{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FJ7UEKJLJ5IBDKA7K2ZD56BXZ3","short_pith_number":"pith:FJ7UEKJL","canonical_record":{"source":{"id":"2409.01507","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-03T00:15:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0021375f80a4c49f5ceba987195d8ab2f898167a6a23d3638f1de70a0c18e12f","abstract_canon_sha256":"9428228b52e06eba20ff3dfbe7df91e62cfb404ac83dfd1d737c1c696a21d146"},"schema_version":"1.0"},"canonical_sha256":"2a7f42292b4f5011a81f56b23ef837ceea34c9fbca4879a4956d6b3f06cb3727","source":{"kind":"arxiv","id":"2409.01507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.01507","created_at":"2026-07-05T09:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"2409.01507v1","created_at":"2026-07-05T09:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.01507","created_at":"2026-07-05T09:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"FJ7UEKJLJ5IB","created_at":"2026-07-05T09:02:29Z"},{"alias_kind":"pith_short_16","alias_value":"FJ7UEKJLJ5IBDKA7","created_at":"2026-07-05T09:02:29Z"},{"alias_kind":"pith_short_8","alias_value":"FJ7UEKJL","created_at":"2026-07-05T09:02:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FJ7UEKJLJ5IBDKA7K2ZD56BXZ3","target":"record","payload":{"canonical_record":{"source":{"id":"2409.01507","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-03T00:15:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0021375f80a4c49f5ceba987195d8ab2f898167a6a23d3638f1de70a0c18e12f","abstract_canon_sha256":"9428228b52e06eba20ff3dfbe7df91e62cfb404ac83dfd1d737c1c696a21d146"},"schema_version":"1.0"},"canonical_sha256":"2a7f42292b4f5011a81f56b23ef837ceea34c9fbca4879a4956d6b3f06cb3727","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:02:29.964650Z","signature_b64":"33DrA8bivOgJjLJ9Iilk6rFaMYCZ9GT97M9w1fn9QZhpl0GVcLYk7bx7CVQN6BIZSBzQ++m1nq79UJUpqboRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a7f42292b4f5011a81f56b23ef837ceea34c9fbca4879a4956d6b3f06cb3727","last_reissued_at":"2026-07-05T09:02:29.964153Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:02:29.964153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.01507","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":"2026-07-05T09:02:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FEiYn2tG7J5ZYqMBqBQMcISUzWG8pec3dZj5u0qC0g7PCOeoyrWxqGyvcumo5of9game5GwEUWxgQFrkGd3ECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:22:27.696555Z"},"content_sha256":"5f991fa5f5b073d8d9c2d7794fa2f9a74ba259142e8c109ebbcc65f1ea3835af","schema_version":"1.0","event_id":"sha256:5f991fa5f5b073d8d9c2d7794fa2f9a74ba259142e8c109ebbcc65f1ea3835af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FJ7UEKJLJ5IBDKA7K2ZD56BXZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of Rayleigh-Jeans equilibria in the kinetic FPU equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Angeliki Menegaki, Joonhyun La, Pierre Germain","submitted_at":"2024-09-03T00:15:44Z","abstract_excerpt":"We study the nonlinear dynamics of the kinetic wave equation associated to the FPU problem and prove stability of the non-singular Rayleigh-Jeans equilibria. The lack of a spectral gap for the linearized problem leads to polynomial decay, which we are able to leverage to obtain nonlinear stability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01507","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/2409.01507/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":"2026-07-05T09:02:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ijWvMd0hrYjfKutdMFh3o+5wNhvq3tWBJ2/kpyIzW7i4PtPdy6MAkjnrS9eheRdQ7oQXGTtc3i+loTdWllyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:22:27.697046Z"},"content_sha256":"7ee450878f5dea6aecdfe7fe54c53718a050005169971293697bfe72baaee2e4","schema_version":"1.0","event_id":"sha256:7ee450878f5dea6aecdfe7fe54c53718a050005169971293697bfe72baaee2e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FJ7UEKJLJ5IBDKA7K2ZD56BXZ3/bundle.json","state_url":"https://pith.science