{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WU4VUE3JFMOJO4HLJ3E6CHSLQV","short_pith_number":"pith:WU4VUE3J","schema_version":"1.0","canonical_sha256":"b5395a13692b1c9770eb4ec9e11e4b85422b4aa0120bde2fa3100fd30fb027f0","source":{"kind":"arxiv","id":"1007.3384","version":2},"attestation_state":"computed","paper":{"title":"Relative entropy via non-sequential recursive pair substitutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.IT"],"primary_cat":"cs.IT","authors_text":"D. Benedetto, E. Caglioti, G. Cristadoro, M. Degli Esposti","submitted_at":"2010-07-20T09:55:41Z","abstract_excerpt":"The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E. Caglioti and D. Gabrielli 2006 Jour. Stat. Mech. Theo. Exp. 09 doi:10.1088/1742.-5468/2006/09/P09011). In this paper we prove that the cross entropy and the Kullback-Leibler divergence can be obtained in a similar way."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1007.3384","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-20T09:55:41Z","cross_cats_sorted":["cond-mat.stat-mech","math.IT"],"title_canon_sha256":"90903ba642505e9d3ddea53dda1c164eb6c9fe552e1b44f312dbb44e140e4359","abstract_canon_sha256":"7cb9b51d191c02c7d61c149179876f4031c7aec3fb501342f180fc189d7b61d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:06:12.495843Z","signature_b64":"mJ141xFOnjqx64vhg05IfGbhFyoqh3m313PztxvxHRpaMcbhlXuhvRTSccUq3H0Y2ALuaFSgTjrh9PS5LNKBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5395a13692b1c9770eb4ec9e11e4b85422b4aa0120bde2fa3100fd30fb027f0","last_reissued_at":"2026-05-18T02:06:12.495285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:06:12.495285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative entropy via non-sequential recursive pair substitutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.IT"],"primary_cat":"cs.IT","authors_text":"D. Benedetto, E. Caglioti, G. Cristadoro, M. Degli Esposti","submitted_at":"2010-07-20T09:55:41Z","abstract_excerpt":"The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E. Caglioti and D. Gabrielli 2006 Jour. Stat. Mech. Theo. Exp. 09 doi:10.1088/1742.-5468/2006/09/P09011). In this paper we prove that the cross entropy and the Kullback-Leibler divergence can be obtained in a similar way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3384","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1007.3384","created_at":"2026-05-18T02:06:12.495385+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.3384v2","created_at":"2026-05-18T02:06:12.495385+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3384","created_at":"2026-05-18T02:06:12.495385+00:00"},{"alias_kind":"pith_short_12","alias_value":"WU4VUE3JFMOJ","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"WU4VUE3JFMOJO4HL","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"WU4VUE3J","created_at":"2026-05-18T12:26:17.028572+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WU4VUE3JFMOJO4HLJ3E6CHSLQV","json":"https://pith.science/pith/WU4VUE3JFMOJO4HLJ3E6CHSLQV.json","graph_json":"https://pith.science/api/pith-number/WU4VUE3JFMOJO4HLJ3E6CHSLQV/graph.json","events_json":"https://pith.science/api/pith-number/WU4VUE3JFMOJO4HLJ3E6CHSLQV/events.json","paper":"https://pith.science/paper/WU4VUE3J"},"agent_actions":{"view_html":"https://pith.science/pith/WU4VUE3JFMOJO4HLJ3E6CHSLQV","download_json":"https://pith.science/pith/WU4VUE3JFMOJO4HLJ3E6CHSLQV.json","view_paper":"https://pith.science/paper/WU4VUE3J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.3384&json=true","fetch_graph":"https://pith.science/api/pith-number/WU4VUE3JFMOJO4HLJ3E6CHSLQV/graph.json","fetch_events":"https://pith.science/api/pith-number/WU4VUE3JFMOJO4HLJ3E6CHSLQV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WU4VUE3JFMOJO4HLJ3E6CHSLQV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WU4VUE3JFMOJO4HLJ3E6CHSLQV/action/storage_attestation","attest_author":"https://pith.science/pith/WU4VUE3JFMOJO4HLJ3E6CHSLQV/action/author_attestation","sign_citation":"https://pith.science/pith/WU4VUE3JFMOJO4HLJ3E6CHSLQV/action/citation_signature","submit_replication":"https://pith.science/pith/WU4VUE3JFMOJO4HLJ3E6CHSLQV/action/replication_record"}},"created_at":"2026-05-18T02:06:12.495385+00:00","updated_at":"2026-05-18T02:06:12.495385+00:00"}