{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NTOGSBGRTV25FXRZOKIHIUYNK6","short_pith_number":"pith:NTOGSBGR","canonical_record":{"source":{"id":"1610.03707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-12T13:33:58Z","cross_cats_sorted":[],"title_canon_sha256":"d894acdf55dec443c185d544fd76e27590666d041d403aac66dd72aa633552fb","abstract_canon_sha256":"9f59c6d4ffbe829d12c39df46410d6bd046c0e8353444e772d68e2dd68568dde"},"schema_version":"1.0"},"canonical_sha256":"6cdc6904d19d75d2de39729074530d5790aae3f1fc2cbc935e3cdfff3fd2e64f","source":{"kind":"arxiv","id":"1610.03707","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03707","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03707v1","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03707","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"NTOGSBGRTV25","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NTOGSBGRTV25FXRZ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NTOGSBGR","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NTOGSBGRTV25FXRZOKIHIUYNK6","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-12T13:33:58Z","cross_cats_sorted":[],"title_canon_sha256":"d894acdf55dec443c185d544fd76e27590666d041d403aac66dd72aa633552fb","abstract_canon_sha256":"9f59c6d4ffbe829d12c39df46410d6bd046c0e8353444e772d68e2dd68568dde"},"schema_version":"1.0"},"canonical_sha256":"6cdc6904d19d75d2de39729074530d5790aae3f1fc2cbc935e3cdfff3fd2e64f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:29.493310Z","signature_b64":"mtjYxw6W/h7oY1x6xORdJfNrWI7UD8YY103tSUMZy+/erJr836ff+JyeI3UbpMIFIs8ecLRLtKrzb57oiPEWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cdc6904d19d75d2de39729074530d5790aae3f1fc2cbc935e3cdfff3fd2e64f","last_reissued_at":"2026-05-18T01:02:29.492664Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:29.492664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03707","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":"2026-05-18T01:02:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vihLsVHOXeVDCmFTruouz1h+DG5uiqIvduW4qmYByOZG0v3twWPLn00kqqdKa9BNYv9MfUVOCxAYTvU8VJIADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:35:51.897582Z"},"content_sha256":"8db8fe34d04fd976d635860c17666c622ce193a8dc4abe9f7f0e6b9420b91d1a","schema_version":"1.0","event_id":"sha256:8db8fe34d04fd976d635860c17666c622ce193a8dc4abe9f7f0e6b9420b91d1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NTOGSBGRTV25FXRZOKIHIUYNK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cauchy problem to the homogeneous Boltzmann equation with Debye-Yukawa potential for measure initial datum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hao-Guang Li","submitted_at":"2016-10-12T13:33:58Z","abstract_excerpt":"In this work, we prove the existence, uniqueness and smoothing properties of the solution to the Cauchy problem for the spatially homogeneous Boltzmann equation with Debye-Yukawa potential for probability measure initial datum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03707","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":"2026-05-18T01:02:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fEiBt2/wjDnNb0dLYQyD09bhU7gsh9nnX34vYz6jViSNxDBfLa/n0Dq5tvfAhAuu/OIhOyZJgsygstpZeFFhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:35:51.897923Z"},"content_sha256":"c7f453c3a723217b898ec0251ddd3c5bcd8ddda7111516c973ce7217b6b751ad","schema_version":"1.0","event_id":"sha256:c7f453c3a723217b898ec0251ddd3c5bcd8ddda7111516c973ce7217b6b751ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NTOGSBGRTV25FXRZOKIHIUYNK6/bundle.json","state_url":"https://pith.science/pith/NTOGSBGRTV25FXRZOKIHIUYNK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NTOGSBGRTV25FXRZOKIHIUYNK6/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":"2026-06-20T10:35:51Z","links":{"resolver":"https://pith.science/pith/NTOGSBGRTV25FXRZOKIHIUYNK6","bundle":"https://pith.science/pith/NTOGSBGRTV25FXRZOKIHIUYNK6/bundle.json","state":"https://pith.science/pith/NTOGSBGRTV25FXRZOKIHIUYNK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NTOGSBGRTV25FXRZOKIHIUYNK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NTOGSBGRTV25FXRZOKIHIUYNK6","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":"9f59c6d4ffbe829d12c39df46410d6bd046c0e8353444e772d68e2dd68568dde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-12T13:33:58Z","title_canon_sha256":"d894acdf55dec443c185d544fd76e27590666d041d403aac66dd72aa633552fb"},"schema_version":"1.0","source":{"id":"1610.03707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03707","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03707v1","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03707","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"NTOGSBGRTV25","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NTOGSBGRTV25FXRZ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NTOGSBGR","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:c7f453c3a723217b898ec0251ddd3c5bcd8ddda7111516c973ce7217b6b751ad","target":"graph","created_at":"2026-05-18T01:02:29Z","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 work, we prove the existence, uniqueness and smoothing properties of the solution to the Cauchy problem for the spatially homogeneous Boltzmann equation with Debye-Yukawa potential for probability measure initial datum.","authors_text":"Hao-Guang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-12T13:33:58Z","title":"Cauchy problem to the homogeneous Boltzmann equation with Debye-Yukawa potential for measure initial datum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03707","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":"sha256:8db8fe34d04fd976d635860c17666c622ce193a8dc4abe9f7f0e6b9420b91d1a","target":"record","created_at":"2026-05-18T01:02:29Z","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":"9f59c6d4ffbe829d12c39df46410d6bd046c0e8353444e772d68e2dd68568dde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-12T13:33:58Z","title_canon_sha256":"d894acdf55dec443c185d544fd76e27590666d041d403aac66dd72aa633552fb"},"schema_version":"1.0","source":{"id":"1610.03707","kind":"arxiv","version":1}},"canonical_sha256":"6cdc6904d19d75d2de39729074530d5790aae3f1fc2cbc935e3cdfff3fd2e64f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cdc6904d19d75d2de39729074530d5790aae3f1fc2cbc935e3cdfff3fd2e64f","first_computed_at":"2026-05-18T01:02:29.492664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:29.492664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mtjYxw6W/h7oY1x6xORdJfNrWI7UD8YY103tSUMZy+/erJr836ff+JyeI3UbpMIFIs8ecLRLtKrzb57oiPEWDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:29.493310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8db8fe34d04fd976d635860c17666c622ce193a8dc4abe9f7f0e6b9420b91d1a","sha256:c7f453c3a723217b898ec0251ddd3c5bcd8ddda7111516c973ce7217b6b751ad"],"state_sha256":"d2e04a1e8425cf262ff03b608c214435db642046faf784fb5a3c8099d863f97e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1bqe35Bj95tYPMOFyOl7gAKnrTDehMoJBpywLMu6R7fsoldG0n1KiMCv0nWsXxeqo2wX3260QKK1XA0uD4k6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T10:35:51.899828Z","bundle_sha256":"6bcfc8ce1c2524138279cd3e487b044339581329748d545bef038e99e3845ec6"}}