/pith/FJ7UEKJLJ5IBDKA7K2ZD56BXZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FJ7UEKJLJ5IBDKA7K2ZD56BXZ3/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":"2026-08-08T16:22:27Z","links":{"resolver":"https://pith.science/pith/FJ7UEKJLJ5IBDKA7K2ZD56BXZ3","bundle":"https://pith.science/pith/FJ7UEKJLJ5IBDKA7K2ZD56BXZ3/bundle.json","state":"https://pith.science/pith/FJ7UEKJLJ5IBDKA7K2ZD56BXZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FJ7UEKJLJ5IBDKA7K2ZD56BXZ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FJ7UEKJLJ5IBDKA7K2ZD56BXZ3","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":"9428228b52e06eba20ff3dfbe7df91e62cfb404ac83dfd1d737c1c696a21d146","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-03T00:15:44Z","title_canon_sha256":"0021375f80a4c49f5ceba987195d8ab2f898167a6a23d3638f1de70a0c18e12f"},"schema_version":"1.0","source":{"id":"2409.01507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.01507","created_at":"2026-07-05T09:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"2409.01507v1","created_at":"2026-07-05T09:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.01507","created_at":"2026-07-05T09:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"FJ7UEKJLJ5IB","created_at":"2026-07-05T09:02:29Z"},{"alias_kind":"pith_short_16","alias_value":"FJ7UEKJLJ5IBDKA7","created_at":"2026-07-05T09:02:29Z"},{"alias_kind":"pith_short_8","alias_value":"FJ7UEKJL","created_at":"2026-07-05T09:02:29Z"}],"graph_snapshots":[{"event_id":"sha256:7ee450878f5dea6aecdfe7fe54c53718a050005169971293697bfe72baaee2e4","target":"graph","created_at":"2026-07-05T09:02:29Z","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/2409.01507/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the nonlinear dynamics of the kinetic wave equation associated to the FPU problem and prove stability of the non-singular Rayleigh-Jeans equilibria. The lack of a spectral gap for the linearized problem leads to polynomial decay, which we are able to leverage to obtain nonlinear stability.","authors_text":"Angeliki Menegaki, Joonhyun La, Pierre Germain","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-03T00:15:44Z","title":"Stability of Rayleigh-Jeans equilibria in the kinetic FPU equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01507","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":"sha256:5f991fa5f5b073d8d9c2d7794fa2f9a74ba259142e8c109ebbcc65f1ea3835af","target":"record","created_at":"2026-07-05T09:02:29Z","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":"9428228b52e06eba20ff3dfbe7df91e62cfb404ac83dfd1d737c1c696a21d146","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-03T00:15:44Z","title_canon_sha256":"0021375f80a4c49f5ceba987195d8ab2f898167a6a23d3638f1de70a0c18e12f"},"schema_version":"1.0","source":{"id":"2409.01507","kind":"arxiv","version":1}},"canonical_sha256":"2a7f42292b4f5011a81f56b23ef837ceea34c9fbca4879a4956d6b3f06cb3727","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a7f42292b4f5011a81f56b23ef837ceea34c9fbca4879a4956d6b3f06cb3727","first_computed_at":"2026-07-05T09:02:29.964153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:02:29.964153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"33DrA8bivOgJjLJ9Iilk6rFaMYCZ9GT97M9w1fn9QZhpl0GVcLYk7bx7CVQN6BIZSBzQ++m1nq79UJUpqboRBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:02:29.964650Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.01507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f991fa5f5b073d8d9c2d7794fa2f9a74ba259142e8c109ebbcc65f1ea3835af","sha256:7ee450878f5dea6aecdfe7fe54c53718a050005169971293697bfe72baaee2e4"],"state_sha256":"a9c30b343aeacb2ffbc8bde95dc1231605aedb21ce9f88ee911c3789f98b5e75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4cT0jJWAnq4JnnVLEQ0FwKTflq8WeN9LkWhtOIF6FNdABo5qo1BdYBfsQ5xu/TDkkLXuWdR/21N1kfslAx7CAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:22:27.700731Z","bundle_sha256":"f688e77e940cb500594239e41c37ccd6a9250db107b1df51bf886088264e6e4f"}}