{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2ERWS4NV5RYOYJVQ6OISLR57VJ","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":"3e77c18d72bd6610c8be41f6471bc0aa40902dd4c638d89d63554f705dfe97be","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2025-01-24T15:24:34Z","title_canon_sha256":"433f3a485d9c000a87cb101af293eda2526ac342b4722277e0a128edb808c6d3"},"schema_version":"1.0","source":{"id":"2501.14569","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.14569","created_at":"2026-07-05T10:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"2501.14569v1","created_at":"2026-07-05T10:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.14569","created_at":"2026-07-05T10:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"2ERWS4NV5RYO","created_at":"2026-07-05T10:05:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ERWS4NV5RYOYJVQ","created_at":"2026-07-05T10:05:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ERWS4NV","created_at":"2026-07-05T10:05:02Z"}],"graph_snapshots":[{"event_id":"sha256:d40be98cbc563b25e5c68702f62dd4a909207d74cf0ea0d0659b1eb638a4fc2e","target":"graph","created_at":"2026-07-05T10:05:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.14569/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"I present an analytic approach to establishing the presence of phase transitions in a large set of decision problems. This approach does not require extensive computational study of the problems considered. The set -- that of all paddable problems over even-sized alphabets satisfying a condition similar to not being sparse -- shown to exhibit phase transitions contains many \"practical\" decision problems, is very large, and also contains extremely intractable problems.","authors_text":"Andrew Jackson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2025-01-24T15:24:34Z","title":"Explaining the Ubiquity of Phase Transitions in Decision Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.14569","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:aea7cdb7a4b6fac7f720c00b1a69e7025f5546a8029c7ce58d54187a23523779","target":"record","created_at":"2026-07-05T10:05:02Z","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":"3e77c18d72bd6610c8be41f6471bc0aa40902dd4c638d89d63554f705dfe97be","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2025-01-24T15:24:34Z","title_canon_sha256":"433f3a485d9c000a87cb101af293eda2526ac342b4722277e0a128edb808c6d3"},"schema_version":"1.0","source":{"id":"2501.14569","kind":"arxiv","version":1}},"canonical_sha256":"d1236971b5ec70ec26b0f39125c7bfaa6dd9336b2934364953aec81fef92df41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1236971b5ec70ec26b0f39125c7bfaa6dd9336b2934364953aec81fef92df41","first_computed_at":"2026-07-05T10:05:02.871810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:05:02.871810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GAASNGSGk82U+qvFzKxGq2qJw0a7MbMikIr51+6jaadUnA02EGZGRnSinwH8wS+/pB5jt33i76V0UuI1qUGkBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:05:02.872209Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.14569","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aea7cdb7a4b6fac7f720c00b1a69e7025f5546a8029c7ce58d54187a23523779","sha256:d40be98cbc563b25e5c68702f62dd4a909207d74cf0ea0d0659b1eb638a4fc2e"],"state_sha256":"a601b398ad47c8fba78b19f8e9766fb0a225aac43a92c33715f4a1fffce5b719"}