{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VPYFY455L3PRFG4PKWM23ELFBT","short_pith_number":"pith:VPYFY455","canonical_record":{"source":{"id":"1804.06135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-17T09:45:42Z","cross_cats_sorted":[],"title_canon_sha256":"ea9e0d4a8bf7dd9e5cd6fe4c06b0e8a3f720b4a3f93f50c065f9e618a1140ce8","abstract_canon_sha256":"baa08bba9de7fef056b698bf11dbb4a4721ed7dcf462e3614db4790868e488b1"},"schema_version":"1.0"},"canonical_sha256":"abf05c73bd5edf129b8f5599ad91650cd3051c6d88b109c8d3081c266937e9fa","source":{"kind":"arxiv","id":"1804.06135","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06135","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06135v2","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06135","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"VPYFY455L3PR","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VPYFY455L3PRFG4P","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VPYFY455","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VPYFY455L3PRFG4PKWM23ELFBT","target":"record","payload":{"canonical_record":{"source":{"id":"1804.06135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-17T09:45:42Z","cross_cats_sorted":[],"title_canon_sha256":"ea9e0d4a8bf7dd9e5cd6fe4c06b0e8a3f720b4a3f93f50c065f9e618a1140ce8","abstract_canon_sha256":"baa08bba9de7fef056b698bf11dbb4a4721ed7dcf462e3614db4790868e488b1"},"schema_version":"1.0"},"canonical_sha256":"abf05c73bd5edf129b8f5599ad91650cd3051c6d88b109c8d3081c266937e9fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:57.322738Z","signature_b64":"BVJCqmIhphnNOotc+GQB+1kB3vo1POhltDZpcT+Qi8QPaTmgKkcHuSnYAx0UDypJ8V+f9TBnblh8xT3YZDWHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abf05c73bd5edf129b8f5599ad91650cd3051c6d88b109c8d3081c266937e9fa","last_reissued_at":"2026-05-17T23:49:57.322011Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:57.322011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.06135","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":"2026-05-17T23:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TtEwH7nWx8DTlCrI7R89nAlwKxoz1BKTdy6apXE8kYWt8DGZIvAUX4DRJjS4qzw7iebop6f7axCbSrzt4F0+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:58:54.335347Z"},"content_sha256":"c1146342f8fc65f23791286eed39caf486e397a365690ca77f369e82117e34c5","schema_version":"1.0","event_id":"sha256:c1146342f8fc65f23791286eed39caf486e397a365690ca77f369e82117e34c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VPYFY455L3PRFG4PKWM23ELFBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decay estimates for large velocities in the Boltzmann equation without cutoff","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cl\\'ement Mouhot, Cyril Imbert (DMA), Luis Silvestre","submitted_at":"2018-04-17T09:45:42Z","abstract_excerpt":"We consider solutions $f=f(t,x,v)$ to the full (spatially  inhomogeneous) Boltzmann equation with periodic spatial conditions  $x \\in \\mathbb T^d$, for hard and moderately soft potentials  \\emph{without the angular cutoff assumption}, and under the \\emph{a    priori} assumption that the main hydrodynamic fields, namely the  local mass $\\int\\_v f(t,x,v)$ and local energy $\\int\\_v f(t,x,v)|v|^2$  and local entropy $\\int\\_v f(t,x,v) \\ln f(t,x,v)$, are controlled  along time.  We establish quantitative estimates of  \\emph{propagation} in time of \"pointwise polynomial moments\", i.e.  $\\sup\\_{x,v} f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06135","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":""},"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":"2026-05-17T23:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G/S0SaRsb7G40XzbdrPgD80+mc9FP1v+E/SQFBUjkdSut+odIJEyn0ojn7x/8ADdJSiNI05Qbzi8jNWNIZz7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:58:54.335705Z"},"content_sha256":"60a01b1dc661d9e0ed731c2c58c31eb640f4fb07172d3320abe8c0dabad927a2","schema_version":"1.0","event_id":"sha256:60a01b1dc661d9e0ed731c2c58c31eb640f4fb07172d3320abe8c0dabad927a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VPYFY455L3PRFG4PKWM23ELFBT/bundle.json","state_url":"https