{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:YZ2HS3S26SK7J4U2K6X4GJCK35","short_pith_number":"pith:YZ2HS3S2","canonical_record":{"source":{"id":"2105.12829","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2021-04-29T09:32:18Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"90cc1cce2efe44c431f578859b9a3bbdf68faf89430f93bf9a4763179d5e9bfa","abstract_canon_sha256":"590a2680d5aab2b73698a07290575f36a67a678282829f08c548ef7d84dd70d8"},"schema_version":"1.0"},"canonical_sha256":"c674796e5af495f4f29a57afc3244adf5434b394b6a5eb9d39e55ca31407c02f","source":{"kind":"arxiv","id":"2105.12829","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.12829","created_at":"2026-07-05T03:10:32Z"},{"alias_kind":"arxiv_version","alias_value":"2105.12829v2","created_at":"2026-07-05T03:10:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.12829","created_at":"2026-07-05T03:10:32Z"},{"alias_kind":"pith_short_12","alias_value":"YZ2HS3S26SK7","created_at":"2026-07-05T03:10:32Z"},{"alias_kind":"pith_short_16","alias_value":"YZ2HS3S26SK7J4U2","created_at":"2026-07-05T03:10:32Z"},{"alias_kind":"pith_short_8","alias_value":"YZ2HS3S2","created_at":"2026-07-05T03:10:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:YZ2HS3S26SK7J4U2K6X4GJCK35","target":"record","payload":{"canonical_record":{"source":{"id":"2105.12829","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2021-04-29T09:32:18Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"90cc1cce2efe44c431f578859b9a3bbdf68faf89430f93bf9a4763179d5e9bfa","abstract_canon_sha256":"590a2680d5aab2b73698a07290575f36a67a678282829f08c548ef7d84dd70d8"},"schema_version":"1.0"},"canonical_sha256":"c674796e5af495f4f29a57afc3244adf5434b394b6a5eb9d39e55ca31407c02f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:10:32.716931Z","signature_b64":"j+2Q+pdNVFoZDpEjzYF12thkw39xrq+TWbcNfcetHhHEP4o2jN4ckoV6ufrRYwyEe+SGJrHQfq9+U1zcRbFtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c674796e5af495f4f29a57afc3244adf5434b394b6a5eb9d39e55ca31407c02f","last_reissued_at":"2026-07-05T03:10:32.716496Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:10:32.716496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.12829","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":"2026-07-05T03:10:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+5iytljorS3xGe5MQB1a/i6CnMafS2xqscJXZwiQ8xqCu8C6cz16EX4XUpcvYfHQMdbbnu0jskJPBeOnKLJOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:43:53.499909Z"},"content_sha256":"62df74704041e2c65910fd7a82f2bc747e17dda861be22309fc895cd041c121d","schema_version":"1.0","event_id":"sha256:62df74704041e2c65910fd7a82f2bc747e17dda861be22309fc895cd041c121d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:YZ2HS3S26SK7J4U2K6X4GJCK35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimating the variance of Shannon entropy","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alessio Perinelli, Leonardo Ricci, Michele Castelluzzo","submitted_at":"2021-04-29T09:32:18Z","abstract_excerpt":"The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly the most widespread tool is provided by the so-called plug-in estimator, whose statistical properties in terms of bias and variance were investigated since the first decade after the publication of Shannon's seminal works. In the case of an underlying multinomial distribution, while the bias can be evaluated by knowing support and data set size, variance is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.12829","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.12829/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:10:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cxLJV9jczgrM5H1T1AWIJ8+OhPPx7Uzx+srogDDXmdzwD3d4w81aG6oxk0SUgZW5YqY94+eQ2eDftGp/k4fwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:43:53.500281Z"},"content_sha256":"16064ff5d5f8e901bd7f78a15a62bb6d11314b5450b0bc451ea04c1affd37711","schema_version":"1.0","event_id":"sha256:16064ff5d5f8e901bd7f78a15a62bb6d11314b5450b0bc451ea04c1affd37711"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZ2HS3S26SK7J4U2K6X4GJCK35/bundle.json","state_url":