/YdRkkYVxOtxGSSht3M8KPtKCJijC4pNgKCU+ABW/fZfWDNdrnn1A4SnLBg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:40:41.238536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02370","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f511804012ec955fd6aeb67b21d6c72f7fe8dda8b8b35e53d7969ac12b3baba0","sha256:6dd0c2907f2cf73f79ff0b69018e72f17d2fbf3fab8088c8ba5cd7f978f16f3c"],"state_sha256":"fd725c0f02d2ca86d3d4764e5e288b25dbbbd49731095abb4558632fedc7f9e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ggqgfwwbEmvjyPq1FaphTKESmWYKSp99ViBs+jOTGIMuXdUJkv1+V8yFbVzn+glQa3+93ONNcX/fxRI2KSDuBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T12:51:30.987620Z","bundle_sha256":"b81d240205f56efca39847f9b0655510295e3d9a015e13943fcff97af445a178"}}