{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:IWXSUOCDA7BJLV3EAIMONOHDVY","short_pith_number":"pith:IWXSUOCD","schema_version":"1.0","canonical_sha256":"45af2a384307c295d7640218e6b8e3ae0bfb0c749e63821db48f61b01ce8cbd4","source":{"kind":"arxiv","id":"0709.3820","version":1},"attestation_state":"computed","paper":{"title":"A pathway to multivariate Gaussian density","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A.M. Mathai, H.J. Haubold, S. Thomas","submitted_at":"2007-09-24T18:43:54Z","abstract_excerpt":"A general principle called \"conservation of the ellipsoid of concentration\" is introduced and a generalized entropic form of order 'alpha' is optimized under this principle. It is shown that this can produce a density which can act as a pathway to multivariate Gaussian density. The resulting entropic pathway contains as special cases the Boltzmann-Gibbs (Shannon) and Tsallis (Havrda-Charvat) entropic forms."},"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":"0709.3820","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-09-24T18:43:54Z","cross_cats_sorted":[],"title_canon_sha256":"9cab73955f3324d4a4142cc41c01a140706283bbeeb43787388dc5c2310d2af1","abstract_canon_sha256":"0ee89daafb952d8ae2cbcdf0bb208d7c8543b0fac711b634be2daec7951bcf41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:24.829610Z","signature_b64":"vJ6Ptjqr+AF6NtLJlKnBr93g+6hqOa480qUCkOtYZFt6wOCzb34mRLXygRZZaLttKXMJtWV4xs6HDicoJSuVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45af2a384307c295d7640218e6b8e3ae0bfb0c749e63821db48f61b01ce8cbd4","last_reissued_at":"2026-05-18T02:43:24.829040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:24.829040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A pathway to multivariate Gaussian density","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A.M. Mathai, H.J. Haubold, S. Thomas","submitted_at":"2007-09-24T18:43:54Z","abstract_excerpt":"A general principle called \"conservation of the ellipsoid of concentration\" is introduced and a generalized entropic form of order 'alpha' is optimized under this principle. It is shown that this can produce a density which can act as a pathway to multivariate Gaussian density. The resulting entropic pathway contains as special cases the Boltzmann-Gibbs (Shannon) and Tsallis (Havrda-Charvat) entropic forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.3820","kind":"arxiv","version":1},"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":"0709.3820","created_at":"2026-05-18T02:43:24.829123+00:00"},{"alias_kind":"arxiv_version","alias_value":"0709.3820v1","created_at":"2026-05-18T02:43:24.829123+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.3820","created_at":"2026-05-18T02:43:24.829123+00:00"},{"alias_kind":"pith_short_12","alias_value":"IWXSUOCDA7BJ","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"IWXSUOCDA7BJLV3E","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"IWXSUOCD","created_at":"2026-05-18T12:25:55.427421+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/IWXSUOCDA7BJLV3EAIMONOHDVY","json":"https://pith.science/pith/IWXSUOCDA7BJLV3EAIMONOHDVY.json","graph_json":"https://pith.science/api/pith-number/IWXSUOCDA7BJLV3EAIMONOHDVY/graph.json","events_json":"https://pith.science/api/pith-number/IWXSUOCDA7BJLV3EAIMONOHDVY/events.json","paper":"https://pith.science/paper/IWXSUOCD"},"agent_actions":{"view_html":"https://pith.science/pith/IWXSUOCDA7BJLV3EAIMONOHDVY","download_json":"https://pith.science/pith/IWXSUOCDA7BJLV3EAIMONOHDVY.json","view_paper":"https://pith.science/paper/IWXSUOCD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0709.3820&json=true","fetch_graph":"https://pith.science/api/pith-number/IWXSUOCDA7BJLV3EAIMONOHDVY/graph.json","fetch_events":"https://pith.science/api/pith-number/IWXSUOCDA7BJLV3EAIMONOHDVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IWXSUOCDA7BJLV3EAIMONOHDVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IWXSUOCDA7BJLV3EAIMONOHDVY/action/storage_attestation","attest_author":"https://pith.science/pith/IWXSUOCDA7BJLV3EAIMONOHDVY/action/author_attestation","sign_citation":"https://pith.science/pith/IWXSUOCDA7BJLV3EAIMONOHDVY/action/citation_signature","submit_replication":"https://pith.science/pith/IWXSUOCDA7BJLV3EAIMONOHDVY/action/replication_record"}},"created_at":"2026-05-18T02:43:24.829123+00:00","updated_at":"2026-05-18T02:43:24.829123+00:00"}