{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FPNYBAYGOC4O2GHVXOVZVXQFPT","short_pith_number":"pith:FPNYBAYG","canonical_record":{"source":{"id":"1203.2364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-11T19:15:53Z","cross_cats_sorted":[],"title_canon_sha256":"ea35a4d608ba31a493e6387dcbcbe7ca792c5a0b156ac683d3e539649a415e62","abstract_canon_sha256":"92ee60f2c4083b8ea2f9b15c52361162cea20160b9c81d5b81fa5ae2cf2a6b8d"},"schema_version":"1.0"},"canonical_sha256":"2bdb80830670b8ed18f5bbab9ade057cc87193aaa5481a9f48698a9f7e94f088","source":{"kind":"arxiv","id":"1203.2364","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2364","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2364v2","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2364","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"FPNYBAYGOC4O","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FPNYBAYGOC4O2GHV","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FPNYBAYG","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FPNYBAYGOC4O2GHVXOVZVXQFPT","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-11T19:15:53Z","cross_cats_sorted":[],"title_canon_sha256":"ea35a4d608ba31a493e6387dcbcbe7ca792c5a0b156ac683d3e539649a415e62","abstract_canon_sha256":"92ee60f2c4083b8ea2f9b15c52361162cea20160b9c81d5b81fa5ae2cf2a6b8d"},"schema_version":"1.0"},"canonical_sha256":"2bdb80830670b8ed18f5bbab9ade057cc87193aaa5481a9f48698a9f7e94f088","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:21.413520Z","signature_b64":"Z4C+y/yBLpqUfbyt99a0yolGIL3zyKcZo4oIKO2ePp5IlENPgVp3ZHKkIaueNooulJRl02v+zo7J2/iXf2yGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bdb80830670b8ed18f5bbab9ade057cc87193aaa5481a9f48698a9f7e94f088","last_reissued_at":"2026-05-18T03:02:21.412819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:21.412819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2364","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":"2026-05-18T03:02:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nj4EgiMAdymJd96LWhTuw61sn43S4dQPKW8h3SAPC+YLIE2Ja86iL//78s1XiKMA9jbOxElslnBVQsT/+xjVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:02:10.338198Z"},"content_sha256":"d0bd306c5d1f77d740f8c8ae3f44f180db4e30b2a58e6853c76d04d3c8cf1839","schema_version":"1.0","event_id":"sha256:d0bd306c5d1f77d740f8c8ae3f44f180db4e30b2a58e6853c76d04d3c8cf1839"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FPNYBAYGOC4O2GHVXOVZVXQFPT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new approach to the creation and propagation of exponential moments in the Boltzmann equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cl\\'ement Mouhot, Irene Gamba (UT, Jos\\'e Alfredo Ca\\~nizo, Ricardo Alonso, USA)","submitted_at":"2012-03-11T19:15:53Z","abstract_excerpt":"We study the creation and propagation of exponential moments of solutions to the spatially homogeneous $d$-dimensional Boltzmann equation. In particular, when the collision kernel is of the form $|v-v_*|^\\beta b(\\cos(\\theta))$ for $\\beta \\in (0,2]$ with $\\cos(\\theta)= |v-v_*|^{-1}(v-v_*)\\cdot \\sigma$ and $\\sigma \\in \\mathbb{S}^{d-1}$, and assuming the classical cut-off condition $ b(\\cos(\\theta))$ integrable in $\\mathbb{S}^{d-1}$, we prove that there exists $a > 0$ such that moments with weight $\\exp(a \\min{t,1} |v|^\\beta)$ are finite for $t>0$, where $a$ only depends on the collision kernel a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2364","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":""},"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":"2026-05-18T03:02:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H+NrBa9y2c4yLLScTpAglGCuKzsMcHf9qbicmUBJhxFiUjmF7r5HlNzwd+28LuLSckg2k3YXeLX+r2rdES07BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:02:10.338664Z"},"content_sha256":"f8e2fed9f42bab5395df461b3f1ee1d4696ec1fddd6bbc4da8533ee86b5842bc","schema_version":"1.0","event_id":"sha256:f8e2fed9f42bab5395df461b3f1ee1d4696ec1fddd6bbc4da8533ee86b5842bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FPNYBAYGOC4O2GHVXOVZVXQFPT/bundle.json","state