{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PH574SOQT4CKEYCIAW4QZCCDKL","short_pith_number":"pith:PH574SOQ","canonical_record":{"source":{"id":"1808.10739","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-07-30T10:39:49Z","cross_cats_sorted":[],"title_canon_sha256":"92113b1cf08beee2600a72b301cb921396e61e08f4234534e0e3a0232d35c825","abstract_canon_sha256":"c433a30e0c7ed90b1fff217abc9eedd7b7538b6cf997e661e0b9133c295fbda1"},"schema_version":"1.0"},"canonical_sha256":"79fbfe49d09f04a2604805b90c884352fc5aa5e2cf63ecda0f6dac40b180b349","source":{"kind":"arxiv","id":"1808.10739","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10739","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10739v1","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10739","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"PH574SOQT4CK","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PH574SOQT4CKEYCI","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PH574SOQ","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PH574SOQT4CKEYCIAW4QZCCDKL","target":"record","payload":{"canonical_record":{"source":{"id":"1808.10739","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-07-30T10:39:49Z","cross_cats_sorted":[],"title_canon_sha256":"92113b1cf08beee2600a72b301cb921396e61e08f4234534e0e3a0232d35c825","abstract_canon_sha256":"c433a30e0c7ed90b1fff217abc9eedd7b7538b6cf997e661e0b9133c295fbda1"},"schema_version":"1.0"},"canonical_sha256":"79fbfe49d09f04a2604805b90c884352fc5aa5e2cf63ecda0f6dac40b180b349","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:44.904711Z","signature_b64":"8rXIdsDpPrwUODmMhr8j2mZWDyc/fPjNqsI4UxXVkQTwARp0DgPlsJy6zxwZgarlmz5lrA2X7oH7o9kgipKgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79fbfe49d09f04a2604805b90c884352fc5aa5e2cf63ecda0f6dac40b180b349","last_reissued_at":"2026-05-18T00:06:44.904178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:44.904178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.10739","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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sdcaFxGTiRe+aL+rYcsQD3v57Jy57571zgXLuuO7EnMl4UTpNeKI7vcn3GNQv7/aIzS+WMX7Qt/I5S/Py8jPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:06:42.069019Z"},"content_sha256":"d1bf3950092513b7b48d9f4af56af129cd7bc1406f872dc6d31dfec2e9a6c542","schema_version":"1.0","event_id":"sha256:d1bf3950092513b7b48d9f4af56af129cd7bc1406f872dc6d31dfec2e9a6c542"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PH574SOQT4CKEYCIAW4QZCCDKL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Note on Divergence of the Chapman-Enskog Expansion for Solving Boltzmann Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Bohua Sun, Nanxian Chen","submitted_at":"2018-07-30T10:39:49Z","abstract_excerpt":"Within about a year (1916-1917) Chapman and Enskog independently proposed an important expansion for solving the Boltzmann equation. However, the expansion is divergent or indeterminant in the case of relaxation time $\\tau \\geq 1$. Even since this divergence problem has puzzled this subject for a century. By using a modified M\\\"obius series inversion formula, this paper proposes a modified Chapman-Enskog expansion with a variable upper limit of the summation. The new expansion can give not only a convergent summation but also provide the best-so-far explanation on some unbelievable scenarios o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10739","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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4jqAsWBLC0fD3wZjHRTCMEbfHbxomJ01suDRBrRTYXVEgVFvW46AZh6sbsYd6NCvNvLTbrOk3xHpetA9mywPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:06:42.069724Z"},"content_sha256":"3c8743408d637e6ab835023c5770be1b77264309b0fae9d9285c24781e06fadb","schema_version":"1.0","event_id":"sha256:3c8743408d637e6ab835023c5770be1b77264309b0fae9d9285c24781e06fadb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PH574SOQT4CKEYCIAW4QZCCDKL/bundle.json","state_url":"https://pith.science/pith/PH574SOQT4CKEYCIAW4QZCCDKL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PH574SOQT4CKEYCIAW4QZCCDKL/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":"2026-05-31T20:06:42Z","links":{"resolver":"https://pith.science/pith/PH574SOQT4CKEYCIAW4QZCCDKL","bundle":"https://pith.science/pith/PH574SOQT4CKEYCIAW4QZCCDKL/bundle.json","state":"https://pith.science/pith/PH574SOQT4CKEYCIAW4QZCCDKL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PH574SOQT4CKEYCIAW4QZCCDKL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PH574SOQT4CKEYCIAW4QZCCDKL","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":"c433a30e0c7ed90b1fff217abc9eedd7b7538b6cf997e661e0b9133c295fbda1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-07-30T10:39:49Z","title_canon_sha256":"92113b1cf08beee2600a72b301cb921396e61e08f4234534e0e3a0232d35c825"},"schema_version":"1.0","source":{"id":"1808.10739","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10739","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10739v1","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10739","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"PH574SOQT4CK","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PH574SOQT4CKEYCI","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PH574SOQ","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:3c8743408d637e6ab835023c5770be1b77264309b0fae9d9285c24781e06fadb","target":"graph","created_at":"2026-05-18T00:06:44Z","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":"Within about a year (1916-1917) Chapman and Enskog independently proposed an important expansion for solving the Boltzmann equation. However, the expansion is divergent or indeterminant in the case of relaxation time $\\tau \\geq 1$. Even since this divergence problem has puzzled this subject for a century. By using a modified M\\\"obius series inversion formula, this paper proposes a modified Chapman-Enskog expansion with a variable upper limit of the summation. The new expansion can give not only a convergent summation but also provide the best-so-far explanation on some unbelievable scenarios o","authors_text":"Bohua Sun, Nanxian Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-07-30T10:39:49Z","title":"Note on Divergence of the Chapman-Enskog Expansion for Solving Boltzmann Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10739","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:d1bf3950092513b7b48d9f4af56af129cd7bc1406f872dc6d31dfec2e9a6c542","target":"record","created_at":"2026-05-18T00:06:44Z","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":"c433a30e0c7ed90b1fff217abc9eedd7b7538b6cf997e661e0b9133c295fbda1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-07-30T10:39:49Z","title_canon_sha256":"92113b1cf08beee2600a72b301cb921396e61e08f4234534e0e3a0232d35c825"},"schema_version":"1.0","source":{"id":"1808.10739","kind":"arxiv","version":1}},"canonical_sha256":"79fbfe49d09f04a2604805b90c884352fc5aa5e2cf63ecda0f6dac40b180b349","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79fbfe49d09f04a2604805b90c884352fc5aa5e2cf63ecda0f6dac40b180b349","first_computed_at":"2026-05-18T00:06:44.904178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:44.904178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8rXIdsDpPrwUODmMhr8j2mZWDyc/fPjNqsI4UxXVkQTwARp0DgPlsJy6zxwZgarlmz5lrA2X7oH7o9kgipKgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:44.904711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.10739","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1bf3950092513b7b48d9f4af56af129cd7bc1406f872dc6d31dfec2e9a6c542","sha256:3c8743408d637e6ab835023c5770be1b77264309b0fae9d9285c24781e06fadb"],"state_sha256":"b97831ed5e745f14fdc0688bb82bf14a20b74bcd16b000adc3e982a9244ae63f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+cF0Om/qzkbHHIBSPFeARjgyLh1mpbCCtjYiEGg1ZiqR5rc17pzKmKupvXy//S1A+ej7jJIbM2LxzjsA76TICg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:06:42.073563Z","bundle_sha256":"243aaeb351b4a391de155d6b13d849e007a0acad7cf85de1735b53cf21f80b90"}}