{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UQ4CI62NRNEJEQD2IEL3FT3FKQ","short_pith_number":"pith:UQ4CI62N","canonical_record":{"source":{"id":"2602.15601","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-17T14:12:51Z","cross_cats_sorted":[],"title_canon_sha256":"ca3edc53c9a5ed265f556f7c2d9867d2c2f37827f72cd45cb0d110dffeb459e9","abstract_canon_sha256":"acce3be16d368e8ff2c29ad06772e5066daf1fa3433136d8960069b563bd1fcf"},"schema_version":"1.0"},"canonical_sha256":"a438247b4d8b4892407a4117b2cf6554174d86ff394c97565bb17a718db942f6","source":{"kind":"arxiv","id":"2602.15601","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.15601","created_at":"2026-07-03T01:17:17Z"},{"alias_kind":"arxiv_version","alias_value":"2602.15601v3","created_at":"2026-07-03T01:17:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.15601","created_at":"2026-07-03T01:17:17Z"},{"alias_kind":"pith_short_12","alias_value":"UQ4CI62NRNEJ","created_at":"2026-07-03T01:17:17Z"},{"alias_kind":"pith_short_16","alias_value":"UQ4CI62NRNEJEQD2","created_at":"2026-07-03T01:17:17Z"},{"alias_kind":"pith_short_8","alias_value":"UQ4CI62N","created_at":"2026-07-03T01:17:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UQ4CI62NRNEJEQD2IEL3FT3FKQ","target":"record","payload":{"canonical_record":{"source":{"id":"2602.15601","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-17T14:12:51Z","cross_cats_sorted":[],"title_canon_sha256":"ca3edc53c9a5ed265f556f7c2d9867d2c2f37827f72cd45cb0d110dffeb459e9","abstract_canon_sha256":"acce3be16d368e8ff2c29ad06772e5066daf1fa3433136d8960069b563bd1fcf"},"schema_version":"1.0"},"canonical_sha256":"a438247b4d8b4892407a4117b2cf6554174d86ff394c97565bb17a718db942f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:17.640586Z","signature_b64":"UVGHq0msycrTh1ZoC8x87s+lnBrS7qrhKK7DW9oPipqGpBkq333Ra1FUk4sEXnbIFtqyjXoKQ4rR5L90409HAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a438247b4d8b4892407a4117b2cf6554174d86ff394c97565bb17a718db942f6","last_reissued_at":"2026-07-03T01:17:17.640102Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:17.640102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.15601","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-03T01:17:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O44jHl2bLG01yqpl5t+y36FW6GzZA8Fe2DgwDlKMBIBekPNm+BXbdRjzwQum2SD7LL73tl6cr28ur6MJatWxAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T10:17:11.894340Z"},"content_sha256":"3fa074c9e0f08d80d2b99f675e14a8cdf828499bf629ce4107e1827dddfb4e5a","schema_version":"1.0","event_id":"sha256:3fa074c9e0f08d80d2b99f675e14a8cdf828499bf629ce4107e1827dddfb4e5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UQ4CI62NRNEJEQD2IEL3FT3FKQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness and Zeroth-Order Analysis of Weak Solutions to the Non-cutoff Boltzmann equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dingqun Deng, Shota Sakamoto","submitted_at":"2026-02-17T14:12:51Z","abstract_excerpt":"We establish the uniqueness of large solutions to the non-cutoff Boltzmann equation with moderate soft potentials. Specifically, the weak solution $F=\\mu+\\mu^{\\frac{1}{2}}f$ is unique as long as it has finite energy, in the sense that the norm $\\|f\\|_{L^\\infty_t L^{r}_{x,v}}+\\|f\\|_{L^\\infty_t L^2_{x,v}}$ remains bounded for some sufficiently large $r>0$. As a byproduct, we establish $L^2_{t,x,v}$ stability for initial data $f_0\\in L^r_{x,v}\\cap L^2_{x,v}$. Our approach employs dilated dyadic decompositions in phase space $(v,\\xi,\\eta)$ to capture hypoellipticity and to reduce the fractional de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.15601","kind":"arxiv","version":3},"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/2602.15601/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":"2026-07-03T01:17:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3MTXOjWgGRwbaBDHX9n+R9pwiMpWCaH55rrJD9P+FUSoJ9HBDOoIw5CjM+6QrCStza12/94Vv5t+ws+eI9bHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T10:17:11.895103Z"},"content_sha256":"c869804f42b1b0b73a878031749f0e506fe710240bac722d17fa5f309a44b57d","schema_version":"1.0","event_id":"sha256:c869804f42b1b0b73a878031749f0e506fe710240bac722d17fa5f309a44b57d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQ4CI62NRNEJEQD2IEL3FT3FKQ/bundle.json","state_url":"https://pith.science