{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EZNV6P3W77KRQMHQI7J7AHDB5P","short_pith_number":"pith:EZNV6P3W","canonical_record":{"source":{"id":"2505.11092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-16T10:24:39Z","cross_cats_sorted":[],"title_canon_sha256":"32eded1188067e881309dc684132b859534e21c6406aa885bc4d9fcc8f9ebbeb","abstract_canon_sha256":"f34f78c095245eba917078dc90470d3171c81dcc86408421ffb44937b1b52197"},"schema_version":"1.0"},"canonical_sha256":"265b5f3f76ffd51830f047d3f01c61ebe6ca442975dddb7178c74c84a2bd12e4","source":{"kind":"arxiv","id":"2505.11092","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.11092","created_at":"2026-07-05T11:04:10Z"},{"alias_kind":"arxiv_version","alias_value":"2505.11092v1","created_at":"2026-07-05T11:04:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.11092","created_at":"2026-07-05T11:04:10Z"},{"alias_kind":"pith_short_12","alias_value":"EZNV6P3W77KR","created_at":"2026-07-05T11:04:10Z"},{"alias_kind":"pith_short_16","alias_value":"EZNV6P3W77KRQMHQ","created_at":"2026-07-05T11:04:10Z"},{"alias_kind":"pith_short_8","alias_value":"EZNV6P3W","created_at":"2026-07-05T11:04:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EZNV6P3W77KRQMHQI7J7AHDB5P","target":"record","payload":{"canonical_record":{"source":{"id":"2505.11092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-16T10:24:39Z","cross_cats_sorted":[],"title_canon_sha256":"32eded1188067e881309dc684132b859534e21c6406aa885bc4d9fcc8f9ebbeb","abstract_canon_sha256":"f34f78c095245eba917078dc90470d3171c81dcc86408421ffb44937b1b52197"},"schema_version":"1.0"},"canonical_sha256":"265b5f3f76ffd51830f047d3f01c61ebe6ca442975dddb7178c74c84a2bd12e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:04:10.596429Z","signature_b64":"7UV2aksbWub1IwjIISenl/e1hRZCHrCWl+3CsKDaSFbCbW6hL9K1LJpQbp5aL+Pcia6dcSQJLABkqEvZAerlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"265b5f3f76ffd51830f047d3f01c61ebe6ca442975dddb7178c74c84a2bd12e4","last_reissued_at":"2026-07-05T11:04:10.595847Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:04:10.595847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.11092","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:04:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lLTI7+MHFQN3jtoPg9civdczlDFZWFjoa9km7M1jzS5LbJpMTTg2srfnGnfRxRpbz7xybbMdSPun+ss3mJ6CCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T11:46:39.644339Z"},"content_sha256":"7a97c2c40d95219481e43d96c43dbee8014263fde87eecb677e8ccd6d2772b50","schema_version":"1.0","event_id":"sha256:7a97c2c40d95219481e43d96c43dbee8014263fde87eecb677e8ccd6d2772b50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EZNV6P3W77KRQMHQI7J7AHDB5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hydrodynamic limit for some gradient and attractive spin models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chiara Franceschini, Kohei Hayashi, Makiko Sasada, Patr\\'icia Gon\\c{c}alves","submitted_at":"2025-05-16T10:24:39Z","abstract_excerpt":"We study the hydrodynamic limit for three gradient spin models: generalized Kipnis-Marchioro-Presutti (KMP), its discrete version and a family of harmonic models, under symmetric and nearest-neighbor interactions. These three models share some universal properties: occupation variables are unbounded, all these processes are of gradient type, their invariant measures are product with spatially homogeneous weights, and, notably, they are all attractive, meaning that the process preserves the partial order of measures along the dynamics. In view of hydrodynamics of large-scale interacting systems"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.11092","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/2505.11092/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:04:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tXoDs4b5aNtS0yyVajPudKcHZzlbdrjx7+uAzoG1LiNai0bxS0jNqHmi/clnDT5qtfB29t5RQrU2yrh95S9RDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T11:46:39.644997Z"},"content_sha256":"fdb9629676835294038855ccc0d1a0128d47d309455dc6b659641e23383ef584","schema_version":"1.0","event_id":"sha256:fdb9629676835294038855ccc0d1a0128d47d309455dc6b659641e23383ef584"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EZNV6P3W77KRQMHQI7J7AHDB5P/bundle.json","state_url":"https://pith.science/