{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RK2YMFBHGNVQ5LGSZQQFBCWXSK","short_pith_number":"pith:RK2YMFBH","canonical_record":{"source":{"id":"2405.02625","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-04T09:54:26Z","cross_cats_sorted":[],"title_canon_sha256":"e884253fc43e12c15a9e62d86be82df3a23b04c38388dddbce54cc39528e8bb3","abstract_canon_sha256":"f8f339927d07a2b9ac0d201924dbb0c627bb9b186fa55ab8f6fd05dffc05662f"},"schema_version":"1.0"},"canonical_sha256":"8ab5861427336b0eacd2cc20508ad7929031bd4bb31ff98df283ebdba4680dec","source":{"kind":"arxiv","id":"2405.02625","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.02625","created_at":"2026-07-05T11:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"2405.02625v2","created_at":"2026-07-05T11:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.02625","created_at":"2026-07-05T11:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"RK2YMFBHGNVQ","created_at":"2026-07-05T11:22:30Z"},{"alias_kind":"pith_short_16","alias_value":"RK2YMFBHGNVQ5LGS","created_at":"2026-07-05T11:22:30Z"},{"alias_kind":"pith_short_8","alias_value":"RK2YMFBH","created_at":"2026-07-05T11:22:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RK2YMFBHGNVQ5LGSZQQFBCWXSK","target":"record","payload":{"canonical_record":{"source":{"id":"2405.02625","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-04T09:54:26Z","cross_cats_sorted":[],"title_canon_sha256":"e884253fc43e12c15a9e62d86be82df3a23b04c38388dddbce54cc39528e8bb3","abstract_canon_sha256":"f8f339927d07a2b9ac0d201924dbb0c627bb9b186fa55ab8f6fd05dffc05662f"},"schema_version":"1.0"},"canonical_sha256":"8ab5861427336b0eacd2cc20508ad7929031bd4bb31ff98df283ebdba4680dec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:30.405299Z","signature_b64":"mQofxMVbQH0QqUeU6iTbH6NEo7oN4zYbm3+kSqxeWqOfx0X39nbaaDcYy0SjlpcwP6vMzDJswIK1yclDlgiNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ab5861427336b0eacd2cc20508ad7929031bd4bb31ff98df283ebdba4680dec","last_reissued_at":"2026-07-05T11:22:30.404773Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:30.404773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.02625","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptGxNWg1kdcCN6CMyOZ3xP1HdPsWioi4EqLIiIX0tpwBYicW0+bmORr7D8pgX3Ahn3hp9TcOYwIFLRNydUxKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:13:53.313728Z"},"content_sha256":"5f60c8424ad01513d7446b1d17f91d1c9346894d3086b0d7a94e22bfbf8ddc91","schema_version":"1.0","event_id":"sha256:5f60c8424ad01513d7446b1d17f91d1c9346894d3086b0d7a94e22bfbf8ddc91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RK2YMFBHGNVQ5LGSZQQFBCWXSK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Emergence of a Poisson process in weakly interacting particle systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Padilla-Garza, Eric Thoma, Luke Peilen","submitted_at":"2024-05-04T09:54:26Z","abstract_excerpt":"We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting\" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse temperature $\\beta$ satisfies $N^{-1} \\ll \\beta \\ll N^{-\\frac{1}{2}}$, where $N$ is the number of particles. This expands the temperature regime for which convergence to a Poisson point process has been proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.02625","kind":"arxiv","version":2},"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/2405.02625/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":"2026-07-05T11:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KWeYyqcdqng2FLZRUmEfv6yPNCCHg5zn7gkiQUfEZnkx1P+qJK+U1LkipLOFS44FxHfIxjCG3b0sRiKBp0jXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:13:53.314235Z"},"content_sha256":"550ba84592d3a3671d1c383df89e9b98d8bdc027e328ba4f51a1d5c02abdf131","schema_version":"1.0","event_id":"sha256:550ba84592d3a3671d1c383df89e9b98d8bdc027e328ba4f51a1d5c02abdf131"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RK2YMFBHGNVQ5LGSZQQFBCWXSK/bundle.json","state_url":"https://pith.science/pith/RK2YMFBHGNVQ5LGSZQQFBCWXSK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RK2YMFBHGNVQ5LGSZQQFBCWXSK/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":"2026-08-09T20:13:53Z","links":{"resolver":"https://pith.science/pith/RK2YMFBHGNVQ5LGSZQQFBCWXSK","bundle":"https://pith.science/pith/RK2YMFBHGNVQ5LGSZQQFBCWXSK/bundle.json","state":"https://pith.science/pith/RK2YMFBHGNVQ5LGSZQQFBCWXSK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RK2YMFBHGNVQ5LGSZQQFBCWXSK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RK2YMFBHGNVQ5LGSZQQFBCWXSK","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":"f8f339927d07a2b9ac0d201924dbb0c627bb9b186fa55ab8f6fd05dffc05662f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-04T09:54:26Z","title_canon_sha256":"e884253fc43e12c15a9e62d86be82df3a23b04c38388dddbce54cc39528e8bb3"},"schema_version":"1.0","source":{"id":"2405.02625","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.02625","created_at":"2026-07-05T11:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"2405.02625v2","created_at":"2026-07-05T11:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.02625","created_at":"2026-07-05T11:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"RK2YMFBHGNVQ","created_at":"2026-07-05T11:22:30Z"},{"alias_kind":"pith_short_16","alias_value":"RK2YMFBHGNVQ5LGS","created_at":"2026-07-05T11:22:30Z"},{"alias_kind":"pith_short_8","alias_value":"RK2YMFBH","created_at":"2026-07-05T11:22:30Z"}],"graph_snapshots":[{"event_id":"sha256:550ba84592d3a3671d1c383df89e9b98d8bdc027e328ba4f51a1d5c02abdf131","target":"graph","created_at":"2026-07-05T11:22:30Z","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/2405.02625/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting\" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse temperature $\\beta$ satisfies $N^{-1} \\ll \\beta \\ll N^{-\\frac{1}{2}}$, where $N$ is the number of particles. This expands the temperature regime for which convergence to a Poisson point process has been proved.","authors_text":"David Padilla-Garza, Eric Thoma, Luke Peilen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-04T09:54:26Z","title":"Emergence of a Poisson process in weakly interacting particle systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.02625","kind":"arxiv","version":2},"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":"sha256:5f60c8424ad01513d7446b1d17f91d1c9346894d3086b0d7a94e22bfbf8ddc91","target":"record","created_at":"2026-07-05T11:22:30Z","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":"f8f339927d07a2b9ac0d201924dbb0c627bb9b186fa55ab8f6fd05dffc05662f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-04T09:54:26Z","title_canon_sha256":"e884253fc43e12c15a9e62d86be82df3a23b04c38388dddbce54cc39528e8bb3"},"schema_version":"1.0","source":{"id":"2405.02625","kind":"arxiv","version":2}},"canonical_sha256":"8ab5861427336b0eacd2cc20508ad7929031bd4bb31ff98df283ebdba4680dec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ab5861427336b0eacd2cc20508ad7929031bd4bb31ff98df283ebdba4680dec","first_computed_at":"2026-07-05T11:22:30.404773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:22:30.404773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mQofxMVbQH0QqUeU6iTbH6NEo7oN4zYbm3+kSqxeWqOfx0X39nbaaDcYy0SjlpcwP6vMzDJswIK1yclDlgiNBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:22:30.405299Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.02625","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f60c8424ad01513d7446b1d17f91d1c9346894d3086b0d7a94e22bfbf8ddc91","sha256:550ba84592d3a3671d1c383df89e9b98d8bdc027e328ba4f51a1d5c02abdf131"],"state_sha256":"21de66007ce3ed87d62617bd41d085e0dc3d8e9c8c7836ce9aab1a4aa56cf071"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJJ4poseqkYZnWnZjgVTbEpsZC5trJKDUdze9i2cAXppdALqco+AFdd2Pd5QctW1JMaRVHCrhhveFsLGY+skDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:13:53.319453Z","bundle_sha256":"1ad23c001611cb1de127a36900f981fdc33095f4497ce62f2555fbc5521471b2"}}