{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GKT6ZJZWKTOCM7SEPNYEQBE4TL","short_pith_number":"pith:GKT6ZJZW","canonical_record":{"source":{"id":"1012.2086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-09T19:23:35Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"ec161c5f92a140d8646887ad83376c2a507f9861f31c2adcedb46d552b22017d","abstract_canon_sha256":"0ebc71c935ead414ff18a9c3e59bb8c0994b527c86ab64f9f4e1aaa1a7a3bacb"},"schema_version":"1.0"},"canonical_sha256":"32a7eca73654dc267e447b7048049c9ae2fc944b4b824aef8f4ecdebeb5c8551","source":{"kind":"arxiv","id":"1012.2086","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2086","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2086v1","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2086","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"GKT6ZJZWKTOC","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GKT6ZJZWKTOCM7SE","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GKT6ZJZW","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GKT6ZJZWKTOCM7SEPNYEQBE4TL","target":"record","payload":{"canonical_record":{"source":{"id":"1012.2086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-09T19:23:35Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"ec161c5f92a140d8646887ad83376c2a507f9861f31c2adcedb46d552b22017d","abstract_canon_sha256":"0ebc71c935ead414ff18a9c3e59bb8c0994b527c86ab64f9f4e1aaa1a7a3bacb"},"schema_version":"1.0"},"canonical_sha256":"32a7eca73654dc267e447b7048049c9ae2fc944b4b824aef8f4ecdebeb5c8551","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:49.018244Z","signature_b64":"r8zQAYQjcG95NrPuD9aTRPxZv/jpa2Oy2UrjYQXw2yt0YJR5UtoGbnljy1DCCDywPLXRg5z5BbRDNrnhoreUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32a7eca73654dc267e447b7048049c9ae2fc944b4b824aef8f4ecdebeb5c8551","last_reissued_at":"2026-05-18T04:33:49.017780Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:49.017780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.2086","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p5yZY70tgd9z+fqCeTM8wp3xX1ZV5x0xTTzYGH3o1a5UpMXOZagOUntrFKaeSQYrCFzbxHsvsCVLmaHhaVkfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:49:27.013401Z"},"content_sha256":"5fbc4bd8bfbc920cd8bd6306ff6295b13ab57fc3b57350a469f05433cd847e8b","schema_version":"1.0","event_id":"sha256:5fbc4bd8bfbc920cd8bd6306ff6295b13ab57fc3b57350a469f05433cd847e8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GKT6ZJZWKTOCM7SEPNYEQBE4TL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropy Rate for Hidden Markov Chains with rare transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Anthony Quas, Yuval Peres","submitted_at":"2010-12-09T19:23:35Z","abstract_excerpt":"We consider Hidden Markov Chains obtained by passing a Markov Chain with rare transitions through a noisy memoryless channel. We obtain asymptotic estimates for the entropy of the resulting Hidden Markov Chain as the transition rate is reduced to zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2086","kind":"arxiv","version":1},"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":"2026-05-18T04:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/SOnlCust9OIYh3Kbh5ow0EIOTS9HKva7mV7O6ZgeDKXS1Hweq3PXqA2urB9InCSKzK/8+7XO3KSpAvD+/k0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:49:27.013746Z"},"content_sha256":"6b408ca622c13530e1dfb31715376b994cd25fb74a109a14b48b070f173a03c5","schema_version":"1.0","event_id":"sha256:6b408ca622c13530e1dfb31715376b994cd25fb74a109a14b48b070f173a03c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKT6ZJZWKTOCM7SEPNYEQBE4TL/bundle.json","state_url":"https://pith.science/pith/GKT6ZJZWKTOCM7SEPNYEQBE4TL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKT6ZJZWKTOCM7SEPNYEQBE4TL/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":"2026-06-26T12:49:27Z","links":{"resolver":"https://pith.science/pith/GKT6ZJZWKTOCM7SEPNYEQBE4TL","bundle":"https://pith.science/pith/GKT6ZJZWKTOCM7SEPNYEQBE4TL/bundle.json","state":"https://pith.science/pith/GKT6ZJZWKTOCM7SEPNYEQBE4TL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKT6ZJZWKTOCM7SEPNYEQBE4TL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GKT6ZJZWKTOCM7SEPNYEQBE4TL","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":"0ebc71c935ead414ff18a9c3e59bb8c0994b527c86ab64f9f4e1aaa1a7a3bacb","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-09T19:23:35Z","title_canon_sha256":"ec161c5f92a140d8646887ad83376c2a507f9861f31c2adcedb46d552b22017d"},"schema_version":"1.0","source":{"id":"1012.2086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2086","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2086v1","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2086","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"GKT6ZJZWKTOC","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GKT6ZJZWKTOCM7SE","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GKT6ZJZW","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:6b408ca622c13530e1dfb31715376b994cd25fb74a109a14b48b070f173a03c5","target":"graph","created_at":"2026-05-18T04:33:49Z","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 consider Hidden Markov Chains obtained by passing a Markov Chain with rare transitions through a noisy memoryless channel. We obtain asymptotic estimates for the entropy of the resulting Hidden Markov Chain as the transition rate is reduced to zero.","authors_text":"Anthony Quas, Yuval Peres","cross_cats":["math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-09T19:23:35Z","title":"Entropy Rate for Hidden Markov Chains with rare transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2086","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":"sha256:5fbc4bd8bfbc920cd8bd6306ff6295b13ab57fc3b57350a469f05433cd847e8b","target":"record","created_at":"2026-05-18T04:33:49Z","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":"0ebc71c935ead414ff18a9c3e59bb8c0994b527c86ab64f9f4e1aaa1a7a3bacb","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-09T19:23:35Z","title_canon_sha256":"ec161c5f92a140d8646887ad83376c2a507f9861f31c2adcedb46d552b22017d"},"schema_version":"1.0","source":{"id":"1012.2086","kind":"arxiv","version":1}},"canonical_sha256":"32a7eca73654dc267e447b7048049c9ae2fc944b4b824aef8f4ecdebeb5c8551","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32a7eca73654dc267e447b7048049c9ae2fc944b4b824aef8f4ecdebeb5c8551","first_computed_at":"2026-05-18T04:33:49.017780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:49.017780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r8zQAYQjcG95NrPuD9aTRPxZv/jpa2Oy2UrjYQXw2yt0YJR5UtoGbnljy1DCCDywPLXRg5z5BbRDNrnhoreUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:49.018244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fbc4bd8bfbc920cd8bd6306ff6295b13ab57fc3b57350a469f05433cd847e8b","sha256:6b408ca622c13530e1dfb31715376b994cd25fb74a109a14b48b070f173a03c5"],"state_sha256":"b57c8df643ff832831fe26fd2a8811c6f0df2c2b2dba5262519868250a56e085"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jpJsusXHjp+EhU5KZYaSTpRi2LJb7T9hLUC/FIbdL0BB/cVZJPWHulU3/Vn2ueEzQuB02Ilq/4lkfWAo8gC7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:49:27.015715Z","bundle_sha256":"63f8c414f5c83edcfa14b75e5a47a85d2e0615879b7845997d7303d45f82a375"}}