{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6HTKV3EUCS5BCQSMRZWT6WR6QI","short_pith_number":"pith:6HTKV3EU","canonical_record":{"source":{"id":"1604.03653","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-13T05:00:45Z","cross_cats_sorted":[],"title_canon_sha256":"bf9d7995d815d37b00df83776cf0e531fef40f2c57412b9cee6fda3f7bdd256b","abstract_canon_sha256":"4813eebf41a2d6edea0a01dfd0ada84fe47e926d093224c1632fb97d3cd234ed"},"schema_version":"1.0"},"canonical_sha256":"f1e6aaec9414ba11424c8e6d3f5a3e821dcd373b68701f5f0e4c643a6ed40d21","source":{"kind":"arxiv","id":"1604.03653","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03653","created_at":"2026-05-18T01:03:26Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03653v4","created_at":"2026-05-18T01:03:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03653","created_at":"2026-05-18T01:03:26Z"},{"alias_kind":"pith_short_12","alias_value":"6HTKV3EUCS5B","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6HTKV3EUCS5BCQSM","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6HTKV3EU","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6HTKV3EUCS5BCQSMRZWT6WR6QI","target":"record","payload":{"canonical_record":{"source":{"id":"1604.03653","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-13T05:00:45Z","cross_cats_sorted":[],"title_canon_sha256":"bf9d7995d815d37b00df83776cf0e531fef40f2c57412b9cee6fda3f7bdd256b","abstract_canon_sha256":"4813eebf41a2d6edea0a01dfd0ada84fe47e926d093224c1632fb97d3cd234ed"},"schema_version":"1.0"},"canonical_sha256":"f1e6aaec9414ba11424c8e6d3f5a3e821dcd373b68701f5f0e4c643a6ed40d21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:26.616190Z","signature_b64":"rdR882GZh899ObfrLkDVGOWuOngRzO4w2yc0neiJGwd580yNkUr4CNkMuGlb7rKYqlhhU2uYCoXCA7eup8siAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1e6aaec9414ba11424c8e6d3f5a3e821dcd373b68701f5f0e4c643a6ed40d21","last_reissued_at":"2026-05-18T01:03:26.615600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:26.615600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.03653","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+teE4JNJpksoxbaYcDK8Z9vAWStiYLdKqeDygXANssk4gLkC+IxLJoXqJY8/uAKTkQhvsPxNUGCD7ASqJeIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:38:50.157064Z"},"content_sha256":"149b6c8cbb71a36c1aa54ca6c1b29f69ed8f901e42c4a22b5c5c7d16bbf1713a","schema_version":"1.0","event_id":"sha256:149b6c8cbb71a36c1aa54ca6c1b29f69ed8f901e42c4a22b5c5c7d16bbf1713a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6HTKV3EUCS5BCQSMRZWT6WR6QI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of stationary solutions to the linearized Boltzmann equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"I-Kun Chen","submitted_at":"2016-04-13T05:00:45Z","abstract_excerpt":"We consider the regularity of stationary solutions to the linearized Boltzmann equations in bounded $C^1$ convex domains in $\\mathbb{R}^3$ for gases with cutoff hard potential and cutoff Maxwellian gases. We prove that the stationary solutions solutions are H\\\"{o}lder continuous with order $\\frac1{2}^-$ away from the boundary provided the incoming data have the same regularity. The key idea is to partially transfer the regularity in velocity obtained by collision to space through transport and collision."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03653","kind":"arxiv","version":4},"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":"2026-05-18T01:03:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4lHwPOfzYlKxJ346Zqwb6Q2mk5gWyYgfHp99LcWM4stfV8zRL0QufwNiwbLGpGVe+czcgbDA5oL+TmBL1GsKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:38:50.157713Z"},"content_sha256":"281baa60b624882c8a2830666ce3cc69674592be676318eda99ca6663939b613","schema_version":"1.0","event_id":"sha256:281baa60b624882c8a2830666ce3cc69674592be676318eda99ca6663939b613"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6HTKV3EUCS5BCQSMRZWT6WR6QI/bundle.json","state_url":"https://pith.science/pith/6HTKV3EUCS5BCQSMRZWT6WR