{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:B6L3SO4QNQNA6WIW4MBTL5DEBI","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":"5f0ed50cd3f7888f1303bab87aeb6d4469d3c0414ae6583585bacd923be0f578","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-08-10T08:47:41Z","title_canon_sha256":"8bd5912500faacdcf737a21796813b54bf8e814bc6e6384d64df73913cdb38c6"},"schema_version":"1.0","source":{"id":"2608.09297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.09297","created_at":"2026-08-11T02:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"2608.09297v1","created_at":"2026-08-11T02:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.09297","created_at":"2026-08-11T02:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"B6L3SO4QNQNA","created_at":"2026-08-11T02:22:17Z"},{"alias_kind":"pith_short_16","alias_value":"B6L3SO4QNQNA6WIW","created_at":"2026-08-11T02:22:17Z"},{"alias_kind":"pith_short_8","alias_value":"B6L3SO4Q","created_at":"2026-08-11T02:22:17Z"}],"graph_snapshots":[{"event_id":"sha256:07f581c565916bbdac61ab70610ae0cdd338dddbc4b2e65104b265a636030412","target":"graph","created_at":"2026-08-11T02:22:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.09297/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a consistent pseudo-analytic framework based on $g$-calculus for constructing deformed statistical distributions. By mapping standard algebraic operations through a monotone generator function, we systematically derive the associated pseudo-logarithmic and pseudo-exponential structures. Applying this formalism, we introduce a new family of pseudo-distributions that generalizes nonextensive statistical mechanics at both the probability density and cumulative distribution levels, recovering classical and standard nonextensive statistics as limiting cases. We investigate the thermodyna","authors_text":"Hamzeh Agahi, Hosein Mohammadzadeh, Hossein Mehri-Dehnavi, Negin Bayrami, Zahra Ebadi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-08-10T08:47:41Z","title":"Pseudo-Distributions: Thermodynamic Geometry and an Empirical Application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09297","kind":"arxiv","version":1},"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":"sha256:22890f1d9fe517aecc50601cb2cb979e93c2358b619f2edacb3b7ce7e366b033","target":"record","created_at":"2026-08-11T02:22:17Z","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":"5f0ed50cd3f7888f1303bab87aeb6d4469d3c0414ae6583585bacd923be0f578","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-08-10T08:47:41Z","title_canon_sha256":"8bd5912500faacdcf737a21796813b54bf8e814bc6e6384d64df73913cdb38c6"},"schema_version":"1.0","source":{"id":"2608.09297","kind":"arxiv","version":1}},"canonical_sha256":"0f97b93b906c1a0f5916e30335f4640a0bccd143176b9ab0020690e716f7cc86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f97b93b906c1a0f5916e30335f4640a0bccd143176b9ab0020690e716f7cc86","first_computed_at":"2026-08-11T02:22:17.309810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T02:22:17.309810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Aac+kbdC1pPAjtyjWnF2C4ICNOISNVstkgi2VZMH+WTxZaWVFzuW4xcgQumboaKgXF7F2/3T/ZpSZM+10MFhAA==","signature_status":"signed_v1","signed_at":"2026-08-11T02:22:17.311478Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.09297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22890f1d9fe517aecc50601cb2cb979e93c2358b619f2edacb3b7ce7e366b033","sha256:07f581c565916bbdac61ab70610ae0cdd338dddbc4b2e65104b265a636030412"],"state_sha256":"eb800a24959779fecd8c29ae586e0c70cb122062c0f2aff3966aa394d6626a73"}