{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:D4REQMGXYGVWHIAOMLZT3KKO5B","short_pith_number":"pith:D4REQMGX","canonical_record":{"source":{"id":"1712.08498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-22T15:14:52Z","cross_cats_sorted":[],"title_canon_sha256":"3b0a5dba24ae550d59f5b01b242244db4adaaf84df85fdf8ad5fbc155605aeb8","abstract_canon_sha256":"9ac379cc99579a8a87a432b356e2a8f5a2e39ff44482dcd143355b9f5bd2368f"},"schema_version":"1.0"},"canonical_sha256":"1f224830d7c1ab63a00e62f33da94ee875f8968d5f287186999e0802e0db9ffd","source":{"kind":"arxiv","id":"1712.08498","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08498","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08498v1","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08498","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"D4REQMGXYGVW","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D4REQMGXYGVWHIAO","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D4REQMGX","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:D4REQMGXYGVWHIAOMLZT3KKO5B","target":"record","payload":{"canonical_record":{"source":{"id":"1712.08498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-22T15:14:52Z","cross_cats_sorted":[],"title_canon_sha256":"3b0a5dba24ae550d59f5b01b242244db4adaaf84df85fdf8ad5fbc155605aeb8","abstract_canon_sha256":"9ac379cc99579a8a87a432b356e2a8f5a2e39ff44482dcd143355b9f5bd2368f"},"schema_version":"1.0"},"canonical_sha256":"1f224830d7c1ab63a00e62f33da94ee875f8968d5f287186999e0802e0db9ffd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:23.255330Z","signature_b64":"pYu6nuo3xUdlNl0IE+7rxhqNYeyNmP9RVNSSiab/oCTjL6OOmZFr3SLrDPqbB+99zv2IO6EbS+kKjWU96FBwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f224830d7c1ab63a00e62f33da94ee875f8968d5f287186999e0802e0db9ffd","last_reissued_at":"2026-05-18T00:27:23.254763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:23.254763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.08498","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":"2026-05-18T00:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gmFEzPCRPaWJ1cMCXcib+1CAJx1wdQlnDdKTDFsr+Pd1OoObdFT/E1/gtkrM/sQkmrua3cPAaUTvRv4T1VH5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:31:48.669258Z"},"content_sha256":"ee62ab0de5c1ad6327556b360633fe29b8e8fe3d9a020ab5d13a287c292b0513","schema_version":"1.0","event_id":"sha256:ee62ab0de5c1ad6327556b360633fe29b8e8fe3d9a020ab5d13a287c292b0513"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:D4REQMGXYGVWHIAOMLZT3KKO5B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A brief summary of nonlinear echoes and Landau damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacob Bedrossian","submitted_at":"2017-12-22T15:14:52Z","abstract_excerpt":"In this expository note we review some recent results on Landau damping in the nonlinear Vlasov equations, focusing specifically on the recent construction of nonlinear echo solutions by the author [arXiv:1605.06841] and the associated background. These solutions show that a straightforward extension of Mouhot and Villani's theorem on Landau damping to Sobolev spaces on $\\mathbb T^n_x \\times \\mathbb R^n_v $ is impossible and hence emphasize the subtle dependence on regularity of phase mixing problems. This expository note is specifically aimed at mathematicians who study the analysis of PDEs, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08498","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":""},"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":"2026-05-18T00:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QT6SFTRilbPABc5BIIhTdCTvHJFc515K1hvvXJu6DWxs1gfSkADhJpHKmd7D1LcsGJy4n2HNRbfq0z3s23rDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:31:48.669672Z"},"content_sha256":"8b6f1ff17e2baa1d42a092abcbefd78f08b2ff77f809f2be7d7967f16beb61c6","schema_version":"1.0","event_id":"sha256:8b6f1ff17e2baa1d42a092abcbefd78f08b2ff77f809f2be7d7967f16beb61c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4REQMGXYGVWHIAOMLZT3KKO5B/bundle.json","state