{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AKNZQ42LTJG634ZGRF4NWLJREV","short_pith_number":"pith:AKNZQ42L","canonical_record":{"source":{"id":"1211.6466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-27T22:15:52Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d32c5bb6d1e8641c25dc39de301500098510665b80177b3f44c74ff08a51c9b6","abstract_canon_sha256":"0640876a911aaa3e7ee3490a160b08c19b9022ecf77597bd38fab596854f38f7"},"schema_version":"1.0"},"canonical_sha256":"029b98734b9a4dedf3268978db2d312561764d4209f10295e6e7fce3dd547e1d","source":{"kind":"arxiv","id":"1211.6466","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6466","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6466v1","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6466","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"AKNZQ42LTJG6","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AKNZQ42LTJG634ZG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AKNZQ42L","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AKNZQ42LTJG634ZGRF4NWLJREV","target":"record","payload":{"canonical_record":{"source":{"id":"1211.6466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-27T22:15:52Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d32c5bb6d1e8641c25dc39de301500098510665b80177b3f44c74ff08a51c9b6","abstract_canon_sha256":"0640876a911aaa3e7ee3490a160b08c19b9022ecf77597bd38fab596854f38f7"},"schema_version":"1.0"},"canonical_sha256":"029b98734b9a4dedf3268978db2d312561764d4209f10295e6e7fce3dd547e1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:51.468503Z","signature_b64":"WG2Wywvd0zYX4dZMpmfBY5W6excBDfKQ/mtwEVF53ckw+jTGN6RWM8LZ8NzgXuAibGTCEIn4EP1C8W2vzew7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"029b98734b9a4dedf3268978db2d312561764d4209f10295e6e7fce3dd547e1d","last_reissued_at":"2026-05-18T03:39:51.467692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:51.467692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.6466","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":"2026-05-18T03:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXYVXnlnlGnm8kaGOg7nGF8Y+SO1sgHnpNykQ12ka3DvZ3FbRdT/HwVhKltV4u9j+T1NooNh+pWQ3K0JPLLzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:44:35.124094Z"},"content_sha256":"d1b3d1eb4701f9d3886741d5d72a5e5dd1705c11b0ea759f7d5f5e8f14042266","schema_version":"1.0","event_id":"sha256:d1b3d1eb4701f9d3886741d5d72a5e5dd1705c11b0ea759f7d5f5e8f14042266"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AKNZQ42LTJG634ZGRF4NWLJREV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small H-coloring problems for bounded degree digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Aurosish Mishra, Pavol Hell","submitted_at":"2012-11-27T22:15:52Z","abstract_excerpt":"An NP-complete coloring or homomorphism problem may become polynomial time solvable when restricted to graphs with degrees bounded by a small number, but remain NP-complete if the bound is higher. For instance, 3-colorability of graphs with degrees bounded by 3 can be decided by Brooks' theorem, while for graphs with degrees bounded by 4, the 3-colorability problem is NP-complete. We investigate an analogous phenomenon for digraphs, focusing on the three smallest digraphs H with NP-complete H-colorability problems. It turns out that in all three cases the H-coloring problem is polynomial time "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6466","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":"2026-05-18T03:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2YecH5xrRHBaquMiwzSJeFXhxqJzzNj4uhocX34rkSvutDgaaQsK/ZrhrLwNsCxCJKLt6pLZNIjMsAgjoFHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:44:35.124464Z"},"content_sha256":"00a44bd1cf54d7e58776ea9a4045dd2f1ddd945583a23620d6fe101e23ba33fd","schema_version":"1.0","event_id":"sha256:00a44bd1cf54d7e58776ea9a4045dd2f1ddd945583a23620d6fe101e23ba33fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AKNZQ42LTJG634ZGRF4NWLJREV/bundle.json","state_url":"https://pith.science/pith/AKNZQ42LTJG634ZGRF4NWLJREV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AKNZQ42LTJG634ZGRF4NWLJREV/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":"2026-06-03T02:44:35Z","links":{"resolver":"https://pith.science/pith/AKNZQ42LTJG634ZGRF4NWLJREV","bundle":"https://pith.science/pith/AKNZQ42LTJG634ZGRF4NWLJREV/bundle.json","state":"https://pith.science/pith/AKNZQ42LTJG634ZGRF4NWLJREV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AKNZQ42LTJG634ZGRF4NWLJREV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AKNZQ42LTJG634ZGRF4NWLJREV","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":"0640876a911aaa3e7ee3490a160b08c19b9022ecf77597bd38fab596854f38f7","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-27T22:15:52Z","title_canon_sha256":"d32c5bb6d1e8641c25dc39de301500098510665b80177b3f44c74ff08a51c9b6"},"schema_version":"1.0","source":{"id":"1211.6466","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6466","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6466v1","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6466","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"AKNZQ42LTJG6","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AKNZQ42LTJG634ZG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AKNZQ42L","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:00a44bd1cf54d7e58776ea9a4045dd2f1ddd945583a23620d6fe101e23ba33fd","target":"graph","created_at":"2026-05-18T03:39:51Z","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":"An NP-complete coloring or homomorphism problem may become polynomial time solvable when restricted to graphs with degrees bounded by a small number, but remain NP-complete if the bound is higher. For instance, 3-colorability of graphs with degrees bounded by 3 can be decided by Brooks' theorem, while for graphs with degrees bounded by 4, the 3-colorability problem is NP-complete. We investigate an analogous phenomenon for digraphs, focusing on the three smallest digraphs H with NP-complete H-colorability problems. It turns out that in all three cases the H-coloring problem is polynomial time ","authors_text":"Aurosish Mishra, Pavol Hell","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-27T22:15:52Z","title":"Small H-coloring problems for bounded degree digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6466","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:d1b3d1eb4701f9d3886741d5d72a5e5dd1705c11b0ea759f7d5f5e8f14042266","target":"record","created_at":"2026-05-18T03:39:51Z","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":"0640876a911aaa3e7ee3490a160b08c19b9022ecf77597bd38fab596854f38f7","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-27T22:15:52Z","title_canon_sha256":"d32c5bb6d1e8641c25dc39de301500098510665b80177b3f44c74ff08a51c9b6"},"schema_version":"1.0","source":{"id":"1211.6466","kind":"arxiv","version":1}},"canonical_sha256":"029b98734b9a4dedf3268978db2d312561764d4209f10295e6e7fce3dd547e1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"029b98734b9a4dedf3268978db2d312561764d4209f10295e6e7fce3dd547e1d","first_computed_at":"2026-05-18T03:39:51.467692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:51.467692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WG2Wywvd0zYX4dZMpmfBY5W6excBDfKQ/mtwEVF53ckw+jTGN6RWM8LZ8NzgXuAibGTCEIn4EP1C8W2vzew7Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:51.468503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6466","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1b3d1eb4701f9d3886741d5d72a5e5dd1705c11b0ea759f7d5f5e8f14042266","sha256:00a44bd1cf54d7e58776ea9a4045dd2f1ddd945583a23620d6fe101e23ba33fd"],"state_sha256":"a2392ab19908a3719c5fc153f02ab0500337dbc66217ebeac96414417748b5f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gEYuSToZW60VP8TRbLKYhwQx2I9QzSqQO4FNNyGDg4+I6XdseWTDI4InihWYlEpxYvw+mprZuAjHdmt5j14qAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:44:35.126416Z","bundle_sha256":"050762a0f8b63b894ac57bd50e53c061ed0b8c5b2d7d3cfd8e7d961f01f1b4fd"}}