{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4MIJONLMYTHA456KC3PD2R4OIW","short_pith_number":"pith:4MIJONLM","canonical_record":{"source":{"id":"1102.3202","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-02-15T22:53:49Z","cross_cats_sorted":[],"title_canon_sha256":"28cf498a5465d47799982dd7071a05feb1166b61157aa583922f4af34249dca8","abstract_canon_sha256":"38d66d13b1d95c3d98f78cfe18452c808dde528f1a2880a7019feded27f8fca3"},"schema_version":"1.0"},"canonical_sha256":"e31097356cc4ce0e77ca16de3d478e4580123964cdeeafbeba02c55a7ee6cad8","source":{"kind":"arxiv","id":"1102.3202","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3202","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3202v2","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3202","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"pith_short_12","alias_value":"4MIJONLMYTHA","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4MIJONLMYTHA456K","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4MIJONLM","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4MIJONLMYTHA456KC3PD2R4OIW","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3202","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-02-15T22:53:49Z","cross_cats_sorted":[],"title_canon_sha256":"28cf498a5465d47799982dd7071a05feb1166b61157aa583922f4af34249dca8","abstract_canon_sha256":"38d66d13b1d95c3d98f78cfe18452c808dde528f1a2880a7019feded27f8fca3"},"schema_version":"1.0"},"canonical_sha256":"e31097356cc4ce0e77ca16de3d478e4580123964cdeeafbeba02c55a7ee6cad8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:08.744979Z","signature_b64":"Ur1Fn9/FSOdsPuaUL5XNz/2wKh2V35Gbv7+HJtyOocSrfE7xlHNM/hEIwpgh5Ht+6ya1wPINFvtFUj+m0lb6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e31097356cc4ce0e77ca16de3d478e4580123964cdeeafbeba02c55a7ee6cad8","last_reissued_at":"2026-05-18T02:44:08.744479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:08.744479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3202","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J46S5UM3SCMVLxWxGBZiH0F6sgOu7UdI8isy3c1LujD/OYafkNvMPNVFCW55I3TWrTYtk6TzowwvpTVvxqsEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:34:31.325177Z"},"content_sha256":"8fdcd01de497611f64b24d013c54a00556e4a3e450ac280459730506052948c8","schema_version":"1.0","event_id":"sha256:8fdcd01de497611f64b24d013c54a00556e4a3e450ac280459730506052948c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4MIJONLMYTHA456KC3PD2R4OIW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Metric Entropy and the Optimal Prediction of Chaotic Signals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Divakar Viswanath, Kirill Serkh, Xuan Liang","submitted_at":"2011-02-15T22:53:49Z","abstract_excerpt":"Suppose we are given a time series or a signal $x(t)$ for $0\\leq t\\leq T$. We consider the problem of predicting the signal in the interval $T<t\\leq T+t_{f}$ from a knowledge of its history and nothing more. We ask the following question: what is the largest value of $t_{f}$ for which a prediction can be made? We show that the answer to this question is contained in a fundamental result of information theory due to Wyner, Ziv, Ornstein, and Weiss. In particular, for the class of chaotic signals, the upper bound is $t_{f}\\leq\\log_{2}T/H$ in the limit $T\\rightarrow\\infty$, with $H$ being entropy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3202","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Isx8tQqCEClzpYeR3mrZERSq5RtHKGj7YT5mx93pTHCyeJWZAZuC8ny+EGDc2NJ8nEsTAHgMndSQqyBUHwX8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:34:31.325746Z"},"content_sha256":"7635ef5b3ab9e695abd03281a33f0ea4680c2081c07559e2f4bc520f16ab52b5","schema_version":"1.0","event_id":"sha256:7635ef5b3ab9e695abd03281a33f0ea4680c2081c07559e2f4bc520f16ab52b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4MIJONLMYTHA456KC3PD2R4OIW/bundle.json","state_url":"https://pith.science/pith/4MIJONLMYTHA456KC3PD2R4OIW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