{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:ILZKSSMTD3OO65XU6J25MO7RVR","short_pith_number":"pith:ILZKSSMT","schema_version":"1.0","canonical_sha256":"42f2a949931edcef76f4f275d63bf1ac6c634b6a6847f5a0f01eccd365f3f184","source":{"kind":"arxiv","id":"2307.02481","version":1},"attestation_state":"computed","paper":{"title":"Non-equilibrium steady state of the symmetric exclusion process with reservoirs","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":"Adri\\'an Gonz\\'alez Casanova, Simone Floreani","submitted_at":"2023-07-05T17:55:39Z","abstract_excerpt":"Consider the open symmetric exclusion process on a connected graph with vertexes in $[N-1]:=\\{1,\\ldots, N-1\\}$ where points $1$ and $N-1$ are connected, respectively, to a left reservoir and a right reservoir with densities $\\rho_L,\\rho_R\\in(0,1)$. We prove that the non-equilibrium steady state of such system is $$\\mu_{\\text{stat}} = \\sum_{I\\subset \\mathcal P([N-1]) }F(I)\\bigg(\\otimes_{x\\in I}\\rm{Bernoulli}(\\rho_R)\\otimes_{y\\in [N-1]\\setminus I}\\rm{Bernoulli}(\\rho_L) \\bigg).$$ In the formula above $ \\mathcal P([N-1])$ denotes the power set of $[N-1]$ while the numbers $F(I)> 0$ are such that $"},"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":"2307.02481","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-07-05T17:55:39Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"2979f67f34e9084cfb56c248c4b44d4a2f5287b6047832c72519fea592b354c2","abstract_canon_sha256":"52613834c877fcb207f7c0b97ad4e7361e13ae61a74f55520809919929d8a714"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:28:10.273990Z","signature_b64":"IoDrzyj4Zq/lmTZwYm/2YbsxeFEEW6Jm7VCYy9aIMuD+ehaOa6V16+wCW5d3BG5a+kov60iEXaHsJMSuudhMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42f2a949931edcef76f4f275d63bf1ac6c634b6a6847f5a0f01eccd365f3f184","last_reissued_at":"2026-07-05T06:28:10.273586Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:28:10.273586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-equilibrium steady state of the symmetric exclusion process with reservoirs","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":"Adri\\'an Gonz\\'alez Casanova, Simone Floreani","submitted_at":"2023-07-05T17:55:39Z","abstract_excerpt":"Consider the open symmetric exclusion process on a connected graph with vertexes in $[N-1]:=\\{1,\\ldots, N-1\\}$ where points $1$ and $N-1$ are connected, respectively, to a left reservoir and a right reservoir with densities $\\rho_L,\\rho_R\\in(0,1)$. We prove that the non-equilibrium steady state of such system is $$\\mu_{\\text{stat}} = \\sum_{I\\subset \\mathcal P([N-1]) }F(I)\\bigg(\\otimes_{x\\in I}\\rm{Bernoulli}(\\rho_R)\\otimes_{y\\in [N-1]\\setminus I}\\rm{Bernoulli}(\\rho_L) \\bigg).$$ In the formula above $ \\mathcal P([N-1])$ denotes the power set of $[N-1]$ while the numbers $F(I)> 0$ are such that $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.02481","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/2307.02481/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":"2307.02481","created_at":"2026-07-05T06:28:10.273642+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.02481v1","created_at":"2026-07-05T06:28:10.273642+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.02481","created_at":"2026-07-05T06:28:10.273642+00:00"},{"alias_kind":"pith_short_12","alias_value":"ILZKSSMTD3OO","created_at":"2026-07-05T06:28:10.273642+00:00"},{"alias_kind":"pith_short_16","alias_value":"ILZKSSMTD3OO65XU","created_at":"2026-07-05T06:28:10.273642+00:00"},{"alias_kind":"pith_short_8","alias_value":"ILZKSSMT","created_at":"2026-07-05T06:28:10.273642+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.07615","citing_title":"Hydrodynamics and boundary-induced phase transitions in the $n$-species particle-exchange process","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ILZKSSMTD3OO65XU6J25MO7RVR","json":"https://pith.science/pith/ILZKSSMTD3OO65XU6J25MO7RVR.json","graph_json":"https://pith.science/api/pith-number/ILZKSSMTD3OO65XU6J25MO7RVR/graph.json","events_json":"https://pith.science/api/pith-number/ILZKSSMTD3OO65XU6J25MO7RVR/events.json","paper":"https://pith.science/paper/ILZKSSMT"},"agent_actions":{"view_html":"https://pith.science/pith/ILZKSSMTD3OO65XU6J25MO7RVR","download_json":"https://pith.science/pith/ILZKSSMTD3OO65XU6J25MO7RVR.json","view_paper":"https://pith.science/paper/ILZKSSMT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.02481&json=true","fetch_graph":"https://pith.science/api/pith-number/ILZKSSMTD3OO65XU6J25MO7RVR/graph.json","fetch_events":"https://pith.science/api/pith-number/ILZKSSMTD3OO65XU6J25MO7RVR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ILZKSSMTD3OO65XU6J25MO7RVR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ILZKSSMTD3OO65XU6J25MO7RVR/action/storage_attestation","attest_author":"https://pith.science/pith/ILZKSSMTD3OO65XU6J25MO7RVR/action/author_attestation","sign_citation":"https://pith.science/pith/ILZKSSMTD3OO65XU6J25MO7RVR/action/citation_signature","submit_replication":"https://pith.science/pith/ILZKSSMTD3OO65XU6J25MO7RVR/action/replication_record"}},"created_at":"2026-07-05T06:28:10.273642+00:00","updated_at":"2026-07-05T06:28:10.273642+00:00"}