{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BV7UGWMJXKKAXMSEZ4TCDZ665B","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":"77c23e3063ce3df70485fffe321345e22f88dd48acbff4f53f3370fe92b39a37","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-18T10:20:27Z","title_canon_sha256":"2eb5cf8ac62e1071fee008ca8688ea9ca2ba6a4bff459c8264c162cfb9f53b95"},"schema_version":"1.0","source":{"id":"2507.13799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13799","created_at":"2026-07-05T11:39:23Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13799v1","created_at":"2026-07-05T11:39:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13799","created_at":"2026-07-05T11:39:23Z"},{"alias_kind":"pith_short_12","alias_value":"BV7UGWMJXKKA","created_at":"2026-07-05T11:39:23Z"},{"alias_kind":"pith_short_16","alias_value":"BV7UGWMJXKKAXMSE","created_at":"2026-07-05T11:39:23Z"},{"alias_kind":"pith_short_8","alias_value":"BV7UGWMJ","created_at":"2026-07-05T11:39:23Z"}],"graph_snapshots":[{"event_id":"sha256:6f5efab076a9a5cd9ca40997436abf60ca58a1e0e6621a49233da179a04a4033","target":"graph","created_at":"2026-07-05T11:39:23Z","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/2507.13799/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high particle density, forming clusters of diverging size. Our main result provides convergence in law of inclusion processes to a novel two-component infinite-dimensional stochastic diffusion, describing the co-evolution of the solid condensed and microscopic fluid phase. In particular, we establish non-trivial mass exchange between the two phases.\n  The resultin","authors_text":"Simon Gabriel","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-18T10:20:27Z","title":"Modulated Poisson-Dirichlet diffusions arising from inclusion processes with a slow phase"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13799","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:a80aea62ec2aa7ef3617215d40d07279263f4d0a0b9f390a5c9b5118c8c04d7f","target":"record","created_at":"2026-07-05T11:39:23Z","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":"77c23e3063ce3df70485fffe321345e22f88dd48acbff4f53f3370fe92b39a37","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-18T10:20:27Z","title_canon_sha256":"2eb5cf8ac62e1071fee008ca8688ea9ca2ba6a4bff459c8264c162cfb9f53b95"},"schema_version":"1.0","source":{"id":"2507.13799","kind":"arxiv","version":1}},"canonical_sha256":"0d7f435989ba940bb244cf2621e7dee85fabd0bc8c14c932531f5ef409b3999e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d7f435989ba940bb244cf2621e7dee85fabd0bc8c14c932531f5ef409b3999e","first_computed_at":"2026-07-05T11:39:23.344838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:23.344838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6+TGGvWv6qrx3uDug2EU/RdylUd1q1RA8JZndayq7cIpBteznArNL8fWBeR4+1avYGne4N7mEPy4IMbvcsI4DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:23.345308Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a80aea62ec2aa7ef3617215d40d07279263f4d0a0b9f390a5c9b5118c8c04d7f","sha256:6f5efab076a9a5cd9ca40997436abf60ca58a1e0e6621a49233da179a04a4033"],"state_sha256":"ce57769c1998a8b530ba378c53b4a589abe265f6e4d57fad382a23d9f866beab"}