_url":"https://pith.science/pith/D4REQMGXYGVWHIAOMLZT3KKO5B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4REQMGXYGVWHIAOMLZT3KKO5B/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":"2026-06-12T08:31:48Z","links":{"resolver":"https://pith.science/pith/D4REQMGXYGVWHIAOMLZT3KKO5B","bundle":"https://pith.science/pith/D4REQMGXYGVWHIAOMLZT3KKO5B/bundle.json","state":"https://pith.science/pith/D4REQMGXYGVWHIAOMLZT3KKO5B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4REQMGXYGVWHIAOMLZT3KKO5B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:D4REQMGXYGVWHIAOMLZT3KKO5B","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":"9ac379cc99579a8a87a432b356e2a8f5a2e39ff44482dcd143355b9f5bd2368f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-22T15:14:52Z","title_canon_sha256":"3b0a5dba24ae550d59f5b01b242244db4adaaf84df85fdf8ad5fbc155605aeb8"},"schema_version":"1.0","source":{"id":"1712.08498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08498","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08498v1","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08498","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"D4REQMGXYGVW","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D4REQMGXYGVWHIAO","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D4REQMGX","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:8b6f1ff17e2baa1d42a092abcbefd78f08b2ff77f809f2be7d7967f16beb61c6","target":"graph","created_at":"2026-05-18T00:27:23Z","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":"In this expository note we review some recent results on Landau damping in the nonlinear Vlasov equations, focusing specifically on the recent construction of nonlinear echo solutions by the author [arXiv:1605.06841] and the associated background. These solutions show that a straightforward extension of Mouhot and Villani's theorem on Landau damping to Sobolev spaces on $\\mathbb T^n_x \\times \\mathbb R^n_v $ is impossible and hence emphasize the subtle dependence on regularity of phase mixing problems. This expository note is specifically aimed at mathematicians who study the analysis of PDEs, ","authors_text":"Jacob Bedrossian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-22T15:14:52Z","title":"A brief summary of nonlinear echoes and Landau damping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08498","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:ee62ab0de5c1ad6327556b360633fe29b8e8fe3d9a020ab5d13a287c292b0513","target":"record","created_at":"2026-05-18T00:27:23Z","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":"9ac379cc99579a8a87a432b356e2a8f5a2e39ff44482dcd143355b9f5bd2368f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-22T15:14:52Z","title_canon_sha256":"3b0a5dba24ae550d59f5b01b242244db4adaaf84df85fdf8ad5fbc155605aeb8"},"schema_version":"1.0","source":{"id":"1712.08498","kind":"arxiv","version":1}},"canonical_sha256":"1f224830d7c1ab63a00e62f33da94ee875f8968d5f287186999e0802e0db9ffd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f224830d7c1ab63a00e62f33da94ee875f8968d5f287186999e0802e0db9ffd","first_computed_at":"2026-05-18T00:27:23.254763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:23.254763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pYu6nuo3xUdlNl0IE+7rxhqNYeyNmP9RVNSSiab/oCTjL6OOmZFr3SLrDPqbB+99zv2IO6EbS+kKjWU96FBwDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:23.255330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.08498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee62ab0de5c1ad6327556b360633fe29b8e8fe3d9a020ab5d13a287c292b0513","sha256:8b6f1ff17e2baa1d42a092abcbefd78f08b2ff77f809f2be7d7967f16beb61c6"],"state_sha256":"50da2c625ec78c1e3d516cdec83cb9b2c7487c6bad85aadcea96c2512efda848"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o/bCKEknkr3aLobGHmxA+nZ0HcjqkiVVX4H7+AA7lZ8HIErtX60YqMBEOLB8p+9U0+/YoHRoJQRf4JwR9vK1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:31:48.671923Z","bundle_sha256":"962ae762dfc4da8e31d8d08114ddd56a4b5da938cf1237d7ecf7fc98efcbb4cb"}}