{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MWYNF7XEFXJFS7GOMI5ADAXKOF","short_pith_number":"pith:MWYNF7XE","schema_version":"1.0","canonical_sha256":"65b0d2fee42dd2597cce623a0182ea717387e6dbcbfb7360ace67af9df70038f","source":{"kind":"arxiv","id":"1811.05954","version":3},"attestation_state":"computed","paper":{"title":"The exchange-driven growth model: basic properties and longtime behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Andr\\'e Schlichting","submitted_at":"2018-11-14T18:41:28Z","abstract_excerpt":"The exchange-driven growth model describes a process in which pairs of clusters interact through the exchange of single monomers. The rate of exchange is given by an interaction kernel $K$ which depends on the size of the two interacting clusters. Well-posedness of the model is established for kernels growing at most linearly and arbitrary initial data.\n  The longtime behavior is established under a detailed balance condition on the kernel. The total mass density $\\varrho$, determined by the initial data, acts as an order parameter, in which the system shows a phase transition. There is a crit"},"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":"1811.05954","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-14T18:41:28Z","cross_cats_sorted":["math.DS","math.MP","math.PR"],"title_canon_sha256":"e9bd1bde43b606abf1009eaa3033f438f690fa01a41d3863139bcfb88e86fd71","abstract_canon_sha256":"09aec049a39dd74e543247733bdf1370d58bd4b7f6897cad29610395cef78eec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:07:36.383900Z","signature_b64":"s/8Odr5D/P2H3aZEmr6U/j8nPiRPIb2O6rstiMBg6iJNuTY2RMDlwgc2NkcU2GL+beP56b8B3TTEwAJdULg9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65b0d2fee42dd2597cce623a0182ea717387e6dbcbfb7360ace67af9df70038f","last_reissued_at":"2026-07-05T01:07:36.383425Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:07:36.383425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The exchange-driven growth model: basic properties and longtime behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Andr\\'e Schlichting","submitted_at":"2018-11-14T18:41:28Z","abstract_excerpt":"The exchange-driven growth model describes a process in which pairs of clusters interact through the exchange of single monomers. The rate of exchange is given by an interaction kernel $K$ which depends on the size of the two interacting clusters. Well-posedness of the model is established for kernels growing at most linearly and arbitrary initial data.\n  The longtime behavior is established under a detailed balance condition on the kernel. The total mass density $\\varrho$, determined by the initial data, acts as an order parameter, in which the system shows a phase transition. There is a crit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05954","kind":"arxiv","version":3},"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/1811.05954/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":"1811.05954","created_at":"2026-07-05T01:07:36.383484+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.05954v3","created_at":"2026-07-05T01:07:36.383484+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05954","created_at":"2026-07-05T01:07:36.383484+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWYNF7XEFXJF","created_at":"2026-07-05T01:07:36.383484+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWYNF7XEFXJFS7GO","created_at":"2026-07-05T01:07:36.383484+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWYNF7XE","created_at":"2026-07-05T01:07:36.383484+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.03397","citing_title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","ref_index":34,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MWYNF7XEFXJFS7GOMI5ADAXKOF","json":"https://pith.science/pith/MWYNF7XEFXJFS7GOMI5ADAXKOF.json","graph_json":"https://pith.science/api/pith-number/MWYNF7XEFXJFS7GOMI5ADAXKOF/graph.json","events_json":"https://pith.science/api/pith-number/MWYNF7XEFXJFS7GOMI5ADAXKOF/events.json","paper":"https://pith.science/paper/MWYNF7XE"},"agent_actions":{"view_html":"https://pith.science/pith/MWYNF7XEFXJFS7GOMI5ADAXKOF","download_json":"https://pith.science/pith/MWYNF7XEFXJFS7GOMI5ADAXKOF.json","view_paper":"https://pith.science/paper/MWYNF7XE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.05954&json=true","fetch_graph":"https://pith.science/api/pith-number/MWYNF7XEFXJFS7GOMI5ADAXKOF/graph.json","fetch_events":"https://pith.science/api/pith-number/MWYNF7XEFXJFS7GOMI5ADAXKOF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWYNF7XEFXJFS7GOMI5ADAXKOF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWYNF7XEFXJFS7GOMI5ADAXKOF/action/storage_attestation","attest_author":"https://pith.science/pith/MWYNF7XEFXJFS7GOMI5ADAXKOF/action/author_attestation","sign_citation":"https://pith.science/pith/MWYNF7XEFXJFS7GOMI5ADAXKOF/action/citation_signature","submit_replication":"https://pith.science/pith/MWYNF7XEFXJFS7GOMI5ADAXKOF/action/replication_record"}},"created_at":"2026-07-05T01:07:36.383484+00:00","updated_at":"2026-07-05T01:07:36.383484+00:00"}