"https://pith.science/pith/YZ2HS3S26SK7J4U2K6X4GJCK35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZ2HS3S26SK7J4U2K6X4GJCK35/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":"2026-07-07T12:43:53Z","links":{"resolver":"https://pith.science/pith/YZ2HS3S26SK7J4U2K6X4GJCK35","bundle":"https://pith.science/pith/YZ2HS3S26SK7J4U2K6X4GJCK35/bundle.json","state":"https://pith.science/pith/YZ2HS3S26SK7J4U2K6X4GJCK35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZ2HS3S26SK7J4U2K6X4GJCK35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YZ2HS3S26SK7J4U2K6X4GJCK35","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":"590a2680d5aab2b73698a07290575f36a67a678282829f08c548ef7d84dd70d8","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2021-04-29T09:32:18Z","title_canon_sha256":"90cc1cce2efe44c431f578859b9a3bbdf68faf89430f93bf9a4763179d5e9bfa"},"schema_version":"1.0","source":{"id":"2105.12829","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.12829","created_at":"2026-07-05T03:10:32Z"},{"alias_kind":"arxiv_version","alias_value":"2105.12829v2","created_at":"2026-07-05T03:10:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.12829","created_at":"2026-07-05T03:10:32Z"},{"alias_kind":"pith_short_12","alias_value":"YZ2HS3S26SK7","created_at":"2026-07-05T03:10:32Z"},{"alias_kind":"pith_short_16","alias_value":"YZ2HS3S26SK7J4U2","created_at":"2026-07-05T03:10:32Z"},{"alias_kind":"pith_short_8","alias_value":"YZ2HS3S2","created_at":"2026-07-05T03:10:32Z"}],"graph_snapshots":[{"event_id":"sha256:16064ff5d5f8e901bd7f78a15a62bb6d11314b5450b0bc451ea04c1affd37711","target":"graph","created_at":"2026-07-05T03:10:32Z","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/2105.12829/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly the most widespread tool is provided by the so-called plug-in estimator, whose statistical properties in terms of bias and variance were investigated since the first decade after the publication of Shannon's seminal works. In the case of an underlying multinomial distribution, while the bias can be evaluated by knowing support and data set size, variance is ","authors_text":"Alessio Perinelli, Leonardo Ricci, Michele Castelluzzo","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2021-04-29T09:32:18Z","title":"Estimating the variance of Shannon entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.12829","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":"sha256:62df74704041e2c65910fd7a82f2bc747e17dda861be22309fc895cd041c121d","target":"record","created_at":"2026-07-05T03:10:32Z","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":"590a2680d5aab2b73698a07290575f36a67a678282829f08c548ef7d84dd70d8","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2021-04-29T09:32:18Z","title_canon_sha256":"90cc1cce2efe44c431f578859b9a3bbdf68faf89430f93bf9a4763179d5e9bfa"},"schema_version":"1.0","source":{"id":"2105.12829","kind":"arxiv","version":2}},"canonical_sha256":"c674796e5af495f4f29a57afc3244adf5434b394b6a5eb9d39e55ca31407c02f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c674796e5af495f4f29a57afc3244adf5434b394b6a5eb9d39e55ca31407c02f","first_computed_at":"2026-07-05T03:10:32.716496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:10:32.716496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j+2Q+pdNVFoZDpEjzYF12thkw39xrq+TWbcNfcetHhHEP4o2jN4ckoV6ufrRYwyEe+SGJrHQfq9+U1zcRbFtDw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:10:32.716931Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.12829","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62df74704041e2c65910fd7a82f2bc747e17dda861be22309fc895cd041c121d","sha256:16064ff5d5f8e901bd7f78a15a62bb6d11314b5450b0bc451ea04c1affd37711"],"state_sha256":"ab2e91c13e4c2a60ba5cee3d305d2174b716d31f01d7f3e104bd9eabef35f56d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"76mae9nUWt2z5M0alWVbYB0yov189O28yDx6QQyw9PvT9k8q1EtAc3PV7KzUU4dOnVzvicPdcyEOrewMal/bCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T12:43:53.502252Z","bundle_sha256":"04d5e353002b14c16c9eae33091d6326079a7ef2ef6f5d0d2801be655ffcf76f"}}