4MIJONLMYTHA456KC3PD2R4OIW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T23:34:31Z","links":{"resolver":"https://pith.science/pith/4MIJONLMYTHA456KC3PD2R4OIW","bundle":"https://pith.science/pith/4MIJONLMYTHA456KC3PD2R4OIW/bundle.json","state":"https://pith.science/pith/4MIJONLMYTHA456KC3PD2R4OIW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4MIJONLMYTHA456KC3PD2R4OIW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4MIJONLMYTHA456KC3PD2R4OIW","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":"38d66d13b1d95c3d98f78cfe18452c808dde528f1a2880a7019feded27f8fca3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-02-15T22:53:49Z","title_canon_sha256":"28cf498a5465d47799982dd7071a05feb1166b61157aa583922f4af34249dca8"},"schema_version":"1.0","source":{"id":"1102.3202","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3202","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3202v2","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3202","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"pith_short_12","alias_value":"4MIJONLMYTHA","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4MIJONLMYTHA456K","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4MIJONLM","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:7635ef5b3ab9e695abd03281a33f0ea4680c2081c07559e2f4bc520f16ab52b5","target":"graph","created_at":"2026-05-18T02:44:08Z","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":"Suppose we are given a time series or a signal $x(t)$ for $0\\leq t\\leq T$. We consider the problem of predicting the signal in the interval $T<t\\leq T+t_{f}$ from a knowledge of its history and nothing more. We ask the following question: what is the largest value of $t_{f}$ for which a prediction can be made? We show that the answer to this question is contained in a fundamental result of information theory due to Wyner, Ziv, Ornstein, and Weiss. In particular, for the class of chaotic signals, the upper bound is $t_{f}\\leq\\log_{2}T/H$ in the limit $T\\rightarrow\\infty$, with $H$ being entropy","authors_text":"Divakar Viswanath, Kirill Serkh, Xuan Liang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-02-15T22:53:49Z","title":"Metric Entropy and the Optimal Prediction of Chaotic Signals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3202","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":"sha256:8fdcd01de497611f64b24d013c54a00556e4a3e450ac280459730506052948c8","target":"record","created_at":"2026-05-18T02:44:08Z","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":"38d66d13b1d95c3d98f78cfe18452c808dde528f1a2880a7019feded27f8fca3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-02-15T22:53:49Z","title_canon_sha256":"28cf498a5465d47799982dd7071a05feb1166b61157aa583922f4af34249dca8"},"schema_version":"1.0","source":{"id":"1102.3202","kind":"arxiv","version":2}},"canonical_sha256":"e31097356cc4ce0e77ca16de3d478e4580123964cdeeafbeba02c55a7ee6cad8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e31097356cc4ce0e77ca16de3d478e4580123964cdeeafbeba02c55a7ee6cad8","first_computed_at":"2026-05-18T02:44:08.744479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:08.744479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ur1Fn9/FSOdsPuaUL5XNz/2wKh2V35Gbv7+HJtyOocSrfE7xlHNM/hEIwpgh5Ht+6ya1wPINFvtFUj+m0lb6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:08.744979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3202","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fdcd01de497611f64b24d013c54a00556e4a3e450ac280459730506052948c8","sha256:7635ef5b3ab9e695abd03281a33f0ea4680c2081c07559e2f4bc520f16ab52b5"],"state_sha256":"02df563c29934c1fc0dca87ac33f42747ce9ae0ceaed2b70d1f4a0e99da61486"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNtd2Rz8MfFtNVhHIhG1ohB+ifyLgT9A90CK2Oj93L8jVr+IDzQquc5HHM0hyFg7uvZb8KNjQ4DBmKNtDt/SDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:34:31.328434Z","bundle_sha256":"6a428a1a23c25197e56767d410f51383dcca453959f48729a2ad476674a68530"}}