{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:OQJIBWPRICLZLKSQHPQAQV7IHP","short_pith_number":"pith:OQJIBWPR","schema_version":"1.0","canonical_sha256":"741280d9f1409795aa503be00857e83be192571877d26f96fcb040eb2cdf8501","source":{"kind":"arxiv","id":"2406.01160","version":1},"attestation_state":"computed","paper":{"title":"Intertwining and propagation of mixtures for generalized KMP models and harmonic models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Berend van Tol, Cristian Giardin\\`a, Frank Redig","submitted_at":"2024-06-03T09:54:27Z","abstract_excerpt":"We study a class of stochastic models of mass transport on discrete vertex set $V$. For these models, a one-parameter family of homogeneous product measures $\\otimes_{i\\in V} \\nu_\\theta$ is reversible. We prove that the set of mixtures of inhomogeneous product measures with equilibrium marginals, i.e., the set of measures of the form \\[ \\int\\Big(\\bigotimes_{i\\in V} \\nu_{\\theta_i}\\Big) \\,\\Xi(\\prod_{i\\in V}d\\theta_i) \\] is left invariant by the dynamics in the course of time, and the ``mixing measure'' $\\Xi$ evolves according to a Markov process which we then call ``the hidden parameter model''."},"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":"2406.01160","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-06-03T09:54:27Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"3b1c5fb0640e54f1a0d16665e4943dbcf0176fa9129b7c47011771d61321bed3","abstract_canon_sha256":"b6ab31f76abd0b6592f3f23a8c10d40a60772cbe4b8a5269c30c9430ce47d8e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:26:36.265741Z","signature_b64":"2ZOLIoUuAPxA43hZ2tdrFWF+zFBrXJJcdIgsGRRthUWMXBjMZ95AA+ZgM/tkQ12gwYJhoWSr+Tp2T0mUcOA7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"741280d9f1409795aa503be00857e83be192571877d26f96fcb040eb2cdf8501","last_reissued_at":"2026-07-05T08:26:36.265245Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:26:36.265245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intertwining and propagation of mixtures for generalized KMP models and harmonic models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Berend van Tol, Cristian Giardin\\`a, Frank Redig","submitted_at":"2024-06-03T09:54:27Z","abstract_excerpt":"We study a class of stochastic models of mass transport on discrete vertex set $V$. For these models, a one-parameter family of homogeneous product measures $\\otimes_{i\\in V} \\nu_\\theta$ is reversible. We prove that the set of mixtures of inhomogeneous product measures with equilibrium marginals, i.e., the set of measures of the form \\[ \\int\\Big(\\bigotimes_{i\\in V} \\nu_{\\theta_i}\\Big) \\,\\Xi(\\prod_{i\\in V}d\\theta_i) \\] is left invariant by the dynamics in the course of time, and the ``mixing measure'' $\\Xi$ evolves according to a Markov process which we then call ``the hidden parameter model''."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01160","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.01160/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2406.01160","created_at":"2026-07-05T08:26:36.265310+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.01160v1","created_at":"2026-07-05T08:26:36.265310+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.01160","created_at":"2026-07-05T08:26:36.265310+00:00"},{"alias_kind":"pith_short_12","alias_value":"OQJIBWPRICLZ","created_at":"2026-07-05T08:26:36.265310+00:00"},{"alias_kind":"pith_short_16","alias_value":"OQJIBWPRICLZLKSQ","created_at":"2026-07-05T08:26:36.265310+00:00"},{"alias_kind":"pith_short_8","alias_value":"OQJIBWPR","created_at":"2026-07-05T08:26:36.265310+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/OQJIBWPRICLZLKSQHPQAQV7IHP","json":"https://pith.science/pith/OQJIBWPRICLZLKSQHPQAQV7IHP.json","graph_json":"https://pith.science/api/pith-number/OQJIBWPRICLZLKSQHPQAQV7IHP/graph.json","events_json":"https://pith.science/api/pith-number/OQJIBWPRICLZLKSQHPQAQV7IHP/events.json","paper":"https://pith.science/paper/OQJIBWPR"},"agent_actions":{"view_html":"https://pith.science/pith/OQJIBWPRICLZLKSQHPQAQV7IHP","download_json":"https://pith.science/pith/OQJIBWPRICLZLKSQHPQAQV7IHP.json","view_paper":"https://pith.science/paper/OQJIBWPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.01160&json=true","fetch_graph":"https://pith.science/api/pith-number/OQJIBWPRICLZLKSQHPQAQV7IHP/graph.json","fetch_events":"https://pith.science/api/pith-number/OQJIBWPRICLZLKSQHPQAQV7IHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OQJIBWPRICLZLKSQHPQAQV7IHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OQJIBWPRICLZLKSQHPQAQV7IHP/action/storage_attestation","attest_author":"https://pith.science/pith/OQJIBWPRICLZLKSQHPQAQV7IHP/action/author_attestation","sign_citation":"https://pith.science/pith/OQJIBWPRICLZLKSQHPQAQV7IHP/action/citation_signature","submit_replication":"https://pith.science/pith/OQJIBWPRICLZLKSQHPQAQV7IHP/action/replication_record"}},"created_at":"2026-07-05T08:26:36.265310+00:00","updated_at":"2026-07-05T08:26:36.265310+00:00"}