{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PJMX43EFM24KJO7WJWHOOWQGRC","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":"0dec70fb17a437137a1ddd147d5e7cc6603a176126c2a55f3fca6de0de3edecd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-01-19T16:58:39Z","title_canon_sha256":"164de20a24bb4213480009cff0c6fed8e90002fe111f869bf2f7e3124f1513ca"},"schema_version":"1.0","source":{"id":"1501.04558","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04558","created_at":"2026-05-18T02:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04558v2","created_at":"2026-05-18T02:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04558","created_at":"2026-05-18T02:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"PJMX43EFM24K","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PJMX43EFM24KJO7W","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PJMX43EF","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:6011a6292ad066259e29952275ebce40b2d763b248c39d678c1f5563b980feb5","target":"graph","created_at":"2026-05-18T02:14:17Z","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":"Inspired by computational complexity results for the quantified constraint satisfaction problem, we study the clones of idempotent polymorphisms of certain digraph classes. Our first results are two algebraic dichotomy, even \"gap\", theorems. Building on and extending [Martin CP'11], we prove that partially reflexive paths bequeath a set of idempotent polymorphisms whose associated clone algebra has: either the polynomially generated powers property (PGP); or the exponentially generated powers property (EGP). Similarly, we build on [DaMM ICALP'14] to prove that semicomplete digraphs have the sa","authors_text":"Barnaby Martin, Catarina Carvalho, Florent Madelaine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-01-19T16:58:39Z","title":"From complexity to algebra and back: digraph classes, collapsibility and the PGP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04558","kind":"arxiv","version":2},"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:b78969c4fc4e23bd240a044cd63d4e9e7f20153f0d27765f0f1c48499a1e67dc","target":"record","created_at":"2026-05-18T02:14:17Z","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":"0dec70fb17a437137a1ddd147d5e7cc6603a176126c2a55f3fca6de0de3edecd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-01-19T16:58:39Z","title_canon_sha256":"164de20a24bb4213480009cff0c6fed8e90002fe111f869bf2f7e3124f1513ca"},"schema_version":"1.0","source":{"id":"1501.04558","kind":"arxiv","version":2}},"canonical_sha256":"7a597e6c8566b8a4bbf64d8ee75a068887d9d2be733da067306089701d738c0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a597e6c8566b8a4bbf64d8ee75a068887d9d2be733da067306089701d738c0c","first_computed_at":"2026-05-18T02:14:17.076606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:17.076606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KwPuONLbpuOMEkfEAZUqwbu/CtExm7bNFolGtiH6D739VvPNEDSg4WCaH3J8qWBQg6ReEnqFJKgP9SXP8hDRDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:17.077302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04558","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b78969c4fc4e23bd240a044cd63d4e9e7f20153f0d27765f0f1c48499a1e67dc","sha256:6011a6292ad066259e29952275ebce40b2d763b248c39d678c1f5563b980feb5"],"state_sha256":"a2c660164c1db845afa2add74d88e8d6d0ca0723ee4f62006bc99d8d61d2f0a6"}