{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OOEM4BX4IDJQ6MJDLS2YUMSO3W","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":"725d66afe013331c9e1824e8a5af0d8b4df2e17886df9d291b6b5d6c50e78df7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-01T11:01:14Z","title_canon_sha256":"5eb3885bb4c5b11787a24e8e9a063e85324b19b393ee0efda2aa62b00d00590d"},"schema_version":"1.0","source":{"id":"1412.0423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0423","created_at":"2026-05-18T02:32:27Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0423v1","created_at":"2026-05-18T02:32:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0423","created_at":"2026-05-18T02:32:27Z"},{"alias_kind":"pith_short_12","alias_value":"OOEM4BX4IDJQ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OOEM4BX4IDJQ6MJD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OOEM4BX4","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:a95fc261211917a4a9573b1c5cc914650994bae7519ad6ad8b78ef3da9469af1","target":"graph","created_at":"2026-05-18T02:32:27Z","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":"In this paper, we will show dichotomy theorems for the computation of polynomials corresponding to evaluation of graph homomorphisms in Valiant's model. We are given a fixed graph $H$ and want to find all graphs, from some graph class, homomorphic to this $H$. These graphs will be encoded by a family of polynomials.\n  We give dichotomies for the polynomials for cycles, cliques, trees, outerplanar graphs, planar graphs and graphs of bounded genus.","authors_text":"Christian Engels","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-01T11:01:14Z","title":"Dichotomy Theorems for Homomorphism Polynomials of Graph Classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0423","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":"sha256:309fdca644a5b0575c5a346dfefa4cb433ddade79109ff0c4d152966021adb50","target":"record","created_at":"2026-05-18T02:32:27Z","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":"725d66afe013331c9e1824e8a5af0d8b4df2e17886df9d291b6b5d6c50e78df7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-01T11:01:14Z","title_canon_sha256":"5eb3885bb4c5b11787a24e8e9a063e85324b19b393ee0efda2aa62b00d00590d"},"schema_version":"1.0","source":{"id":"1412.0423","kind":"arxiv","version":1}},"canonical_sha256":"7388ce06fc40d30f31235cb58a324eddb96729e947f4d171ec90eae9e57fb5b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7388ce06fc40d30f31235cb58a324eddb96729e947f4d171ec90eae9e57fb5b3","first_computed_at":"2026-05-18T02:32:27.906273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:27.906273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Cq8+Jo6FHnO7oOPi9nKLUr4y8Tr6LteyynzO82JjF9ABxRQksB+z/14NuWos5XPXPn8MIcESqg1T9zGVfgxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:27.906662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:309fdca644a5b0575c5a346dfefa4cb433ddade79109ff0c4d152966021adb50","sha256:a95fc261211917a4a9573b1c5cc914650994bae7519ad6ad8b78ef3da9469af1"],"state_sha256":"7ddd19858d6e36f7305a3ba34ec1301984b222b4490348ac5e38b7e9b505f147"}