{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Z3WDEXDMOPIANO3YIDWKVBEGWO","short_pith_number":"pith:Z3WDEXDM","canonical_record":{"source":{"id":"1302.0328","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-02T01:04:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"38f16cb1dddc5c3ad018765158e5ddcd2d7eb8f1c9ceb5abb544d7e5b40b4f3d","abstract_canon_sha256":"551c3a36bd906d426ccadf481eae5429b7c74689eec1172515dd9b2f137504a1"},"schema_version":"1.0"},"canonical_sha256":"ceec325c6c73d006bb7840ecaa8486b383500ebd2b1453a67ccd30866f039735","source":{"kind":"arxiv","id":"1302.0328","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0328","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0328v3","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0328","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"pith_short_12","alias_value":"Z3WDEXDMOPIA","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z3WDEXDMOPIANO3Y","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z3WDEXDM","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Z3WDEXDMOPIANO3YIDWKVBEGWO","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0328","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-02T01:04:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"38f16cb1dddc5c3ad018765158e5ddcd2d7eb8f1c9ceb5abb544d7e5b40b4f3d","abstract_canon_sha256":"551c3a36bd906d426ccadf481eae5429b7c74689eec1172515dd9b2f137504a1"},"schema_version":"1.0"},"canonical_sha256":"ceec325c6c73d006bb7840ecaa8486b383500ebd2b1453a67ccd30866f039735","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:30.856681Z","signature_b64":"/dfYvT30M5rjWMGNLN/50rK31r7ixKI1Kg2913oBSQvN0uviW7q6W0O6LswCmnIMUg3/MWKzvrzlLAhy16e+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceec325c6c73d006bb7840ecaa8486b383500ebd2b1453a67ccd30866f039735","last_reissued_at":"2026-05-18T02:54:30.856180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:30.856180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0328","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ml3zsov+WFZFkeeuYgix7CTYgXkMB3N0MrmpkizdcSgAwrO6/F9EtKhrkhvO9IAtr9ik9YMC2133QYnsoJeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:22:28.037277Z"},"content_sha256":"fff582cf7fa64df620f279ef3c4682b35e6dfdc9cd268821ed27e5ded45e9f5f","schema_version":"1.0","event_id":"sha256:fff582cf7fa64df620f279ef3c4682b35e6dfdc9cd268821ed27e5ded45e9f5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Z3WDEXDMOPIANO3YIDWKVBEGWO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bayesian Entropy Estimation for Countable Discrete Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Evan Archer, Il Memming Park, Jonathan Pillow","submitted_at":"2013-02-02T01:04:11Z","abstract_excerpt":"We consider the problem of estimating Shannon's entropy $H$ from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The Pitman-Yor process, a generalization of Dirichlet process, provides a tractable prior distribution over the space of countably infinite discrete distributions, and has found major applications in Bayesian non-parametric statistics and machine learning. Here we show that it also provides a natural family of priors for Bayesian entropy estimation, due to the fact that moments of the induced posterior distribution over $H$ can be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0328","kind":"arxiv","version":3},"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":"2026-05-18T02:54:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n41N4DJslxV8/P4zjOM9Lem9fOuhdxe6RLlOb1oftyjpn++UZyd7CBvbjL2AoZ9kysxgNW21B59hnX4S+HUAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:22:28.037977Z"},"content_sha256":"8b544d1f4c7e03f93faf7fc27ed122408c81a28cb4f50e22504af0f598e0f540","schema_version":"1.0","event_id":"sha256:8b544d1f4c7e03f93faf7fc27ed122408c81a28cb4f50e22504af0f598e0f540"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3WDEXDMOPIANO3YIDWKVBEGWO/bundle.json","state_url":"https://pith.science/pith/Z3WDEXDMOPIANO3YIDWKVBEGWO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3WDEXDMOPIANO3YIDWKVBEGWO/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":"2026-05-25T09:22:28Z","links":{"resolver":"https://pith.science/pith/Z3WDEXDMOPIANO3YIDWKVBEGWO","bundle":"https://pith.science/pith/Z3WDEXDMOPIANO3YIDWKVBEGWO/bundle.json","state":"https://pith.science/pith/Z3WDEXDMOPIANO3YIDWKVBEGWO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3WDEXDMOPIANO3YIDWKVBEGWO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z3WDEXDMOPIANO3YIDWKVBEGWO","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":"551c3a36bd906d426ccadf481eae5429b7c74689eec1172515dd9b2f137504a1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-02T01:04:11Z","title_canon_sha256":"38f16cb1dddc5c3ad018765158e5ddcd2d7eb8f1c9ceb5abb544d7e5b40b4f3d"},"schema_version":"1.0","source":{"id":"1302.0328","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0328","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0328v3","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0328","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"pith_short_12","alias_value":"Z3WDEXDMOPIA","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z3WDEXDMOPIANO3Y","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z3WDEXDM","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:8b544d1f4c7e03f93faf7fc27ed122408c81a28cb4f50e22504af0f598e0f540","target":"graph","created_at":"2026-05-18T02:54:30Z","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 the problem of estimating Shannon's entropy $H$ from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The Pitman-Yor process, a generalization of Dirichlet process, provides a tractable prior distribution over the space of countably infinite discrete distributions, and has found major applications in Bayesian non-parametric statistics and machine learning. Here we show that it also provides a natural family of priors for Bayesian entropy estimation, due to the fact that moments of the induced posterior distribution over $H$ can be ","authors_text":"Evan Archer, Il Memming Park, Jonathan Pillow","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-02T01:04:11Z","title":"Bayesian Entropy Estimation for Countable Discrete Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0328","kind":"arxiv","version":3},"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:fff582cf7fa64df620f279ef3c4682b35e6dfdc9cd268821ed27e5ded45e9f5f","target":"record","created_at":"2026-05-18T02:54:30Z","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":"551c3a36bd906d426ccadf481eae5429b7c74689eec1172515dd9b2f137504a1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-02T01:04:11Z","title_canon_sha256":"38f16cb1dddc5c3ad018765158e5ddcd2d7eb8f1c9ceb5abb544d7e5b40b4f3d"},"schema_version":"1.0","source":{"id":"1302.0328","kind":"arxiv","version":3}},"canonical_sha256":"ceec325c6c73d006bb7840ecaa8486b383500ebd2b1453a67ccd30866f039735","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceec325c6c73d006bb7840ecaa8486b383500ebd2b1453a67ccd30866f039735","first_computed_at":"2026-05-18T02:54:30.856180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:30.856180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/dfYvT30M5rjWMGNLN/50rK31r7ixKI1Kg2913oBSQvN0uviW7q6W0O6LswCmnIMUg3/MWKzvrzlLAhy16e+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:30.856681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0328","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fff582cf7fa64df620f279ef3c4682b35e6dfdc9cd268821ed27e5ded45e9f5f","sha256:8b544d1f4c7e03f93faf7fc27ed122408c81a28cb4f50e22504af0f598e0f540"],"state_sha256":"8bd1544855c055836f23c0b1abeb5ab9d2b1a964686486017b31c8a346e00f69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u9lqL4esMbdkY9jgPb2luAFvDvbIaMBoa9rr66BeJKBG5hyXYDuGncmj5DQR0z5TdF+BZ8rdRMTQ6h6CZYNRAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:22:28.040988Z","bundle_sha256":"86f94ea2ffd718457ff9b4c564345334bebeb8952161ee0becc32e083b026a38"}}