pith/EZNV6P3W77KRQMHQI7J7AHDB5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EZNV6P3W77KRQMHQI7J7AHDB5P/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-20T11:46:39Z","links":{"resolver":"https://pith.science/pith/EZNV6P3W77KRQMHQI7J7AHDB5P","bundle":"https://pith.science/pith/EZNV6P3W77KRQMHQI7J7AHDB5P/bundle.json","state":"https://pith.science/pith/EZNV6P3W77KRQMHQI7J7AHDB5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EZNV6P3W77KRQMHQI7J7AHDB5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EZNV6P3W77KRQMHQI7J7AHDB5P","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":"f34f78c095245eba917078dc90470d3171c81dcc86408421ffb44937b1b52197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-16T10:24:39Z","title_canon_sha256":"32eded1188067e881309dc684132b859534e21c6406aa885bc4d9fcc8f9ebbeb"},"schema_version":"1.0","source":{"id":"2505.11092","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.11092","created_at":"2026-07-05T11:04:10Z"},{"alias_kind":"arxiv_version","alias_value":"2505.11092v1","created_at":"2026-07-05T11:04:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.11092","created_at":"2026-07-05T11:04:10Z"},{"alias_kind":"pith_short_12","alias_value":"EZNV6P3W77KR","created_at":"2026-07-05T11:04:10Z"},{"alias_kind":"pith_short_16","alias_value":"EZNV6P3W77KRQMHQ","created_at":"2026-07-05T11:04:10Z"},{"alias_kind":"pith_short_8","alias_value":"EZNV6P3W","created_at":"2026-07-05T11:04:10Z"}],"graph_snapshots":[{"event_id":"sha256:fdb9629676835294038855ccc0d1a0128d47d309455dc6b659641e23383ef584","target":"graph","created_at":"2026-07-05T11:04:10Z","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/2505.11092/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the hydrodynamic limit for three gradient spin models: generalized Kipnis-Marchioro-Presutti (KMP), its discrete version and a family of harmonic models, under symmetric and nearest-neighbor interactions. These three models share some universal properties: occupation variables are unbounded, all these processes are of gradient type, their invariant measures are product with spatially homogeneous weights, and, notably, they are all attractive, meaning that the process preserves the partial order of measures along the dynamics. In view of hydrodynamics of large-scale interacting systems","authors_text":"Chiara Franceschini, Kohei Hayashi, Makiko Sasada, Patr\\'icia Gon\\c{c}alves","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-16T10:24:39Z","title":"Hydrodynamic limit for some gradient and attractive spin models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.11092","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":"sha256:7a97c2c40d95219481e43d96c43dbee8014263fde87eecb677e8ccd6d2772b50","target":"record","created_at":"2026-07-05T11:04:10Z","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":"f34f78c095245eba917078dc90470d3171c81dcc86408421ffb44937b1b52197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-16T10:24:39Z","title_canon_sha256":"32eded1188067e881309dc684132b859534e21c6406aa885bc4d9fcc8f9ebbeb"},"schema_version":"1.0","source":{"id":"2505.11092","kind":"arxiv","version":1}},"canonical_sha256":"265b5f3f76ffd51830f047d3f01c61ebe6ca442975dddb7178c74c84a2bd12e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"265b5f3f76ffd51830f047d3f01c61ebe6ca442975dddb7178c74c84a2bd12e4","first_computed_at":"2026-07-05T11:04:10.595847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:04:10.595847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7UV2aksbWub1IwjIISenl/e1hRZCHrCWl+3CsKDaSFbCbW6hL9K1LJpQbp5aL+Pcia6dcSQJLABkqEvZAerlAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:04:10.596429Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.11092","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a97c2c40d95219481e43d96c43dbee8014263fde87eecb677e8ccd6d2772b50","sha256:fdb9629676835294038855ccc0d1a0128d47d309455dc6b659641e23383ef584"],"state_sha256":"1db5dbd4001723a9724c006774a630978ee795d2c18f2f8c3e8c79205406adca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kQ0b1DFMuIKcShn1VdnUISUql21SZI05+SURPLWLtjzbTbyDMcqGLalbT2W6uylSjM+ivDLMu8eUI8oVJjasDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T11:46:39.650090Z","bundle_sha256":"35af57d1f88099a65e4483be23b51a4119e6ff1aca73efec4fc12ba91fdb2403"}}