{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UKWXYWXIEEITAWSRCXKA3TNSM6","short_pith_number":"pith:UKWXYWXI","canonical_record":{"source":{"id":"2509.14845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-18T11:11:24Z","cross_cats_sorted":[],"title_canon_sha256":"22d1b36dac4ef32d42525b7efec61acef6f9c5735046edf04d4534dc86ac3fd1","abstract_canon_sha256":"a89cc3340e6900be7af572844bb5e2e8e0bbce1f15524df641f896eb3bd39403"},"schema_version":"1.0"},"canonical_sha256":"a2ad7c5ae82111305a5115d40dcdb2678fecbc44a1779575415acab16bc95eb4","source":{"kind":"arxiv","id":"2509.14845","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.14845","created_at":"2026-07-22T00:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"2509.14845v2","created_at":"2026-07-22T00:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.14845","created_at":"2026-07-22T00:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"UKWXYWXIEEIT","created_at":"2026-07-22T00:22:12Z"},{"alias_kind":"pith_short_16","alias_value":"UKWXYWXIEEITAWSR","created_at":"2026-07-22T00:22:12Z"},{"alias_kind":"pith_short_8","alias_value":"UKWXYWXI","created_at":"2026-07-22T00:22:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UKWXYWXIEEITAWSRCXKA3TNSM6","target":"record","payload":{"canonical_record":{"source":{"id":"2509.14845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-18T11:11:24Z","cross_cats_sorted":[],"title_canon_sha256":"22d1b36dac4ef32d42525b7efec61acef6f9c5735046edf04d4534dc86ac3fd1","abstract_canon_sha256":"a89cc3340e6900be7af572844bb5e2e8e0bbce1f15524df641f896eb3bd39403"},"schema_version":"1.0"},"canonical_sha256":"a2ad7c5ae82111305a5115d40dcdb2678fecbc44a1779575415acab16bc95eb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T00:22:12.930458Z","signature_b64":"QBM4kqt4YUkTIuvdiQ3i4rG9Cv5XQkpBetJOLsmxzhGCVFAvWMKKFD02v+Pe+tvdRA1nOgfqUsJVvN0qRRgdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2ad7c5ae82111305a5115d40dcdb2678fecbc44a1779575415acab16bc95eb4","last_reissued_at":"2026-07-22T00:22:12.929563Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T00:22:12.929563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.14845","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":"2026-07-22T00:22:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TiaDsmCYUyDFK+rufg3qvs+WVkQlvH5pIy5EE8lfvyxoXcN9DxXOyGpZGl+7nU/fZ7dIGeX6Hqn8Ayy8zuifCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T14:23:44.314447Z"},"content_sha256":"2f718e315c4afd6219ae4e789ba76d3a883ec2925fe8caaa8e023bb5bc6e8713","schema_version":"1.0","event_id":"sha256:2f718e315c4afd6219ae4e789ba76d3a883ec2925fe8caaa8e023bb5bc6e8713"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UKWXYWXIEEITAWSRCXKA3TNSM6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scaling-Critical Theory for the Boltzmann and Landau Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ke Chen, Quoc-Hung Nguyen, Tong Yang","submitted_at":"2025-09-18T11:11:24Z","abstract_excerpt":"For sufficiently small initial perturbations in a localized, weighted, anisotropic Riesz-potential norm, we prove global well-posedness near a Maxwellian in the whole space. This critical phase-space norm captures the Boltzmann--Landau scaling, the velocity-dependent anisotropy, the hypoelliptic transport structure, and the nonnegativity constraint. The proof combines frozen-operator estimates, a critical fixed-point argument, and weighted hypocoercive energy estimates.\n  We also develop a short-time pointwise Green-function theory for variable-coefficient kinetic equations with a nonnegative "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.14845","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.14845/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-22T00:22:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y5+ZVqeFuuNcQgI4x4BGkmTjyzTJ3qmAQbBvHSDXub3U395IqmiKlW/LSiH/hbyy82W7DsnE5vEBn+LutiCbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T14:23:44.315031Z"},"content_sha256":"52c7b8302ef7d5709d411d5d399658e50cbaea633b31a6c54cc76e848ecb3a08","schema_version":"1.0","event_id":"sha256:52c7b8302ef7d5709d411d5d399658e50cbaea633b31a6c54cc76e848ecb3a08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKWXYWXIEEITAWSRCXKA3TNSM6/bundle.json","state_url":"https://pith.science