{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DT7QA6VSGXT2YSNRLCE3C3PMF3","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":"71e61b77cd4cceb2318bcbbae2df2708b815c577906e040002defbc1aaf42ef3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-27T03:01:37Z","title_canon_sha256":"ffb0ab698d460ddb7e2347929fb4933b0e03e5991416c9f7235b860a06d28167"},"schema_version":"1.0","source":{"id":"1706.09283","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09283","created_at":"2026-05-18T00:22:33Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09283v2","created_at":"2026-05-18T00:22:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09283","created_at":"2026-05-18T00:22:33Z"},{"alias_kind":"pith_short_12","alias_value":"DT7QA6VSGXT2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DT7QA6VSGXT2YSNR","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DT7QA6VS","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:4b0411c57a38c32e0615c38a7bae39deb94d6a368390c45e36f544e6aa223445","target":"graph","created_at":"2026-05-18T00:22:33Z","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 has been demonstrated that excitable media with a tree structure performed better than other network topologies, it is natural to consider neural networks defined on Cayley trees. The investigation of a symbolic space called tree-shift of finite type is important when it comes to the discussion of the equilibrium solutions of neural networks on Cayley trees. Entropy is a frequently used invariant for measuring the complexity of a system, and constant entropy for an open set of coupling weights between neurons means that the specific network is stable. This paper gives a complete characteriz","authors_text":"Chih-Hung Chang, Jung-Chao Ban, Nai-Zhu Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-27T03:01:37Z","title":"Entropy bifurcation of neural networks on Cayley trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09283","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":"sha256:67ea22d37c15f2e5d70cfac6d42544910a63abbb8ee1cd558e799d3f864cfef4","target":"record","created_at":"2026-05-18T00:22:33Z","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":"71e61b77cd4cceb2318bcbbae2df2708b815c577906e040002defbc1aaf42ef3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-27T03:01:37Z","title_canon_sha256":"ffb0ab698d460ddb7e2347929fb4933b0e03e5991416c9f7235b860a06d28167"},"schema_version":"1.0","source":{"id":"1706.09283","kind":"arxiv","version":2}},"canonical_sha256":"1cff007ab235e7ac49b15889b16dec2ef18f4fbe19e54ac2951ed6e98d5580fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cff007ab235e7ac49b15889b16dec2ef18f4fbe19e54ac2951ed6e98d5580fe","first_computed_at":"2026-05-18T00:22:33.286381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:33.286381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xaV9MKD+Yzh59TRwnwQVOkiPTez+T1BuGyISsdYLuEnJZvICOzj2yRbkliYLvSXe8o5Vh3V5r/XgfV1ioQAWCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:33.286962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.09283","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67ea22d37c15f2e5d70cfac6d42544910a63abbb8ee1cd558e799d3f864cfef4","sha256:4b0411c57a38c32e0615c38a7bae39deb94d6a368390c45e36f544e6aa223445"],"state_sha256":"645ffbfd44608a5234ea8b0c3ef74eb39a97fa35351bd0e1be7df52a86348bf8"}