6QI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6HTKV3EUCS5BCQSMRZWT6WR6QI/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":"2026-05-30T10:38:50Z","links":{"resolver":"https://pith.science/pith/6HTKV3EUCS5BCQSMRZWT6WR6QI","bundle":"https://pith.science/pith/6HTKV3EUCS5BCQSMRZWT6WR6QI/bundle.json","state":"https://pith.science/pith/6HTKV3EUCS5BCQSMRZWT6WR6QI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6HTKV3EUCS5BCQSMRZWT6WR6QI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6HTKV3EUCS5BCQSMRZWT6WR6QI","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":"4813eebf41a2d6edea0a01dfd0ada84fe47e926d093224c1632fb97d3cd234ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-13T05:00:45Z","title_canon_sha256":"bf9d7995d815d37b00df83776cf0e531fef40f2c57412b9cee6fda3f7bdd256b"},"schema_version":"1.0","source":{"id":"1604.03653","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03653","created_at":"2026-05-18T01:03:26Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03653v4","created_at":"2026-05-18T01:03:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03653","created_at":"2026-05-18T01:03:26Z"},{"alias_kind":"pith_short_12","alias_value":"6HTKV3EUCS5B","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6HTKV3EUCS5BCQSM","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6HTKV3EU","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:281baa60b624882c8a2830666ce3cc69674592be676318eda99ca6663939b613","target":"graph","created_at":"2026-05-18T01:03:26Z","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 the regularity of stationary solutions to the linearized Boltzmann equations in bounded $C^1$ convex domains in $\\mathbb{R}^3$ for gases with cutoff hard potential and cutoff Maxwellian gases. We prove that the stationary solutions solutions are H\\\"{o}lder continuous with order $\\frac1{2}^-$ away from the boundary provided the incoming data have the same regularity. The key idea is to partially transfer the regularity in velocity obtained by collision to space through transport and collision.","authors_text":"I-Kun Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-13T05:00:45Z","title":"Regularity of stationary solutions to the linearized Boltzmann equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03653","kind":"arxiv","version":4},"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":"sha256:149b6c8cbb71a36c1aa54ca6c1b29f69ed8f901e42c4a22b5c5c7d16bbf1713a","target":"record","created_at":"2026-05-18T01:03:26Z","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":"4813eebf41a2d6edea0a01dfd0ada84fe47e926d093224c1632fb97d3cd234ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-13T05:00:45Z","title_canon_sha256":"bf9d7995d815d37b00df83776cf0e531fef40f2c57412b9cee6fda3f7bdd256b"},"schema_version":"1.0","source":{"id":"1604.03653","kind":"arxiv","version":4}},"canonical_sha256":"f1e6aaec9414ba11424c8e6d3f5a3e821dcd373b68701f5f0e4c643a6ed40d21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1e6aaec9414ba11424c8e6d3f5a3e821dcd373b68701f5f0e4c643a6ed40d21","first_computed_at":"2026-05-18T01:03:26.615600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:26.615600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rdR882GZh899ObfrLkDVGOWuOngRzO4w2yc0neiJGwd580yNkUr4CNkMuGlb7rKYqlhhU2uYCoXCA7eup8siAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:26.616190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03653","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:149b6c8cbb71a36c1aa54ca6c1b29f69ed8f901e42c4a22b5c5c7d16bbf1713a","sha256:281baa60b624882c8a2830666ce3cc69674592be676318eda99ca6663939b613"],"state_sha256":"a55bbd0523c8fa317f0961235418fe14d9594988251ea064bf598845f5f893c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vpDDAP70zh6psze3VMjbkMZUUNNjtFCYX9WCz0knOBAUTVxF5UeeekGbfVzD+NkAYsk1grSX+YY2l/N+xXRoBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:38:50.161215Z","bundle_sha256":"fb85b657919e6cbb9daac2ec0e2b869f33b7ae07cea27df214b1c8100aceab2d"}}