{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PORSRLCUBGTB26PWESTH3ZGJRW","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":"bec7d8edf3002fa3da79af59830ebfb63817c73e36a0c23dd0b19d29262f376f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-01T16:22:51Z","title_canon_sha256":"523e306a5f0703e22199f497906d599bfad5891ead35b430f6c3508ddbf7256e"},"schema_version":"1.0","source":{"id":"1712.00391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00391","created_at":"2026-05-18T00:21:09Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00391v1","created_at":"2026-05-18T00:21:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00391","created_at":"2026-05-18T00:21:09Z"},{"alias_kind":"pith_short_12","alias_value":"PORSRLCUBGTB","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PORSRLCUBGTB26PW","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PORSRLCU","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:1f324cb1027d9753783681a713be7d120dd12bbd6f5e75f24d8bf0888f3e4e60","target":"graph","created_at":"2026-05-18T00:21:09Z","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":"It is well known that reconstruction problems, as the interdisciplinary subject, have been studied in numerous contexts including statistical physics, information theory and computational biology, to name a few. We consider a $2q$-state symmetric model, with two categories of $q$ states in each category, and 3 transition probabilities: the probability to remain in the same state, the probability to change states but remain in the same category, and the probability to change categories. We construct a nonlinear second order dynamical system based on this model and show that the Kesten-Stigum re","authors_text":"Ning Ning, S. Rao Jammalamadaka, Wenjian Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-01T16:22:51Z","title":"The Tightness of the Kesten-Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00391","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:c2e7b20db6b1d0ac9051867146e498aea7050edd8848d115fc87399cca5528f4","target":"record","created_at":"2026-05-18T00:21:09Z","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":"bec7d8edf3002fa3da79af59830ebfb63817c73e36a0c23dd0b19d29262f376f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-01T16:22:51Z","title_canon_sha256":"523e306a5f0703e22199f497906d599bfad5891ead35b430f6c3508ddbf7256e"},"schema_version":"1.0","source":{"id":"1712.00391","kind":"arxiv","version":1}},"canonical_sha256":"7ba328ac5409a61d79f624a67de4c98d950756ece2bff4cde81e6a45b6e6f604","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ba328ac5409a61d79f624a67de4c98d950756ece2bff4cde81e6a45b6e6f604","first_computed_at":"2026-05-18T00:21:09.348945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:09.348945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i/r1thcYo5FVLG2+sIYyyb/yInvisDtGpoAlwwMmNUhsyhY+jEZEUYokdQ+h6RTaJkUSSAy4dDEyThPzJBr0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:09.349610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2e7b20db6b1d0ac9051867146e498aea7050edd8848d115fc87399cca5528f4","sha256:1f324cb1027d9753783681a713be7d120dd12bbd6f5e75f24d8bf0888f3e4e60"],"state_sha256":"6168e84ef94db9b419dba680ba8a38ecbaabf280b51b8710799d82586f5b5d4f"}