{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4JKOL4SMTEVFSUZY3IWRRQHEA3","short_pith_number":"pith:4JKOL4SM","canonical_record":{"source":{"id":"1706.07558","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-23T03:47:50Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"177f3c576f5e365959180549f165965f97a0bbc172a4e13639899279a48c3d71","abstract_canon_sha256":"9e38ad95d5fed9c3625372e18aefebf5de2036565a2019a13ae109e438b19e00"},"schema_version":"1.0"},"canonical_sha256":"e254e5f24c992a595338da2d18c0e406fe3bc36c943d51b2044c320294f3398e","source":{"kind":"arxiv","id":"1706.07558","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07558","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07558v2","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07558","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"pith_short_12","alias_value":"4JKOL4SMTEVF","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4JKOL4SMTEVFSUZY","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4JKOL4SM","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4JKOL4SMTEVFSUZY3IWRRQHEA3","target":"record","payload":{"canonical_record":{"source":{"id":"1706.07558","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-23T03:47:50Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"177f3c576f5e365959180549f165965f97a0bbc172a4e13639899279a48c3d71","abstract_canon_sha256":"9e38ad95d5fed9c3625372e18aefebf5de2036565a2019a13ae109e438b19e00"},"schema_version":"1.0"},"canonical_sha256":"e254e5f24c992a595338da2d18c0e406fe3bc36c943d51b2044c320294f3398e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:41.076981Z","signature_b64":"Jn+kNRoeoarnId2t3gZO/ynssnx6UvMKcyO8/WTJL9KF0sKnZMV3WCmwz2YKlS3BzZf2MjdO3/vsBbAiUYfaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e254e5f24c992a595338da2d18c0e406fe3bc36c943d51b2044c320294f3398e","last_reissued_at":"2026-05-18T00:35:41.076366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:41.076366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.07558","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":"2026-05-18T00:35:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o2vi46pbEXwchRaR/5A3bzZEJOYX82au2V+s8ApTh8jVXE8pc5ZoR+fuiobA4b4uU1xq6lgVNRYQol/s/PjGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:02:07.285555Z"},"content_sha256":"f9e2d335b5831955e8235fddaa3e0258eb5848f9539124801276826e514754c2","schema_version":"1.0","event_id":"sha256:f9e2d335b5831955e8235fddaa3e0258eb5848f9539124801276826e514754c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4JKOL4SMTEVFSUZY3IWRRQHEA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smoothing effects and decay estimate of the solution of the linearized two species Landau equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Haitao Wang, Kung-Chien Wu, Yu-Chu Lin","submitted_at":"2017-06-23T03:47:50Z","abstract_excerpt":"We study the Landau equation for a mixture of two species in the whole space, with initial condition of one species near a vacuum and the other near a Maxwellian equilibrium state. For the linearized level, without any smoothness assumption on the initial data, it is shown that the solution becomes smooth instantaneously in both the space and momentum variables. Moreover, the large time behavior of the solution is also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07558","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":"2026-05-18T00:35:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hbR9zT3pgNmiVXMkZIcdP9kEtKMg6luemR1YqapTfZnrJcay9LoYrpR7K0ksyI9Yhrf5sGDcWKSg9mhmUbMTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:02:07.285891Z"},"content_sha256":"57c48b1ded5cd211b7f1d50da0ea7e136ee8e10cd0bd857b463fa508763a99da","schema_version":"1.0","event_id":"sha256:57c48b1ded5cd211b7f1d50da0ea7e136ee8e10cd0bd857b463fa508763a99da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JKOL4SMTEVFSUZY3IWRRQHEA3/bundle.json","state_url":"https://pith.science/pith/4JKOL4SMTEVFSUZY3IWRRQHEA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JKOL4SMTEVFSUZY3IWRRQHEA3/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":"2026-06-20T23:02:07Z","links":{"resolver":"https://pith.science/pith/4JKOL4SMTEVFSUZY3IWRRQHEA3","bundle":"https://pith.science/pith/4JKOL4SMTEVFSUZY3IWRRQHEA3/bundle.json","state":"https://pith.science/pith/4JKOL4SMTEVFSUZY3IWRRQHEA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JKOL4SMTEVFSUZY3IWRRQHEA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4JKOL4SMTEVFSUZY3IWRRQHEA3","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":"9e38ad95d5fed9c3625372e18aefebf5de2036565a2019a13ae109e438b19e00","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-23T03:47:50Z","title_canon_sha256":"177f3c576f5e365959180549f165965f97a0bbc172a4e13639899279a48c3d71"},"schema_version":"1.0","source":{"id":"1706.07558","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07558","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07558v2","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07558","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"pith_short_12","alias_value":"4JKOL4SMTEVF","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4JKOL4SMTEVFSUZY","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4JKOL4SM","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:57c48b1ded5cd211b7f1d50da0ea7e136ee8e10cd0bd857b463fa508763a99da","target":"graph","created_at":"2026-05-18T00:35:41Z","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 study the Landau equation for a mixture of two species in the whole space, with initial condition of one species near a vacuum and the other near a Maxwellian equilibrium state. For the linearized level, without any smoothness assumption on the initial data, it is shown that the solution becomes smooth instantaneously in both the space and momentum variables. Moreover, the large time behavior of the solution is also obtained.","authors_text":"Haitao Wang, Kung-Chien Wu, Yu-Chu Lin","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-23T03:47:50Z","title":"Smoothing effects and decay estimate of the solution of the linearized two species Landau equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07558","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:f9e2d335b5831955e8235fddaa3e0258eb5848f9539124801276826e514754c2","target":"record","created_at":"2026-05-18T00:35:41Z","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":"9e38ad95d5fed9c3625372e18aefebf5de2036565a2019a13ae109e438b19e00","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-23T03:47:50Z","title_canon_sha256":"177f3c576f5e365959180549f165965f97a0bbc172a4e13639899279a48c3d71"},"schema_version":"1.0","source":{"id":"1706.07558","kind":"arxiv","version":2}},"canonical_sha256":"e254e5f24c992a595338da2d18c0e406fe3bc36c943d51b2044c320294f3398e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e254e5f24c992a595338da2d18c0e406fe3bc36c943d51b2044c320294f3398e","first_computed_at":"2026-05-18T00:35:41.076366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:41.076366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jn+kNRoeoarnId2t3gZO/ynssnx6UvMKcyO8/WTJL9KF0sKnZMV3WCmwz2YKlS3BzZf2MjdO3/vsBbAiUYfaAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:41.076981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07558","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9e2d335b5831955e8235fddaa3e0258eb5848f9539124801276826e514754c2","sha256:57c48b1ded5cd211b7f1d50da0ea7e136ee8e10cd0bd857b463fa508763a99da"],"state_sha256":"9d4c942ed4767b672618b5781fb220c7471f5b19332c4bed01fa293bed030511"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MV4aoYNd1xdvJUwOmjrv0EbpHLpUzQrS7gLZE3Mtjp9NQEMYo3bxNg2LpZRrLGOs4wXhKdY44oeGuykrKwNWDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T23:02:07.287875Z","bundle_sha256":"65a230bbfde1ffb4ed77aa4c962da7c1fe115dd1f7f8c6a0aed6aa2bbf2812a2"}}