{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BVNA36F4XHTR4FXJHQ4ASLAI3A","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":"91a9e6c05b674dade7f89621bc535f31055e57febf59b52c32113e913f612df2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.CD","submitted_at":"2026-06-04T04:09:16Z","title_canon_sha256":"233f9336e6b54ef186dc8a721eab615f0608b44f6e7fe0699c7c2ea9bae6278f"},"schema_version":"1.0","source":{"id":"2606.05685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.05685","created_at":"2026-06-05T01:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"2606.05685v1","created_at":"2026-06-05T01:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05685","created_at":"2026-06-05T01:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"BVNA36F4XHTR","created_at":"2026-06-05T01:14:59Z"},{"alias_kind":"pith_short_16","alias_value":"BVNA36F4XHTR4FXJ","created_at":"2026-06-05T01:14:59Z"},{"alias_kind":"pith_short_8","alias_value":"BVNA36F4","created_at":"2026-06-05T01:14:59Z"}],"graph_snapshots":[{"event_id":"sha256:bbcf8ed85c71d8877baa586dd8495ce1a2b8aaa7fa62c99d464116a9849956ca","target":"graph","created_at":"2026-06-05T01:14:59Z","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/2606.05685/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Empirical entropy rates are widely used to quantify unpredictability from symbolic or time-series data, yet their interpretation is subtle in weakly chaotic dynamics, where ordinary Lyapunov exponents vanish and invariant measures are infinite. We address this issue by studying the empirical one-step conditional entropy for the fixed finite partitions considered below in one-dimensional intermittent maps with infinite invariant measures. For the modified Bernoulli map and the Boole transformation in the infinite-measure weak-chaos regime, we prove that this per-step empirical entropy converges","authors_text":"Ken-ichi Okubo","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.CD","submitted_at":"2026-06-04T04:09:16Z","title":"Empirical One-Step Conditional Entropy in Infinite Ergodic Systems: Vanishing Entropy Rate, Sparse-Transition Scaling, and Mittag-Leffler Fluctuations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05685","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:a3580eb9532b32ae6eb7b0b2e1713416d48816ba932c53dcef117e999ad7eb7c","target":"record","created_at":"2026-06-05T01:14:59Z","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":"91a9e6c05b674dade7f89621bc535f31055e57febf59b52c32113e913f612df2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.CD","submitted_at":"2026-06-04T04:09:16Z","title_canon_sha256":"233f9336e6b54ef186dc8a721eab615f0608b44f6e7fe0699c7c2ea9bae6278f"},"schema_version":"1.0","source":{"id":"2606.05685","kind":"arxiv","version":1}},"canonical_sha256":"0d5a0df8bcb9e71e16e93c38092c08d8291c231efc81560637e9045f28dc9fd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d5a0df8bcb9e71e16e93c38092c08d8291c231efc81560637e9045f28dc9fd4","first_computed_at":"2026-06-05T01:14:59.243039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:14:59.243039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jY7qDa8rr86FUEJECa0B2fxqyJegS1/G+vHu+sUaDR1zOAD9sFg2zwHS/J9Cyrp89zxeXn4z4RP+Br4cQJN+Cg==","signature_status":"signed_v1","signed_at":"2026-06-05T01:14:59.243459Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.05685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3580eb9532b32ae6eb7b0b2e1713416d48816ba932c53dcef117e999ad7eb7c","sha256:bbcf8ed85c71d8877baa586dd8495ce1a2b8aaa7fa62c99d464116a9849956ca"],"state_sha256":"e3fdaf301e0df80754f676473308e9d96d4da18242030dc358b9819771e6377b"}