{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7WGK6BN6DGJCBKG4QLEQMYB4W5","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":"9da419fec70ecbc81e5344f350f1a0665286583e1f09a8d3178a2b78e1918a5d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-01T14:35:01Z","title_canon_sha256":"67db7b0745c3507a8585cb48b19aa44a41fa411ed59ada9be4c23418b8403070"},"schema_version":"1.0","source":{"id":"1104.0185","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0185","created_at":"2026-05-18T04:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0185v3","created_at":"2026-05-18T04:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0185","created_at":"2026-05-18T04:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"7WGK6BN6DGJC","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7WGK6BN6DGJCBKG4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7WGK6BN6","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:503fe5a0b53256f649bd1da34ef4d1a4c952b8a0462bd1439d6bd34e39aa8189","target":"graph","created_at":"2026-05-18T04:21:50Z","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":"Homomorphisms between relational structures are not only fundamental mathematical objects, but are also of great importance in an applied computational context. Indeed, constraint satisfaction problems (CSPs), a wide class of algorithmic problems that occur in many different areas of computer science such as artificial intelligence or database theory, may be viewed as asking for homomorphisms between two relational structures [FedVar98]. In a logical setting, homomorphisms may be viewed as witnesses for positive primitive formulas in a relational language. As we shall see, homomorphisms, or mo","authors_text":"Marc Thurley, Martin Grohe","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-01T14:35:01Z","title":"Counting Homomorphisms and Partition Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0185","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":"sha256:3385dbd2b09da33283fc42822126aca4ca7d7b1008035533060a3dd3104f5525","target":"record","created_at":"2026-05-18T04:21:50Z","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":"9da419fec70ecbc81e5344f350f1a0665286583e1f09a8d3178a2b78e1918a5d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-04-01T14:35:01Z","title_canon_sha256":"67db7b0745c3507a8585cb48b19aa44a41fa411ed59ada9be4c23418b8403070"},"schema_version":"1.0","source":{"id":"1104.0185","kind":"arxiv","version":3}},"canonical_sha256":"fd8caf05be199220a8dc82c906603cb77b24f8589922866c2eb0f17c618437c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd8caf05be199220a8dc82c906603cb77b24f8589922866c2eb0f17c618437c3","first_computed_at":"2026-05-18T04:21:50.355992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:50.355992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EVdhULMxCl7Rx/XrDAIqj40ye7UdhcZWwwfeGFTF6AmqEGtpS6dx8Zn+yQZdtO5joolPoP6anmwq2fZ2G3AzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:50.356478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0185","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3385dbd2b09da33283fc42822126aca4ca7d7b1008035533060a3dd3104f5525","sha256:503fe5a0b53256f649bd1da34ef4d1a4c952b8a0462bd1439d6bd34e39aa8189"],"state_sha256":"6c4217102257dd318f15fbacce05abf16358be0b630a4c8beac37c57de143cc0"}