/pith/UQ4CI62NRNEJEQD2IEL3FT3FKQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQ4CI62NRNEJEQD2IEL3FT3FKQ/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":"2026-08-09T10:17:11Z","links":{"resolver":"https://pith.science/pith/UQ4CI62NRNEJEQD2IEL3FT3FKQ","bundle":"https://pith.science/pith/UQ4CI62NRNEJEQD2IEL3FT3FKQ/bundle.json","state":"https://pith.science/pith/UQ4CI62NRNEJEQD2IEL3FT3FKQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQ4CI62NRNEJEQD2IEL3FT3FKQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UQ4CI62NRNEJEQD2IEL3FT3FKQ","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":"acce3be16d368e8ff2c29ad06772e5066daf1fa3433136d8960069b563bd1fcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-17T14:12:51Z","title_canon_sha256":"ca3edc53c9a5ed265f556f7c2d9867d2c2f37827f72cd45cb0d110dffeb459e9"},"schema_version":"1.0","source":{"id":"2602.15601","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.15601","created_at":"2026-07-03T01:17:17Z"},{"alias_kind":"arxiv_version","alias_value":"2602.15601v3","created_at":"2026-07-03T01:17:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.15601","created_at":"2026-07-03T01:17:17Z"},{"alias_kind":"pith_short_12","alias_value":"UQ4CI62NRNEJ","created_at":"2026-07-03T01:17:17Z"},{"alias_kind":"pith_short_16","alias_value":"UQ4CI62NRNEJEQD2","created_at":"2026-07-03T01:17:17Z"},{"alias_kind":"pith_short_8","alias_value":"UQ4CI62N","created_at":"2026-07-03T01:17:17Z"}],"graph_snapshots":[{"event_id":"sha256:c869804f42b1b0b73a878031749f0e506fe710240bac722d17fa5f309a44b57d","target":"graph","created_at":"2026-07-03T01:17:17Z","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/2602.15601/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish the uniqueness of large solutions to the non-cutoff Boltzmann equation with moderate soft potentials. Specifically, the weak solution $F=\\mu+\\mu^{\\frac{1}{2}}f$ is unique as long as it has finite energy, in the sense that the norm $\\|f\\|_{L^\\infty_t L^{r}_{x,v}}+\\|f\\|_{L^\\infty_t L^2_{x,v}}$ remains bounded for some sufficiently large $r>0$. As a byproduct, we establish $L^2_{t,x,v}$ stability for initial data $f_0\\in L^r_{x,v}\\cap L^2_{x,v}$. Our approach employs dilated dyadic decompositions in phase space $(v,\\xi,\\eta)$ to capture hypoellipticity and to reduce the fractional de","authors_text":"Dingqun Deng, Shota Sakamoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-17T14:12:51Z","title":"Uniqueness and Zeroth-Order Analysis of Weak Solutions to the Non-cutoff Boltzmann equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.15601","kind":"arxiv","version":3},"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":"sha256:3fa074c9e0f08d80d2b99f675e14a8cdf828499bf629ce4107e1827dddfb4e5a","target":"record","created_at":"2026-07-03T01:17:17Z","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":"acce3be16d368e8ff2c29ad06772e5066daf1fa3433136d8960069b563bd1fcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-17T14:12:51Z","title_canon_sha256":"ca3edc53c9a5ed265f556f7c2d9867d2c2f37827f72cd45cb0d110dffeb459e9"},"schema_version":"1.0","source":{"id":"2602.15601","kind":"arxiv","version":3}},"canonical_sha256":"a438247b4d8b4892407a4117b2cf6554174d86ff394c97565bb17a718db942f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a438247b4d8b4892407a4117b2cf6554174d86ff394c97565bb17a718db942f6","first_computed_at":"2026-07-03T01:17:17.640102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:17.640102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UVGHq0msycrTh1ZoC8x87s+lnBrS7qrhKK7DW9oPipqGpBkq333Ra1FUk4sEXnbIFtqyjXoKQ4rR5L90409HAQ==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:17.640586Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.15601","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fa074c9e0f08d80d2b99f675e14a8cdf828499bf629ce4107e1827dddfb4e5a","sha256:c869804f42b1b0b73a878031749f0e506fe710240bac722d17fa5f309a44b57d"],"state_sha256":"a0ca6ecdf4dd3a342cd2f7a344fd0ba3885ae866ff68c825bded7a16d583038d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"40q9tpLpz9TsYvQKDuB0UWVGSZC1sNlvHzCcv3dqcwjuAS4J4GTHqBl0qCAnogisKiBFBnUstcHAplifJqPDAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T10:17:11.901965Z","bundle_sha256":"feb4ad167bf54e15747060d64613028cbf1e00e1758599441e1c326e1855d07b"}}