{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:D4P3T4URL5BYGLT5OCTRILSGD2","short_pith_number":"pith:D4P3T4UR","canonical_record":{"source":{"id":"2502.07342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-02-11T08:09:38Z","cross_cats_sorted":[],"title_canon_sha256":"769bc9ba8e2b26398d50b4736812ba6fc88e52a9ce7a6003ff8e225de28f2cd0","abstract_canon_sha256":"2123acbb322dc9771a865c6db408f95020b94e3c84c67a82294186cecf71e0b6"},"schema_version":"1.0"},"canonical_sha256":"1f1fb9f2915f43832e7d70a7142e461ebe033c8d735b16f905233a0d1bc732aa","source":{"kind":"arxiv","id":"2502.07342","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07342","created_at":"2026-07-05T11:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07342v1","created_at":"2026-07-05T11:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07342","created_at":"2026-07-05T11:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"D4P3T4URL5BY","created_at":"2026-07-05T11:33:49Z"},{"alias_kind":"pith_short_16","alias_value":"D4P3T4URL5BYGLT5","created_at":"2026-07-05T11:33:49Z"},{"alias_kind":"pith_short_8","alias_value":"D4P3T4UR","created_at":"2026-07-05T11:33:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:D4P3T4URL5BYGLT5OCTRILSGD2","target":"record","payload":{"canonical_record":{"source":{"id":"2502.07342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-02-11T08:09:38Z","cross_cats_sorted":[],"title_canon_sha256":"769bc9ba8e2b26398d50b4736812ba6fc88e52a9ce7a6003ff8e225de28f2cd0","abstract_canon_sha256":"2123acbb322dc9771a865c6db408f95020b94e3c84c67a82294186cecf71e0b6"},"schema_version":"1.0"},"canonical_sha256":"1f1fb9f2915f43832e7d70a7142e461ebe033c8d735b16f905233a0d1bc732aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:49.472199Z","signature_b64":"UHigV/qxIGU5kl/jESR+YQTm+pMm0CwDD25rs2wL+lvBmsADBRU6dWAPEwFpKGY1apbbuUXa6Vor9fiKy7VSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f1fb9f2915f43832e7d70a7142e461ebe033c8d735b16f905233a0d1bc732aa","last_reissued_at":"2026-07-05T11:33:49.471731Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:49.471731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.07342","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":"2026-07-05T11:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0NXwGghauLNXFlGUOo8oGgDpY1+YGkH+JLmZKbXUVwAfcvPbdDif57hYnUOWo+QKm1Q5qjvfF7wQvbJ2aR5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T21:03:34.533602Z"},"content_sha256":"bc50366f475b3716cbfeb7311a7509d0b3ad7db40c4bbdf411a816abb845eb3d","schema_version":"1.0","event_id":"sha256:bc50366f475b3716cbfeb7311a7509d0b3ad7db40c4bbdf411a816abb845eb3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:D4P3T4URL5BYGLT5OCTRILSGD2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the long-term evolution of razor-thin galactic discs: Balescu-Lenard prediction and perspectives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Christophe Pichon, Jean-Baptiste Fouvry, Mathieu Roule, Pierre-Henri Chavanis","submitted_at":"2025-02-11T08:09:38Z","abstract_excerpt":"In the last five decades, numerical simulations have provided invaluable insights into the evolution of galactic discs over cosmic times. As a complementary approach, developments in kinetic theory now also offer a theoretical framework to understand statistically their long-term evolution. The current state-of-the-art kinetic theory of isolated stellar systems is the inhomogeneous Balescu-Lenard equation. It can describe the long-term evolution of a self-gravitating razor-thin disc under the effect of resonant interactions between collectively amplified noise-driven fluctuations. In this work"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07342","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/2502.07342/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":"2026-07-05T11:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QN0wvKO4wuMEZn1iPspQb8hvz1AUUSEpTh26N5Ms+psKEaC63wCU9uPsIYjpGRQLborjLbYCKPhnLqli+HwUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T21:03:34.534228Z"},"content_sha256":"478fd13df407ade6f7abad616317d65e52f8ebd0cbb0093644142c27f5e1b420","schema_version":"1.0","event_id":"sha256:478fd13df407ade6f7abad616317d65e52f8ebd0cbb0093644142c27f5e1b420"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4P3T4URL5BYGLT5OCTRILSGD2/bundle.json","state_url":"https://pith