{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7OGSCD5LFUCH4SGQXMKFUQ45YU","short_pith_number":"pith:7OGSCD5L","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"},"canonical_sha256":"fb8d210fab2d047e48d0bb145a439dc522fa2c2dc1bc7699024c08710449cce4","source":{"kind":"arxiv","id":"2604.18081","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.18081","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"2604.18081v1","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.18081","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"7OGSCD5LFUCH","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_16","alias_value":"7OGSCD5LFUCH4SGQ","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_8","alias_value":"7OGSCD5L","created_at":"2026-05-21T01:05:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7OGSCD5LFUCH4SGQXMKFUQ45YU","target":"record","payload":{"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"},"canonical_sha256":"fb8d210fab2d047e48d0bb145a439dc522fa2c2dc1bc7699024c08710449cce4","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"},"source_kind":"arxiv","source_id":"2604.18081","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":"2026-05-21T01:05:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2JSJYgUTOcfzZYH2galTNDclB5Iw1RyQKTaHtyE6iXpKLxH4UKpItz6xAsJ620mPtuIoYFNy7lKK2eHfLKOUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:04:08.564784Z"},"content_sha256":"c5d7e7c0a2d680e8d15cf908234844de36f6b11403ea5cd4a96b9fed82ee1779","schema_version":"1.0","event_id":"sha256:c5d7e7c0a2d680e8d15cf908234844de36f6b11403ea5cd4a96b9fed82ee1779"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7OGSCD5LFUCH4SGQXMKFUQ45YU","target":"graph","payload":{"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"},"verdict_id":"560dea0b-1424-4ff4-a496-271853a53c68"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:05:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHFEaUd+geiKT9QVPX00cOhqAP3CbycYw4X2GN7V3giVOIV9n3yhgq6fWFzKEiR76K5SGbhflnmLjASCNvEKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:04:08.565803Z"},"content_sha256":"73917658147e514380522d78644e3ed57442c0157fe47dbbdcd80f0040383cdf","schema_version":"1.0","event_id":"sha256:73917658147e514380522d78644e3ed57442c0157fe47dbbdcd80f0040383cdf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/bundle.json","state_url":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/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":"2026-05-31T19:04:08Z","links":{"resolver":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU","bundle":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/bundle.json","state":"https://pith.science/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7OGSCD5LFUCH4SGQXMKFUQ45YU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7OGSCD5LFUCH4SGQXMKFUQ45YU","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":"060411ab0f7a0326de6f9aa053e3cd5a166e54c53bc78216e5437be63bb778ba","cross_cats_sorted":["physics.chem-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2026-04-20T10:53:35Z","title_canon_sha256":"8b6c9906fff280c75909f0eb859dee82739f429a6f5e4a63fcb56026b49b4d89"},"schema_version":"1.0","source":{"id":"2604.18081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.18081","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"2604.18081v1","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.18081","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"7OGSCD5LFUCH","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_16","alias_value":"7OGSCD5LFUCH4SGQ","created_at":"2026-05-21T01:05:19Z"},{"alias_kind":"pith_short_8","alias_value":"7OGSCD5L","created_at":"2026-05-21T01:05:19Z"}],"graph_snapshots":[{"event_id":"sha256:73917658147e514380522d78644e3ed57442c0157fe47dbbdcd80f0040383cdf","target":"graph","created_at":"2026-05-21T01:05:19Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Shannon and Rényi entropies from molecular electron densities fail to encode static correlation and violate extensivity, indicating density-based descriptors are insufficient."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Electron-density entropies fail to capture static correlation and often violate extensivity."}],"snapshot_sha256":"18313a06274e2cdfa407b8fa5cb6f6fe60649ea2df7fb8db56ba3a28836e3b6f"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-20T04:27:42.378119Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2604.18081/integrity.json","findings":[],"snapshot_sha256":"bb93692a979d3249b491993312c8094c1278676475f38613009010e9a9359995","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"\\'Angel Mart\\'in Pend\\'as, Diogo J. L. Rodrigues, Evelio Francisco","cross_cats":["physics.chem-ph"],"headline":"Electron-density entropies fail to capture static correlation and often violate extensivity.","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2026-04-20T10:53:35Z","title":"Shannon and R\\'enyi entropies of molecular densities: insights into extensivity and the incomplete description of electron correlation"},"references":{"count":109,"internal_anchors":0,"resolved_work":6,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Shannon, C. E. A mathematical theory of communication.Bell System Tech- nical Journal27, 379–423 (1948)","work_id":"","year":1948},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Brillouin, L.Science and information theory(Courier Corporation, 2013)","work_id":"","year":2013},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Frieden, B. R., Luo, S. & Plastino, A. Physics and information.Physics Today 60, 14 (2007)","work_id":"","year":2007},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Jaynes, E. T. Information theory and statistical mechanics.Physical Review 106, 620–630 (1957)","work_id":"","year":1957},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"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":"","year":2007}],"snapshot_sha256":"70192fab5c84f84f4b138dec6089e263dd4ed09067dbf00c76b7838fe8b1b999"},"source":{"id":"2604.18081","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-10T05:19:14.166745Z","id":"560dea0b-1424-4ff4-a496-271853a53c68","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"Electron-density entropies fail to capture static correlation and often violate extensivity.","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.","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."}},"verdict_id":"560dea0b-1424-4ff4-a496-271853a53c68"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c5d7e7c0a2d680e8d15cf908234844de36f6b11403ea5cd4a96b9fed82ee1779","target":"record","created_at":"2026-05-21T01:05:19Z","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":"060411ab0f7a0326de6f9aa053e3cd5a166e54c53bc78216e5437be63bb778ba","cross_cats_sorted":["physics.chem-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2026-04-20T10:53:35Z","title_canon_sha256":"8b6c9906fff280c75909f0eb859dee82739f429a6f5e4a63fcb56026b49b4d89"},"schema_version":"1.0","source":{"id":"2604.18081","kind":"arxiv","version":1}},"canonical_sha256":"fb8d210fab2d047e48d0bb145a439dc522fa2c2dc1bc7699024c08710449cce4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb8d210fab2d047e48d0bb145a439dc522fa2c2dc1bc7699024c08710449cce4","first_computed_at":"2026-05-21T01:05:19.293004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:19.293004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uBe/M19v7+YOVptI0s92ZQwAM/VnpCU6LAApMjgQ4mN4aV0NzxaBqcXIUDLdPTstohegmvwjcWJ4dCvVXLjQBQ==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:19.293476Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.18081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5d7e7c0a2d680e8d15cf908234844de36f6b11403ea5cd4a96b9fed82ee1779","sha256:73917658147e514380522d78644e3ed57442c0157fe47dbbdcd80f0040383cdf"],"state_sha256":"3576e7cbd010ca508e1b2ca1e39a0b2932b5a42b17846da4b8a2a693e85e7941"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GlL9ZxjHiUUkuzCX4s0rs/J/BjhXft9LmUCrC2+S4M2lWTqokl8hMeGAOj1TBnoyqQyZ26mhVDZOli+UsVtrCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:04:08.570056Z","bundle_sha256":"5029fd5971e8261fc1a5dbf05e2110485035ae0f2851310fb7dd3827bcf0c370"}}