{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HVUR3CXRIVY33AFWWZBOY6M7RP","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":"c018e3c89a0d14975372fba03f841e4df7e32325a7643e87a01cdbfb2a30c3b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-01-31T14:22:05Z","title_canon_sha256":"4a0a406209be79b4000e65dce28592a4e4535748e89c1c21cafeb9066fdd75ff"},"schema_version":"1.0","source":{"id":"1401.8175","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.8175","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"arxiv_version","alias_value":"1401.8175v3","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.8175","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"pith_short_12","alias_value":"HVUR3CXRIVY3","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HVUR3CXRIVY33AFW","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HVUR3CXR","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:bcfed44e0d62b2f4a3ab865eb1a55d33828fe94bb56df28e8b7f9ac0f5367d00","target":"graph","created_at":"2026-05-18T01:27:54Z","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":"We study a probability distribution d on the truth assignments to a uniform binary AND-OR tree. Liu and Tanaka [2007, Inform. Process. Lett.] showed the following: If d achieves the equilibrium among independent distributions (ID) then d is an independent identical distribution (IID). We show a stronger form of the above result. Given a real number r such that 0 < r < 1, we consider a constraint that the probability of the root node having the value 0 is r. Our main result is the following: When we restrict ourselves to IDs satisfying this constraint, the above result of Liu and Tanaka still h","authors_text":"Toshio Suzuki, Yoshinao Niida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-01-31T14:22:05Z","title":"Equilibrium Points of an AND-OR Tree: under Constraints on Probability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.8175","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":"sha256:2fec89671dd72349d13c983b5bb15527d29985ca1ab5a67a8cb6b4b7ff3d9630","target":"record","created_at":"2026-05-18T01:27:54Z","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":"c018e3c89a0d14975372fba03f841e4df7e32325a7643e87a01cdbfb2a30c3b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-01-31T14:22:05Z","title_canon_sha256":"4a0a406209be79b4000e65dce28592a4e4535748e89c1c21cafeb9066fdd75ff"},"schema_version":"1.0","source":{"id":"1401.8175","kind":"arxiv","version":3}},"canonical_sha256":"3d691d8af14571bd80b6b642ec799f8be010d9ea78e7ede9c0916b89a425136d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d691d8af14571bd80b6b642ec799f8be010d9ea78e7ede9c0916b89a425136d","first_computed_at":"2026-05-18T01:27:54.883680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:54.883680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pjh8Q3wIohjiy71xu5PmIwRZL95x8xLWG3ZHiCzGk/lIV5zepBohixAtfnFZurewIL2j8htkTHwqNBxTSXONBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:54.884371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.8175","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fec89671dd72349d13c983b5bb15527d29985ca1ab5a67a8cb6b4b7ff3d9630","sha256:bcfed44e0d62b2f4a3ab865eb1a55d33828fe94bb56df28e8b7f9ac0f5367d00"],"state_sha256":"afa8e5fbe732e4de510e9cb95b75a6898d4dd0f98cc3bfc616839213f2a76a37"}