{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6VLXKUM4GXIVB6MQATP4PJUQPP","short_pith_number":"pith:6VLXKUM4","canonical_record":{"source":{"id":"1504.04112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-16T07:13:30Z","cross_cats_sorted":[],"title_canon_sha256":"0e80785049d7c4716c6f49ca54970c1c04dc6628be92f65e74fb3ee604162cb6","abstract_canon_sha256":"6a3a182c4b7325fdf0e0629cc32accaf1c29325c2273fea2b6db0022b132f87d"},"schema_version":"1.0"},"canonical_sha256":"f55775519c35d150f99004dfc7a6907bf2f814f8bd85609619fa2eeaac906c3b","source":{"kind":"arxiv","id":"1504.04112","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04112","created_at":"2026-05-18T02:18:39Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04112v1","created_at":"2026-05-18T02:18:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04112","created_at":"2026-05-18T02:18:39Z"},{"alias_kind":"pith_short_12","alias_value":"6VLXKUM4GXIV","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6VLXKUM4GXIVB6MQ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6VLXKUM4","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6VLXKUM4GXIVB6MQATP4PJUQPP","target":"record","payload":{"canonical_record":{"source":{"id":"1504.04112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-16T07:13:30Z","cross_cats_sorted":[],"title_canon_sha256":"0e80785049d7c4716c6f49ca54970c1c04dc6628be92f65e74fb3ee604162cb6","abstract_canon_sha256":"6a3a182c4b7325fdf0e0629cc32accaf1c29325c2273fea2b6db0022b132f87d"},"schema_version":"1.0"},"canonical_sha256":"f55775519c35d150f99004dfc7a6907bf2f814f8bd85609619fa2eeaac906c3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:39.833871Z","signature_b64":"nvZVhSFC0YsoEKp1nLEISmU7p6+k6quOUlnZZ7SzLeWRIiGnJxfNQxV4rQGmpuEi9Y6ES0g6wrj7asrDmInTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f55775519c35d150f99004dfc7a6907bf2f814f8bd85609619fa2eeaac906c3b","last_reissued_at":"2026-05-18T02:18:39.833162Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:39.833162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.04112","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":"2026-05-18T02:18:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q04TsZ3/PJPF7HAnS2g0lrHRMLKlNZjMSxjGZyTcRQ3ju6J+wWYt0N5JMuEJPZJSIk2hsb/peBKyFWuP55rzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:35:05.884512Z"},"content_sha256":"84a20140a7730dd7200b143a176d32016d2913268ac61ca2150cf7fc5693ebf2","schema_version":"1.0","event_id":"sha256:84a20140a7730dd7200b143a176d32016d2913268ac61ca2150cf7fc5693ebf2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6VLXKUM4GXIVB6MQATP4PJUQPP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Selective Hypergraph Colourings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christina Zarb, Josef Lauri, Yair Caro","submitted_at":"2015-04-16T07:13:30Z","abstract_excerpt":"We look at colourings of $r$-uniform hypergraphs, focusing our attention on unique colourability and gaps in the chromatic spectrum. The pattern of an edge $E$ in an $r$-uniform hypergraph $H$ whose vertices are coloured is the partition of $r$ induced by the colour classes of the vertices in $E$. Let $Q$ be a set of partitions of $r$. A $Q$-colouring of $H$ is a colouring of its vertices such that only patterns appearing in $Q$ are allowed. We first show that many known hypergraph colouring problems, including Ramsey theory, can be stated in the language of $Q$-colourings. Then, using as our "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04112","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":"2026-05-18T02:18:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TxGFo4QvcQ+1bA7mmr/808YyB1evSVsApzfQ/AWlPCyf1p+UwlkAmkG6AiuuHGthlQSW+YhqA3UfF1N11rkQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:35:05.884856Z"},"content_sha256":"6fc57c96b3cb883d2f8774ebe9a330495b6a8c684048bb1fa478e94ecff74021","schema_version":"1.0","event_id":"sha256:6fc57c96b3cb883d2f8774ebe9a330495b6a8c684048bb1fa478e94ecff74021"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6VLXKUM4GXIVB6MQATP4PJUQPP/bundle.json","