/pith/UKWXYWXIEEITAWSRCXKA3TNSM6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKWXYWXIEEITAWSRCXKA3TNSM6/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":"2026-08-10T14:23:44Z","links":{"resolver":"https://pith.science/pith/UKWXYWXIEEITAWSRCXKA3TNSM6","bundle":"https://pith.science/pith/UKWXYWXIEEITAWSRCXKA3TNSM6/bundle.json","state":"https://pith.science/pith/UKWXYWXIEEITAWSRCXKA3TNSM6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKWXYWXIEEITAWSRCXKA3TNSM6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UKWXYWXIEEITAWSRCXKA3TNSM6","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":"a89cc3340e6900be7af572844bb5e2e8e0bbce1f15524df641f896eb3bd39403","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-18T11:11:24Z","title_canon_sha256":"22d1b36dac4ef32d42525b7efec61acef6f9c5735046edf04d4534dc86ac3fd1"},"schema_version":"1.0","source":{"id":"2509.14845","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.14845","created_at":"2026-07-22T00:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"2509.14845v2","created_at":"2026-07-22T00:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.14845","created_at":"2026-07-22T00:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"UKWXYWXIEEIT","created_at":"2026-07-22T00:22:12Z"},{"alias_kind":"pith_short_16","alias_value":"UKWXYWXIEEITAWSR","created_at":"2026-07-22T00:22:12Z"},{"alias_kind":"pith_short_8","alias_value":"UKWXYWXI","created_at":"2026-07-22T00:22:12Z"}],"graph_snapshots":[{"event_id":"sha256:52c7b8302ef7d5709d411d5d399658e50cbaea633b31a6c54cc76e848ecb3a08","target":"graph","created_at":"2026-07-22T00:22:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.14845/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For sufficiently small initial perturbations in a localized, weighted, anisotropic Riesz-potential norm, we prove global well-posedness near a Maxwellian in the whole space. This critical phase-space norm captures the Boltzmann--Landau scaling, the velocity-dependent anisotropy, the hypoelliptic transport structure, and the nonnegativity constraint. The proof combines frozen-operator estimates, a critical fixed-point argument, and weighted hypocoercive energy estimates.\n  We also develop a short-time pointwise Green-function theory for variable-coefficient kinetic equations with a nonnegative ","authors_text":"Ke Chen, Quoc-Hung Nguyen, Tong Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-18T11:11:24Z","title":"Scaling-Critical Theory for the Boltzmann and Landau Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.14845","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":"sha256:2f718e315c4afd6219ae4e789ba76d3a883ec2925fe8caaa8e023bb5bc6e8713","target":"record","created_at":"2026-07-22T00:22:12Z","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":"a89cc3340e6900be7af572844bb5e2e8e0bbce1f15524df641f896eb3bd39403","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-18T11:11:24Z","title_canon_sha256":"22d1b36dac4ef32d42525b7efec61acef6f9c5735046edf04d4534dc86ac3fd1"},"schema_version":"1.0","source":{"id":"2509.14845","kind":"arxiv","version":2}},"canonical_sha256":"a2ad7c5ae82111305a5115d40dcdb2678fecbc44a1779575415acab16bc95eb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2ad7c5ae82111305a5115d40dcdb2678fecbc44a1779575415acab16bc95eb4","first_computed_at":"2026-07-22T00:22:12.929563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T00:22:12.929563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QBM4kqt4YUkTIuvdiQ3i4rG9Cv5XQkpBetJOLsmxzhGCVFAvWMKKFD02v+Pe+tvdRA1nOgfqUsJVvN0qRRgdCg==","signature_status":"signed_v1","signed_at":"2026-07-22T00:22:12.930458Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.14845","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f718e315c4afd6219ae4e789ba76d3a883ec2925fe8caaa8e023bb5bc6e8713","sha256:52c7b8302ef7d5709d411d5d399658e50cbaea633b31a6c54cc76e848ecb3a08"],"state_sha256":"b95f3f7580f3bd35b1eab5a8279bc71a368f24456df8e1486bdc6834d40cae10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6HbTDM2raDbLjr2qmG+dn8vk/t/WHUeGM0jRUgnPLKSgEPQdCUpC3o0FTBD7kimBIZcfx/oXWdggL2B9lNxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T14:23:44.320575Z","bundle_sha256":"10d410f6679bf0dac29a6446829f1dd526b01be2a21361d088e81422c8b7e8bf"}}