{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FVHTCMADII33OLZC74ZBIEU4PT","short_pith_number":"pith:FVHTCMAD","canonical_record":{"source":{"id":"1201.3986","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-19T07:44:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"33ba1cf49972dce2f7265c6d9ac238c5bf169e9e747bc18b32881a0b0e9cbb6a","abstract_canon_sha256":"a6ef8ac43b72b14104812bddef36cb3af39b4750dd87e0159b0bbb31b0ec60c2"},"schema_version":"1.0"},"canonical_sha256":"2d4f3130034237b72f22ff3214129c7ce476b289e689da70cadb5ac5b8f4c164","source":{"kind":"arxiv","id":"1201.3986","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3986","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3986v2","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3986","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"FVHTCMADII33","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FVHTCMADII33OLZC","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FVHTCMAD","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FVHTCMADII33OLZC74ZBIEU4PT","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3986","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-19T07:44:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"33ba1cf49972dce2f7265c6d9ac238c5bf169e9e747bc18b32881a0b0e9cbb6a","abstract_canon_sha256":"a6ef8ac43b72b14104812bddef36cb3af39b4750dd87e0159b0bbb31b0ec60c2"},"schema_version":"1.0"},"canonical_sha256":"2d4f3130034237b72f22ff3214129c7ce476b289e689da70cadb5ac5b8f4c164","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:21.467529Z","signature_b64":"+sbUFwTFem/XW7B47rvrjH2uPzrv+jPen8t7lO7dg4oEsbZV6eS2kbIFU/gSo9DjcFANucoJZxFqVR7UbQGXCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d4f3130034237b72f22ff3214129c7ce476b289e689da70cadb5ac5b8f4c164","last_reissued_at":"2026-05-18T03:02:21.466896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:21.466896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3986","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":"evSBz1FCDXifcyZKr8pGg6G7Nw3FZjlQVCwqWJus5iGcfGgWrR5K0hNux4OijJQZspfkbTwQAEVFg6pdKGtUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:45:32.418393Z"},"content_sha256":"f2c6c665b7cf39c3d23c5829cd2e1e04a9a4d03168301d4557562c6b54d115c6","schema_version":"1.0","event_id":"sha256:f2c6c665b7cf39c3d23c5829cd2e1e04a9a4d03168301d4557562c6b54d115c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FVHTCMADII33OLZC74ZBIEU4PT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Cl\\'ement Mouhot, Lorenzo Pareschi (DPT OF MATH., Thomas Rey (ICJ), Univ. of Ferrara)","submitted_at":"2012-01-19T07:44:48Z","abstract_excerpt":"Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically $O(N^{2d+1})$ where $d$ is the dimension of the velocity space. In this paper, following the ideas introduced in [27,28], we derive fast summation techniques for the evaluation of discrete-velocity schemes which permits to reduce the computational cost from $O(N^{2d+1})$ to $O(\\bar{N}^d N^d\\log_2 N)$, $\\bar{N} << N$, with almost no loss of accuracy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3986","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":"mVZ/6av0HGMMQ0AGLVgecUA0sQVBk4RsSbKc/Suqlat7GepTKA+L2yv8ExAngYmG7CmyLrRve9q0p1qHHYW1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:45:32.418754Z"},"content_sha256":"1e8ac10ceec840fdb28aab413158f654fcc13080e5e99d55484494fa62d24b35","schema_version":"1.0","event_id":"sha256:1e8ac10ceec840fdb28aab413158f654fcc13080e5e99d55484494fa62d24b35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVHTCMADII33OLZC74ZBIEU4PT/bundle.json","state_url":"https://pith.science/pith/FVHTCMADII33OLZC74ZBIEU4PT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVHTCMADII33OLZC74ZBIEU4PT/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":"2026-06-21T13:45:32Z","links":{"resolver":"https://pith.science/pith/FVHTCMADII33OLZC74ZBIEU4PT","bundle":"https://pith.science/pith/FVHTCMADII33OLZC74ZBIEU4PT/bundle.json","state":"https://pith.science/pith/FVHTCMADII33OLZC74ZBIEU4PT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVHTCMADII33OLZC74ZBIEU4PT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FVHTCMADII33OLZC74ZBIEU4PT","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":"a6ef8ac43b72b14104812bddef36cb3af39b4750dd87e0159b0bbb31b0ec60c2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-19T07:44:48Z","title_canon_sha256":"33ba1cf49972dce2f7265c6d9ac238c5bf169e9e747bc18b32881a0b0e9cbb6a"},"schema_version":"1.0","source":{"id":"1201.3986","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3986","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3986v2","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3986","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"FVHTCMADII33","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FVHTCMADII33OLZC","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FVHTCMAD","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:1e8ac10ceec840fdb28aab413158f654fcc13080e5e99d55484494fa62d24b35","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":"Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically $O(N^{2d+1})$ where $d$ is the dimension of the velocity space. In this paper, following the ideas introduced in [27,28], we derive fast summation techniques for the evaluation of discrete-velocity schemes which permits to reduce the computational cost from $O(N^{2d+1})$ to $O(\\bar{N}^d N^d\\log_2 N)$, $\\bar{N} << N$, with almost no loss of accuracy.","authors_text":"Cl\\'ement Mouhot, Lorenzo Pareschi (DPT OF MATH., Thomas Rey (ICJ), Univ. of Ferrara)","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-19T07:44:48Z","title":"Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3986","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:f2c6c665b7cf39c3d23c5829cd2e1e04a9a4d03168301d4557562c6b54d115c6","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":"a6ef8ac43b72b14104812bddef36cb3af39b4750dd87e0159b0bbb31b0ec60c2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-19T07:44:48Z","title_canon_sha256":"33ba1cf49972dce2f7265c6d9ac238c5bf169e9e747bc18b32881a0b0e9cbb6a"},"schema_version":"1.0","source":{"id":"1201.3986","kind":"arxiv","version":2}},"canonical_sha256":"2d4f3130034237b72f22ff3214129c7ce476b289e689da70cadb5ac5b8f4c164","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d4f3130034237b72f22ff3214129c7ce476b289e689da70cadb5ac5b8f4c164","first_computed_at":"2026-05-18T03:02:21.466896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:21.466896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+sbUFwTFem/XW7B47rvrjH2uPzrv+jPen8t7lO7dg4oEsbZV6eS2kbIFU/gSo9DjcFANucoJZxFqVR7UbQGXCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:21.467529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3986","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2c6c665b7cf39c3d23c5829cd2e1e04a9a4d03168301d4557562c6b54d115c6","sha256:1e8ac10ceec840fdb28aab413158f654fcc13080e5e99d55484494fa62d24b35"],"state_sha256":"2afc676463c5104f932c2121cc99e8b0c0d6475d862c381bfb79d4266d55436f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SWf+C/NL6BPcg1/1fpHFP/OKrBFMim9vXRe5u8S8w073gjI5ihW7gCIhWO/BlqvU1YYMX1TGs99o7obzpwrEAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T13:45:32.420745Z","bundle_sha256":"2171817eb26bf6951761c4ab991db5104acfdf8411bfa9f26635d335195725da"}}