_url":"https://pith.science/pith/FPNYBAYGOC4O2GHVXOVZVXQFPT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FPNYBAYGOC4O2GHVXOVZVXQFPT/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":"2026-05-26T19:02:10Z","links":{"resolver":"https://pith.science/pith/FPNYBAYGOC4O2GHVXOVZVXQFPT","bundle":"https://pith.science/pith/FPNYBAYGOC4O2GHVXOVZVXQFPT/bundle.json","state":"https://pith.science/pith/FPNYBAYGOC4O2GHVXOVZVXQFPT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FPNYBAYGOC4O2GHVXOVZVXQFPT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FPNYBAYGOC4O2GHVXOVZVXQFPT","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":"92ee60f2c4083b8ea2f9b15c52361162cea20160b9c81d5b81fa5ae2cf2a6b8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-11T19:15:53Z","title_canon_sha256":"ea35a4d608ba31a493e6387dcbcbe7ca792c5a0b156ac683d3e539649a415e62"},"schema_version":"1.0","source":{"id":"1203.2364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2364","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2364v2","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2364","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"FPNYBAYGOC4O","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FPNYBAYGOC4O2GHV","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FPNYBAYG","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:f8e2fed9f42bab5395df461b3f1ee1d4696ec1fddd6bbc4da8533ee86b5842bc","target":"graph","created_at":"2026-05-18T03:02:21Z","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":"We study the creation and propagation of exponential moments of solutions to the spatially homogeneous $d$-dimensional Boltzmann equation. In particular, when the collision kernel is of the form $|v-v_*|^\\beta b(\\cos(\\theta))$ for $\\beta \\in (0,2]$ with $\\cos(\\theta)= |v-v_*|^{-1}(v-v_*)\\cdot \\sigma$ and $\\sigma \\in \\mathbb{S}^{d-1}$, and assuming the classical cut-off condition $ b(\\cos(\\theta))$ integrable in $\\mathbb{S}^{d-1}$, we prove that there exists $a > 0$ such that moments with weight $\\exp(a \\min{t,1} |v|^\\beta)$ are finite for $t>0$, where $a$ only depends on the collision kernel a","authors_text":"Cl\\'ement Mouhot, Irene Gamba (UT, Jos\\'e Alfredo Ca\\~nizo, Ricardo Alonso, USA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-11T19:15:53Z","title":"A new approach to the creation and propagation of exponential moments in the Boltzmann equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2364","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:d0bd306c5d1f77d740f8c8ae3f44f180db4e30b2a58e6853c76d04d3c8cf1839","target":"record","created_at":"2026-05-18T03:02:21Z","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":"92ee60f2c4083b8ea2f9b15c52361162cea20160b9c81d5b81fa5ae2cf2a6b8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-11T19:15:53Z","title_canon_sha256":"ea35a4d608ba31a493e6387dcbcbe7ca792c5a0b156ac683d3e539649a415e62"},"schema_version":"1.0","source":{"id":"1203.2364","kind":"arxiv","version":2}},"canonical_sha256":"2bdb80830670b8ed18f5bbab9ade057cc87193aaa5481a9f48698a9f7e94f088","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bdb80830670b8ed18f5bbab9ade057cc87193aaa5481a9f48698a9f7e94f088","first_computed_at":"2026-05-18T03:02:21.412819Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:21.412819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z4C+y/yBLpqUfbyt99a0yolGIL3zyKcZo4oIKO2ePp5IlENPgVp3ZHKkIaueNooulJRl02v+zo7J2/iXf2yGBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:21.413520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0bd306c5d1f77d740f8c8ae3f44f180db4e30b2a58e6853c76d04d3c8cf1839","sha256:f8e2fed9f42bab5395df461b3f1ee1d4696ec1fddd6bbc4da8533ee86b5842bc"],"state_sha256":"2f2a48e95ffcad6b10578b647a213e64186a225586816b2a4eaeca9e59f9b5ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4krken+NfBGpuWHCVDTGkDXEi3UTV9QR/r3zHLetyCXJaR9ap/QjxTctQyvl8EEje13GIK8oSD1nkZlmesRCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:02:10.341536Z","bundle_sha256":"97776820019a6c2a344fd3e78401cb8e28d135678002ed66cfd49589310a9079"}}