://pith.science/pith/VPYFY455L3PRFG4PKWM23ELFBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VPYFY455L3PRFG4PKWM23ELFBT/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":"2026-06-23T19:58:54Z","links":{"resolver":"https://pith.science/pith/VPYFY455L3PRFG4PKWM23ELFBT","bundle":"https://pith.science/pith/VPYFY455L3PRFG4PKWM23ELFBT/bundle.json","state":"https://pith.science/pith/VPYFY455L3PRFG4PKWM23ELFBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VPYFY455L3PRFG4PKWM23ELFBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VPYFY455L3PRFG4PKWM23ELFBT","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":"baa08bba9de7fef056b698bf11dbb4a4721ed7dcf462e3614db4790868e488b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-17T09:45:42Z","title_canon_sha256":"ea9e0d4a8bf7dd9e5cd6fe4c06b0e8a3f720b4a3f93f50c065f9e618a1140ce8"},"schema_version":"1.0","source":{"id":"1804.06135","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06135","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06135v2","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06135","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"VPYFY455L3PR","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VPYFY455L3PRFG4P","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VPYFY455","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:60a01b1dc661d9e0ed731c2c58c31eb640f4fb07172d3320abe8c0dabad927a2","target":"graph","created_at":"2026-05-17T23:49:57Z","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"},"paper":{"abstract_excerpt":"We consider solutions $f=f(t,x,v)$ to the full (spatially  inhomogeneous) Boltzmann equation with periodic spatial conditions  $x \\in \\mathbb T^d$, for hard and moderately soft potentials  \\emph{without the angular cutoff assumption}, and under the \\emph{a    priori} assumption that the main hydrodynamic fields, namely the  local mass $\\int\\_v f(t,x,v)$ and local energy $\\int\\_v f(t,x,v)|v|^2$  and local entropy $\\int\\_v f(t,x,v) \\ln f(t,x,v)$, are controlled  along time.  We establish quantitative estimates of  \\emph{propagation} in time of \"pointwise polynomial moments\", i.e.  $\\sup\\_{x,v} f","authors_text":"Cl\\'ement Mouhot, Cyril Imbert (DMA), Luis Silvestre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-17T09:45:42Z","title":"Decay estimates for large velocities in the Boltzmann equation without cutoff"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06135","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:c1146342f8fc65f23791286eed39caf486e397a365690ca77f369e82117e34c5","target":"record","created_at":"2026-05-17T23:49:57Z","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":"baa08bba9de7fef056b698bf11dbb4a4721ed7dcf462e3614db4790868e488b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-17T09:45:42Z","title_canon_sha256":"ea9e0d4a8bf7dd9e5cd6fe4c06b0e8a3f720b4a3f93f50c065f9e618a1140ce8"},"schema_version":"1.0","source":{"id":"1804.06135","kind":"arxiv","version":2}},"canonical_sha256":"abf05c73bd5edf129b8f5599ad91650cd3051c6d88b109c8d3081c266937e9fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abf05c73bd5edf129b8f5599ad91650cd3051c6d88b109c8d3081c266937e9fa","first_computed_at":"2026-05-17T23:49:57.322011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:57.322011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BVJCqmIhphnNOotc+GQB+1kB3vo1POhltDZpcT+Qi8QPaTmgKkcHuSnYAx0UDypJ8V+f9TBnblh8xT3YZDWHBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:57.322738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06135","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1146342f8fc65f23791286eed39caf486e397a365690ca77f369e82117e34c5","sha256:60a01b1dc661d9e0ed731c2c58c31eb640f4fb07172d3320abe8c0dabad927a2"],"state_sha256":"414b86efcdd9b1ffaa6e775a95b1c13d88399fd3faf547d54be5e6eca1aa2acd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KU4fT4SUXRAG2OjYGayPvFM6GdZYmB6x7d4aToNlAPjNrooFY0+YHnn7yb+XrLqohRzURvd2I9/bIfeOwKBWAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:58:54.337693Z","bundle_sha256":"543ae5112639f4c4d79eb3554d3d5c21a15b2bc00a25cdcd2471c2355a82435b"}}