{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LQYWYTNQVX3GWKUYQNX6KJWKWQ","short_pith_number":"pith:LQYWYTNQ","canonical_record":{"source":{"id":"1201.3868","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-01-18T18:09:36Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"6fb8dc06602f6ccc09fc950eec7637aabac412d8ec6dd4da7af8a18cbe71d21f","abstract_canon_sha256":"c973738f8961ef42526ce5cf1d719e4773ba381c7b8b4ba9d55fee76a8332fce"},"schema_version":"1.0"},"canonical_sha256":"5c316c4db0adf66b2a98836fe526cab40b3abc374a02cc224bb2e97ba8491037","source":{"kind":"arxiv","id":"1201.3868","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3868","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3868v1","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3868","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"LQYWYTNQVX3G","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LQYWYTNQVX3GWKUY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LQYWYTNQ","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LQYWYTNQVX3GWKUYQNX6KJWKWQ","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3868","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-01-18T18:09:36Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"6fb8dc06602f6ccc09fc950eec7637aabac412d8ec6dd4da7af8a18cbe71d21f","abstract_canon_sha256":"c973738f8961ef42526ce5cf1d719e4773ba381c7b8b4ba9d55fee76a8332fce"},"schema_version":"1.0"},"canonical_sha256":"5c316c4db0adf66b2a98836fe526cab40b3abc374a02cc224bb2e97ba8491037","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:17.718450Z","signature_b64":"5JQRsCK3pE1caxhYSKs0uR931URzYkpoXExfjcI49m0IXlrZzL/jBVDnlQL/irc8ZEVVw7pS1Fx+jK5kleLzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c316c4db0adf66b2a98836fe526cab40b3abc374a02cc224bb2e97ba8491037","last_reissued_at":"2026-05-18T04:04:17.717635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:17.717635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3868","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":"2026-05-18T04:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4qeD6k3v1sVRXaGCI/HiZg+BrCZohNOvkOKr60jvRotStqnKSweF4rCLLHAku69qsVqHYMvdwUenw7l9JNkAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T04:27:34.744434Z"},"content_sha256":"16c4a659bde51899a03175d5bbd5e35dfed7ccaad048e68f7fc58eb0c12782be","schema_version":"1.0","event_id":"sha256:16c4a659bde51899a03175d5bbd5e35dfed7ccaad048e68f7fc58eb0c12782be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LQYWYTNQVX3GWKUYQNX6KJWKWQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Dichotomy for 2-Constraint Forbidden CSP Patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.AI","authors_text":"Guillaume Escamocher, Martin C. Cooper","submitted_at":"2012-01-18T18:09:36Z","abstract_excerpt":"Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach has recently led to the discovery of novel tractable classes. The complete characterisation of all tractable classes defined by forbidding patterns (where a pattern is simply a compact representation of a set of subproblems) is a challenging problem. We demonstrate a dichotomy in the case of forbidden patterns consisting of either one or two constraints. This"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3868","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":"2026-05-18T04:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wk0jGcdmU5p/XnSlQVNCgifpBBvOwi9EGtssZJdrbJLJi2c0hlIgFD2vujyi3QkYqFscpqyVmrzIvX0Y7A04Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T04:27:34.744783Z"},"content_sha256":"2cdc2e15eb85d4acdf4bc85f3b5c0f403aeb95f01a0d7db222959106c1c23fc3","schema_version":"1.0","event_id":"sha256:2cdc2e15eb85d4acdf4bc85f3b5c0f403aeb95f01a0d7db222959106c1c23fc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LQYWYTNQVX3GWKUYQNX6KJWKWQ/bundle.json","state_url":"https://pith.science/pith/LQYWYTNQVX3GWKUYQNX6KJWKWQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LQYWYTNQVX3GWKUYQNX6KJWKWQ/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":"2026-06-25T04:27:34Z","links":{"resolver":"https://pith.science/pith/LQYWYTNQVX3GWKUYQNX6KJWKWQ","bundle":"https://pith.science/pith/LQYWYTNQVX3GWKUYQNX6KJWKWQ/bundle.json","state":"https://pith.science/pith/LQYWYTNQVX3GWKUYQNX6KJWKWQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LQYWYTNQVX3GWKUYQNX6KJWKWQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LQYWYTNQVX3GWKUYQNX6KJWKWQ","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":"c973738f8961ef42526ce5cf1d719e4773ba381c7b8b4ba9d55fee76a8332fce","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-01-18T18:09:36Z","title_canon_sha256":"6fb8dc06602f6ccc09fc950eec7637aabac412d8ec6dd4da7af8a18cbe71d21f"},"schema_version":"1.0","source":{"id":"1201.3868","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3868","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3868v1","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3868","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"LQYWYTNQVX3G","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LQYWYTNQVX3GWKUY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LQYWYTNQ","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:2cdc2e15eb85d4acdf4bc85f3b5c0f403aeb95f01a0d7db222959106c1c23fc3","target":"graph","created_at":"2026-05-18T04:04:17Z","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":"Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach has recently led to the discovery of novel tractable classes. The complete characterisation of all tractable classes defined by forbidding patterns (where a pattern is simply a compact representation of a set of subproblems) is a challenging problem. We demonstrate a dichotomy in the case of forbidden patterns consisting of either one or two constraints. This","authors_text":"Guillaume Escamocher, Martin C. Cooper","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-01-18T18:09:36Z","title":"A Dichotomy for 2-Constraint Forbidden CSP Patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3868","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":"sha256:16c4a659bde51899a03175d5bbd5e35dfed7ccaad048e68f7fc58eb0c12782be","target":"record","created_at":"2026-05-18T04:04:17Z","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":"c973738f8961ef42526ce5cf1d719e4773ba381c7b8b4ba9d55fee76a8332fce","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-01-18T18:09:36Z","title_canon_sha256":"6fb8dc06602f6ccc09fc950eec7637aabac412d8ec6dd4da7af8a18cbe71d21f"},"schema_version":"1.0","source":{"id":"1201.3868","kind":"arxiv","version":1}},"canonical_sha256":"5c316c4db0adf66b2a98836fe526cab40b3abc374a02cc224bb2e97ba8491037","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c316c4db0adf66b2a98836fe526cab40b3abc374a02cc224bb2e97ba8491037","first_computed_at":"2026-05-18T04:04:17.717635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:17.717635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5JQRsCK3pE1caxhYSKs0uR931URzYkpoXExfjcI49m0IXlrZzL/jBVDnlQL/irc8ZEVVw7pS1Fx+jK5kleLzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:17.718450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3868","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16c4a659bde51899a03175d5bbd5e35dfed7ccaad048e68f7fc58eb0c12782be","sha256:2cdc2e15eb85d4acdf4bc85f3b5c0f403aeb95f01a0d7db222959106c1c23fc3"],"state_sha256":"fa1fdad6cb7afc1ad93e98e811c450574d96602ab2e86ed9b3775869aa85cd62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSFE8P4e7slLND4kAJf9BT+SDWhYc6Hz1x+hcPN6owciMSIUo1zaemnAF8RXNwzq7TQ2A9WuO7xtEshvJL9HCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T04:27:34.746726Z","bundle_sha256":"ae20cec78b818d2deaedc3c86667edcb86cd23c49507831898652c35a1f7c824"}}