{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7OGSCD5LFUCH4SGQXMKFUQ45YU","short_pith_number":"pith:7OGSCD5L","schema_version":"1.0","canonical_sha256":"fb8d210fab2d047e48d0bb145a439dc522fa2c2dc1bc7699024c08710449cce4","source":{"kind":"arxiv","id":"2604.18081","version":1},"attestation_state":"computed","paper":{"title":"Shannon and R\\'enyi entropies of molecular densities: insights into extensivity and the incomplete description of electron correlation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Electron-density entropies fail to capture static correlation and often violate extensivity.","cross_cats":["physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"\\'Angel Mart\\'in Pend\\'as, Diogo J. L. Rodrigues, Evelio Francisco","submitted_at":"2026-04-20T10:53:35Z","abstract_excerpt":"In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and R\\'enyi entropies, as descriptors of electronic correlation. By establishing a rigorous decomposition of these entropic measures into additive and nonadditive contributions, supported on a Mulliken-like atomic partition of molecules, we systematically analyze the asymptotic behavior of the entropies at the infinite-internuclear-distance limit to assess the problem of static correlation and extensivity. Our algebraic and numerical analysis rev"},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2604.18081","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2026-04-20T10:53:35Z","cross_cats_sorted":["physics.chem-ph"],"title_canon_sha256":"8b6c9906fff280c75909f0eb859dee82739f429a6f5e4a63fcb56026b49b4d89","abstract_canon_sha256":"060411ab0f7a0326de6f9aa053e3cd5a166e54c53bc78216e5437be63bb778ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:19.293476Z","signature_b64":"uBe/M19v7+YOVptI0s92ZQwAM/VnpCU6LAApMjgQ4mN4aV0NzxaBqcXIUDLdPTstohegmvwjcWJ4dCvVXLjQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb8d210fab2d047e48d0bb145a439dc522fa2c2dc1bc7699024c08710449cce4","last_reissued_at":"2026-05-21T01:05:19.293004Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:19.293004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shannon and R\\'enyi entropies of molecular densities: insights into extensivity and the incomplete description of electron correlation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Electron-density entropies fail to capture static correlation and often violate extensivity.","cross_cats":["physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"\\'Angel Mart\\'in Pend\\'as, Diogo J. L. Rodrigues, Evelio Francisco","submitted_at":"2026-04-20T10:53:35Z","abstract_excerpt":"In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and R\\'enyi entropies, as descriptors of electronic correlation. By establishing a rigorous decomposition of these entropic measures into additive and nonadditive contributions, supported on a Mulliken-like atomic partition of molecules, we systematically analyze the asymptotic behavior of the entropies at the infinite-internuclear-distance limit to assess the problem of static correlation and extensivity. Our algebraic and numerical analysis rev"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"electron-density-based measures are insufficient for capturing static correlation, suggesting that robust entropic descriptors should be constructed from higher-dimensional Hilbert-space objects.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Mulliken-like atomic partition combined with the infinite-separation asymptotic analysis correctly isolates and quantifies static correlation and extensivity properties of the underlying wavefunction.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Shannon and Rényi entropies from molecular electron densities fail to encode static correlation and violate extensivity, indicating density-based descriptors are insufficient.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Electron-density entropies fail to capture static correlation and often violate extensivity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"18313a06274e2cdfa407b8fa5cb6f6fe60649ea2df7fb8db56ba3a28836e3b6f"},"source":{"id":"2604.18081","kind":"arxiv","version":1},"verdict":{"id":"560dea0b-1424-4ff4-a496-271853a53c68","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T05:19:14.166745Z","strongest_claim":"electron-density-based measures are insufficient for capturing static correlation, suggesting that robust entropic descriptors should be constructed from higher-dimensional Hilbert-space objects.","one_line_summary":"Shannon and Rényi entropies from molecular electron densities fail to encode static correlation and violate extensivity, indicating density-based descriptors are insufficient.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Mulliken-like atomic partition combined with the infinite-separation asymptotic analysis correctly isolates and quantifies static correlation and extensivity properties of the underlying wavefunction.","pith_extraction_headline":"Electron-density entropies fail to capture static correlation and often violate extensivity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.18081/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-20T04:27:42.378119Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"bb93692a979d3249b491993312c8094c1278676475f38613009010e9a9359995"},"references":{"count":109,"sample":[{"doi":"","year":1948,"title":"Shannon, C. E. A mathematical theory of communication.Bell System Tech- nical Journal27, 379–423 (1948)","work_id":"","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"Brillouin, L.Science and information theory(Courier Corporation, 2013)","work_id":"","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"Frieden, B. R., Luo, S. & Plastino, A. Physics and information.Physics Today 60, 14 (2007)","work_id":"","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1957,"title":"Jaynes, E. T. Information theory and statistical mechanics.Physical Review 106, 620–630 (1957)","work_id":"","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"Gatenby, R. A. & Frieden, B. R. Information theory in living systems, meth- ods, applications, and challenges.Bulletin of Mathematical Biology69, 635– 657 (2007)","work_id":"","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":6,"snapshot_sha256":"70192fab5c84f84f4b138dec6089e263dd4ed09067dbf00c76b7838fe8b1b999","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":"2604.18081","created_at":"2026-05-21T01:05:19.293069+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.18081v1","created_at":"2026-05-21T01:05:19.293069+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.18081","created_at":"2026-05-21T01:05:19.293069+00:00"},{"alias_kind":"pith_short_12","alias_value":"7OGSCD5LFUCH","created_at":"2026-05-21T01:05:19.293069+00:00"},{"alias_kind":"pith_short_16","alias_value":"7OGSCD5LFUCH4SGQ","created_at":"2026-05-21T01:05:19.293069+00:00"},{"alias_kind":"pith_short_8","alias_value":"7OGSCD5L","created_at":"2026-05-21T01:05:19.293069+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/7OGSCD5LFUCH4SGQXMKFUQ45YU","json":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU.json","graph_json":"https://pith.science/api/pith-number/7OGSCD5LFUCH4SGQXMKFUQ45YU/graph.json","events_json":"https://pith.science/api/pith-number/7OGSCD5LFUCH4SGQXMKFUQ45YU/events.json","paper":"https://pith.science/paper/7OGSCD5L"},"agent_actions":{"view_html":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU","download_json":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU.json","view_paper":"https://pith.science/paper/7OGSCD5L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.18081&json=true","fetch_graph":"https://pith.science/api/pith-number/7OGSCD5LFUCH4SGQXMKFUQ45YU/graph.json","fetch_events":"https://pith.science/api/pith-number/7OGSCD5LFUCH4SGQXMKFUQ45YU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/action/storage_attestation","attest_author":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/action/author_attestation","sign_citation":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/action/citation_signature","submit_replication":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/action/replication_record"}},"created_at":"2026-05-21T01:05:19.293069+00:00","updated_at":"2026-05-21T01:05:19.293069+00:00"}