{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EYZSLJTRE3SJCRQ3ORSS7JUKOB","short_pith_number":"pith:EYZSLJTR","canonical_record":{"source":{"id":"1807.07267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-19T07:18:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"de5c0d266c893f7a8805ffd3ba768d64c445eed61a02a911cede7e23e7cb019f","abstract_canon_sha256":"b3ec725caff3c7760459d73b2d31f0eeb0a7f3748c4c0935bb3ca11132980c18"},"schema_version":"1.0"},"canonical_sha256":"263325a67126e491461b74652fa68a7048364c5935a437781308260df2670c87","source":{"kind":"arxiv","id":"1807.07267","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07267","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07267v1","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07267","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"pith_short_12","alias_value":"EYZSLJTRE3SJ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EYZSLJTRE3SJCRQ3","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EYZSLJTR","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EYZSLJTRE3SJCRQ3ORSS7JUKOB","target":"record","payload":{"canonical_record":{"source":{"id":"1807.07267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-19T07:18:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"de5c0d266c893f7a8805ffd3ba768d64c445eed61a02a911cede7e23e7cb019f","abstract_canon_sha256":"b3ec725caff3c7760459d73b2d31f0eeb0a7f3748c4c0935bb3ca11132980c18"},"schema_version":"1.0"},"canonical_sha256":"263325a67126e491461b74652fa68a7048364c5935a437781308260df2670c87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:20.699390Z","signature_b64":"7zfTKzvoyZNooPHLQSF4FnzkBARzOhbw5FSztkqzjeptSDIF/9xNMTNGBfIp8tGUnWHO9fuTzWnceVp2NdknAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"263325a67126e491461b74652fa68a7048364c5935a437781308260df2670c87","last_reissued_at":"2026-05-18T00:10:20.698583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:20.698583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.07267","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":"2026-05-18T00:10:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dV1otiISXJe4dC2gV1wpNRqYznE2WgNpGfrN5vOmm2eomhnby0yceslp9WbwlOAJgjcv/tUK5Rdw6kb3FYg0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:26:32.126402Z"},"content_sha256":"3cdb51a8fa784d441abb446d65cac163b0a9f8f5542dcd531ebb28b59debbfee","schema_version":"1.0","event_id":"sha256:3cdb51a8fa784d441abb446d65cac163b0a9f8f5542dcd531ebb28b59debbfee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EYZSLJTRE3SJCRQ3ORSS7JUKOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Boltzmann equation with time-periodic boundary temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Renjun Duan, Yong Wang, Zhu Zhang","submitted_at":"2018-07-19T07:18:56Z","abstract_excerpt":"This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions with the same period for both hard and soft potentials, provided that the time-periodic boundary temperature is sufficiently close to a stationary one which has small variations around a positive constant. The dynamical stability of time-periodic profiles is also proved under small perturbations, and this in turn yields the non-negativity of the profile. For th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07267","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":"2026-05-18T00:10:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqLjQAZP1a9Q7VPrDKWpFm3mVraG05zaaYpgBuVZQ5NIJJe//PWUI1wbUOAwJ2liBD7XbUntmeXg+IqEKYb6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:26:32.126793Z"},"content_sha256":"272b932286d3d6fd8e671a7e21ab43d01d3a912907b047dd74e75c2ae115f839","schema_version":"1.0","event_id":"sha256:272b932286d3d6fd8e671a7e21ab43d01d3a912907b047dd74e75c2ae115f839"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYZSLJTRE3SJCRQ3ORSS7JUKOB/bundle.json","state_url":"https://pith.science/pith/EYZSLJTRE3SJCRQ3ORSS7JUKOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYZSLJTRE3SJCRQ3ORSS7JUKOB/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":"2026-05-28T15:26:32Z","links":{"resolver":"https://pith.science/pith/EYZSLJTRE3SJCRQ3ORSS7JUKOB","bundle":"https://pith.science/pith/EYZSLJTRE3SJCRQ3ORSS7JUKOB/bundle.json","state":"https://pith.science/pith/EYZSLJTRE3SJCRQ3ORSS7JUKOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYZSLJTRE3SJCRQ3ORSS7JUKOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EYZSLJTRE3SJCRQ3ORSS7JUKOB","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":"b3ec725caff3c7760459d73b2d31f0eeb0a7f3748c4c0935bb3ca11132980c18","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-19T07:18:56Z","title_canon_sha256":"de5c0d266c893f7a8805ffd3ba768d64c445eed61a02a911cede7e23e7cb019f"},"schema_version":"1.0","source":{"id":"1807.07267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07267","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07267v1","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07267","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"pith_short_12","alias_value":"EYZSLJTRE3SJ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EYZSLJTRE3SJCRQ3","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EYZSLJTR","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:272b932286d3d6fd8e671a7e21ab43d01d3a912907b047dd74e75c2ae115f839","target":"graph","created_at":"2026-05-18T00:10:20Z","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":"This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions with the same period for both hard and soft potentials, provided that the time-periodic boundary temperature is sufficiently close to a stationary one which has small variations around a positive constant. The dynamical stability of time-periodic profiles is also proved under small perturbations, and this in turn yields the non-negativity of the profile. For th","authors_text":"Renjun Duan, Yong Wang, Zhu Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-19T07:18:56Z","title":"The Boltzmann equation with time-periodic boundary temperature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07267","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":"sha256:3cdb51a8fa784d441abb446d65cac163b0a9f8f5542dcd531ebb28b59debbfee","target":"record","created_at":"2026-05-18T00:10:20Z","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":"b3ec725caff3c7760459d73b2d31f0eeb0a7f3748c4c0935bb3ca11132980c18","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-19T07:18:56Z","title_canon_sha256":"de5c0d266c893f7a8805ffd3ba768d64c445eed61a02a911cede7e23e7cb019f"},"schema_version":"1.0","source":{"id":"1807.07267","kind":"arxiv","version":1}},"canonical_sha256":"263325a67126e491461b74652fa68a7048364c5935a437781308260df2670c87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"263325a67126e491461b74652fa68a7048364c5935a437781308260df2670c87","first_computed_at":"2026-05-18T00:10:20.698583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:20.698583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7zfTKzvoyZNooPHLQSF4FnzkBARzOhbw5FSztkqzjeptSDIF/9xNMTNGBfIp8tGUnWHO9fuTzWnceVp2NdknAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:20.699390Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cdb51a8fa784d441abb446d65cac163b0a9f8f5542dcd531ebb28b59debbfee","sha256:272b932286d3d6fd8e671a7e21ab43d01d3a912907b047dd74e75c2ae115f839"],"state_sha256":"5ee53b11812bce30855c45109ffeb0627ad797a45c0dc9a8f7d3ab44702e6a1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qz7TJye/ewi0DrvucgJGtG7EF8MS5FXxgySbqpsTR+3x9GGy0K+8RU02R6oCPS/J/eJz42EbuI2jlXxtkdrmCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:26:32.129039Z","bundle_sha256":"737ce6e3377686cbb50e1f589b9cda7f73b308ca9dde1c00433b556fa6432ea4"}}