state_url":"https://pith.science/pith/6VLXKUM4GXIVB6MQATP4PJUQPP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6VLXKUM4GXIVB6MQATP4PJUQPP/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":"2026-06-25T09:35:05Z","links":{"resolver":"https://pith.science/pith/6VLXKUM4GXIVB6MQATP4PJUQPP","bundle":"https://pith.science/pith/6VLXKUM4GXIVB6MQATP4PJUQPP/bundle.json","state":"https://pith.science/pith/6VLXKUM4GXIVB6MQATP4PJUQPP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6VLXKUM4GXIVB6MQATP4PJUQPP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6VLXKUM4GXIVB6MQATP4PJUQPP","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":"6a3a182c4b7325fdf0e0629cc32accaf1c29325c2273fea2b6db0022b132f87d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-16T07:13:30Z","title_canon_sha256":"0e80785049d7c4716c6f49ca54970c1c04dc6628be92f65e74fb3ee604162cb6"},"schema_version":"1.0","source":{"id":"1504.04112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04112","created_at":"2026-05-18T02:18:39Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04112v1","created_at":"2026-05-18T02:18:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04112","created_at":"2026-05-18T02:18:39Z"},{"alias_kind":"pith_short_12","alias_value":"6VLXKUM4GXIV","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6VLXKUM4GXIVB6MQ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6VLXKUM4","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:6fc57c96b3cb883d2f8774ebe9a330495b6a8c684048bb1fa478e94ecff74021","target":"graph","created_at":"2026-05-18T02:18:39Z","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 look at colourings of $r$-uniform hypergraphs, focusing our attention on unique colourability and gaps in the chromatic spectrum. The pattern of an edge $E$ in an $r$-uniform hypergraph $H$ whose vertices are coloured is the partition of $r$ induced by the colour classes of the vertices in $E$. Let $Q$ be a set of partitions of $r$. A $Q$-colouring of $H$ is a colouring of its vertices such that only patterns appearing in $Q$ are allowed. We first show that many known hypergraph colouring problems, including Ramsey theory, can be stated in the language of $Q$-colourings. Then, using as our ","authors_text":"Christina Zarb, Josef Lauri, Yair Caro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-16T07:13:30Z","title":"Selective Hypergraph Colourings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04112","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":"sha256:84a20140a7730dd7200b143a176d32016d2913268ac61ca2150cf7fc5693ebf2","target":"record","created_at":"2026-05-18T02:18:39Z","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":"6a3a182c4b7325fdf0e0629cc32accaf1c29325c2273fea2b6db0022b132f87d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-16T07:13:30Z","title_canon_sha256":"0e80785049d7c4716c6f49ca54970c1c04dc6628be92f65e74fb3ee604162cb6"},"schema_version":"1.0","source":{"id":"1504.04112","kind":"arxiv","version":1}},"canonical_sha256":"f55775519c35d150f99004dfc7a6907bf2f814f8bd85609619fa2eeaac906c3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f55775519c35d150f99004dfc7a6907bf2f814f8bd85609619fa2eeaac906c3b","first_computed_at":"2026-05-18T02:18:39.833162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:39.833162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nvZVhSFC0YsoEKp1nLEISmU7p6+k6quOUlnZZ7SzLeWRIiGnJxfNQxV4rQGmpuEi9Y6ES0g6wrj7asrDmInTCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:39.833871Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84a20140a7730dd7200b143a176d32016d2913268ac61ca2150cf7fc5693ebf2","sha256:6fc57c96b3cb883d2f8774ebe9a330495b6a8c684048bb1fa478e94ecff74021"],"state_sha256":"a3ee32a7cf03b0f0b89359bb69b7fd221a9ebbfa1dcd2f9f9353b13eb156c6a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+r+ZVpF+Tk2jmvcghA1obX6Ql2klJ6d5b4xgUNppG4G6bhpXUX29P2xY+i9qJ06k6EBZiyC6skNJYCBMmzDAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:35:05.886838Z","bundle_sha256":"e376270cb837f184f33181ec0cd6be4f23a58bc42e80201a6f4d1c6c3e96af59"}}