.science/pith/D4P3T4URL5BYGLT5OCTRILSGD2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4P3T4URL5BYGLT5OCTRILSGD2/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":"2026-08-17T21:03:34Z","links":{"resolver":"https://pith.science/pith/D4P3T4URL5BYGLT5OCTRILSGD2","bundle":"https://pith.science/pith/D4P3T4URL5BYGLT5OCTRILSGD2/bundle.json","state":"https://pith.science/pith/D4P3T4URL5BYGLT5OCTRILSGD2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4P3T4URL5BYGLT5OCTRILSGD2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:D4P3T4URL5BYGLT5OCTRILSGD2","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":"2123acbb322dc9771a865c6db408f95020b94e3c84c67a82294186cecf71e0b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-02-11T08:09:38Z","title_canon_sha256":"769bc9ba8e2b26398d50b4736812ba6fc88e52a9ce7a6003ff8e225de28f2cd0"},"schema_version":"1.0","source":{"id":"2502.07342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07342","created_at":"2026-07-05T11:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07342v1","created_at":"2026-07-05T11:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07342","created_at":"2026-07-05T11:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"D4P3T4URL5BY","created_at":"2026-07-05T11:33:49Z"},{"alias_kind":"pith_short_16","alias_value":"D4P3T4URL5BYGLT5","created_at":"2026-07-05T11:33:49Z"},{"alias_kind":"pith_short_8","alias_value":"D4P3T4UR","created_at":"2026-07-05T11:33:49Z"}],"graph_snapshots":[{"event_id":"sha256:478fd13df407ade6f7abad616317d65e52f8ebd0cbb0093644142c27f5e1b420","target":"graph","created_at":"2026-07-05T11:33:49Z","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/2502.07342/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the last five decades, numerical simulations have provided invaluable insights into the evolution of galactic discs over cosmic times. As a complementary approach, developments in kinetic theory now also offer a theoretical framework to understand statistically their long-term evolution. The current state-of-the-art kinetic theory of isolated stellar systems is the inhomogeneous Balescu-Lenard equation. It can describe the long-term evolution of a self-gravitating razor-thin disc under the effect of resonant interactions between collectively amplified noise-driven fluctuations. In this work","authors_text":"Christophe Pichon, Jean-Baptiste Fouvry, Mathieu Roule, Pierre-Henri Chavanis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-02-11T08:09:38Z","title":"On the long-term evolution of razor-thin galactic discs: Balescu-Lenard prediction and perspectives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07342","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:bc50366f475b3716cbfeb7311a7509d0b3ad7db40c4bbdf411a816abb845eb3d","target":"record","created_at":"2026-07-05T11:33:49Z","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":"2123acbb322dc9771a865c6db408f95020b94e3c84c67a82294186cecf71e0b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-02-11T08:09:38Z","title_canon_sha256":"769bc9ba8e2b26398d50b4736812ba6fc88e52a9ce7a6003ff8e225de28f2cd0"},"schema_version":"1.0","source":{"id":"2502.07342","kind":"arxiv","version":1}},"canonical_sha256":"1f1fb9f2915f43832e7d70a7142e461ebe033c8d735b16f905233a0d1bc732aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f1fb9f2915f43832e7d70a7142e461ebe033c8d735b16f905233a0d1bc732aa","first_computed_at":"2026-07-05T11:33:49.471731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:49.471731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UHigV/qxIGU5kl/jESR+YQTm+pMm0CwDD25rs2wL+lvBmsADBRU6dWAPEwFpKGY1apbbuUXa6Vor9fiKy7VSDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:49.472199Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.07342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc50366f475b3716cbfeb7311a7509d0b3ad7db40c4bbdf411a816abb845eb3d","sha256:478fd13df407ade6f7abad616317d65e52f8ebd0cbb0093644142c27f5e1b420"],"state_sha256":"cf9d7e5e3ba025cf18e3ca04b9c134839f8e2628346d1413ebe2a25311580f79"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2bejF1qDmezJkfx36OQKuSTgZPxdKCL/s7/DSYoTiUSLjCi3USqzH0JPDTS2OTnt8hatK508GuyAdLyfRROsCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T21:03:34.540176Z","bundle_sha256":"31b0a20d39664c6cdb50983f89ade5e83395161d1a5450771a2e496c8259d900"}}