{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HUD6WGZEJYTJWQO6QZAIRPICE7","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":"b27eb18388e6690b3d6a6580b02da2d5bbbc1fb0292d6650bd2052d91cc115da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-10-17T14:01:37Z","title_canon_sha256":"d4dab4a1cb63c3a95ead4a46524c0deefc013df4455be57be932f4c719ff400f"},"schema_version":"1.0","source":{"id":"1410.4727","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4727","created_at":"2026-05-18T02:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4727v3","created_at":"2026-05-18T02:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4727","created_at":"2026-05-18T02:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"HUD6WGZEJYTJ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HUD6WGZEJYTJWQO6","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HUD6WGZE","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:8d5000a322efb610d829e1fff8c2b4cf42424a12d007871f343647ec0eed2e19","target":"graph","created_at":"2026-05-18T02:27:44Z","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"},"paper":{"abstract_excerpt":"The coupled-product and coupled-exponential of the generalized calculus of nonextensive statistical mechanics are defined for multivariate functions. The nonlinear statistical coupling is indexed such that k_d = k/(1+dk), where d is the dimensions of the argument of the multivariate coupled-exponential. The coupled-Gaussian distribution is defined such that the argument of the coupled-exponential depends on the coupled-moments but not the coupling parameter. The multivariate version of the coupled-product is defined such that the output dimensions are the sum of the input dimensions. This enab","authors_text":"Kenric P. Nelson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-10-17T14:01:37Z","title":"A definition of the coupled-product for multivariate coupled-exponentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4727","kind":"arxiv","version":3},"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":"sha256:5219fe725e0cf8d8140c35b58ea878f787a66ce35d951f81755f4a8d0279042e","target":"record","created_at":"2026-05-18T02:27:44Z","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":"b27eb18388e6690b3d6a6580b02da2d5bbbc1fb0292d6650bd2052d91cc115da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-10-17T14:01:37Z","title_canon_sha256":"d4dab4a1cb63c3a95ead4a46524c0deefc013df4455be57be932f4c719ff400f"},"schema_version":"1.0","source":{"id":"1410.4727","kind":"arxiv","version":3}},"canonical_sha256":"3d07eb1b244e269b41de864088bd0227e834e8c0f85e5a0223edc1d80d81bb3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d07eb1b244e269b41de864088bd0227e834e8c0f85e5a0223edc1d80d81bb3e","first_computed_at":"2026-05-18T02:27:44.131448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:44.131448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ayVvleFMdkU8NT7CjuPGjjQf5S7jc3XMgW/JUumF5JLpTIi2JFBK4lxaH5VJnHvmgkRTz4d2k3HbHxvffBLlAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:44.131894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.4727","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5219fe725e0cf8d8140c35b58ea878f787a66ce35d951f81755f4a8d0279042e","sha256:8d5000a322efb610d829e1fff8c2b4cf42424a12d007871f343647ec0eed2e19"],"state_sha256":"458273f5a3da2f2dac0c398c1ffa87dfdac461a91cfa36df0cfe9f5316d90bf8"}