{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TW7EVKAMQJMDL5YVPVRATJRQPG","short_pith_number":"pith:TW7EVKAM","canonical_record":{"source":{"id":"1211.0327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-01T23:04:17Z","cross_cats_sorted":[],"title_canon_sha256":"f91353c43546fa320a7ac7c4b7968ae78acc26db7af00f0ee3df0cb6b369b6ee","abstract_canon_sha256":"fb46ccbc84410103595116dd89dc1f21e7ae8bcc2ef9afc9048c40e1f632a9cf"},"schema_version":"1.0"},"canonical_sha256":"9dbe4aa80c825835f7157d6209a6307994efce0a26c3f180418eb33181b23eda","source":{"kind":"arxiv","id":"1211.0327","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0327","created_at":"2026-05-18T03:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0327v1","created_at":"2026-05-18T03:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0327","created_at":"2026-05-18T03:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"TW7EVKAMQJMD","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TW7EVKAMQJMDL5YV","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TW7EVKAM","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TW7EVKAMQJMDL5YVPVRATJRQPG","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-01T23:04:17Z","cross_cats_sorted":[],"title_canon_sha256":"f91353c43546fa320a7ac7c4b7968ae78acc26db7af00f0ee3df0cb6b369b6ee","abstract_canon_sha256":"fb46ccbc84410103595116dd89dc1f21e7ae8bcc2ef9afc9048c40e1f632a9cf"},"schema_version":"1.0"},"canonical_sha256":"9dbe4aa80c825835f7157d6209a6307994efce0a26c3f180418eb33181b23eda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:41.549842Z","signature_b64":"KCAATrHSmvAYMBzHMJ4nGNQgAEvexcxLH8kWhtVPlO5BAYabtP6uLsKX23QkRPMVT6o8nImAgOusaS0cCwBPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dbe4aa80c825835f7157d6209a6307994efce0a26c3f180418eb33181b23eda","last_reissued_at":"2026-05-18T03:41:41.548919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:41.548919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0327","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":"2026-05-18T03:41:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"75wbpbxzwJV9/UJfxKl+NNeB92F9zsOgsM5fuFZSEQtEASnmx26Oax25mhvGNaHgIk/DqdTYFHzmUbFWr4clCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T22:03:49.925492Z"},"content_sha256":"59c274e39b05cdbbb31e5d42e1f394f1277d8cb36d3fd5e2515ae750092bfc49","schema_version":"1.0","event_id":"sha256:59c274e39b05cdbbb31e5d42e1f394f1277d8cb36d3fd5e2515ae750092bfc49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TW7EVKAMQJMDL5YVPVRATJRQPG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conservative Deterministic Spectral Boltzmann Solver Near the Grazing Collisions Limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Irene M. Gamba, Jeffrey R. Haack","submitted_at":"2012-11-01T23:04:17Z","abstract_excerpt":"We present new results building on the conservative deterministic spectral method for the space homogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the Boltzmann equation, and uses the machinery of the Fourier transform to reformulate the collisional integral into a weighted convolution in Fourier space. A constrained optimization problem is solved to preserve the mass, momentum, and energy of the resulting distribution.\n  Within this framework we have extended the formulation to the case of more general case "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0327","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":"2026-05-18T03:41:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9xunZnfgwi81bKOAGa6aZ1PkIPij2R43NCS4DiwFR9WqDUpq0bhFPp8AVGTAICNifoWKPhrNOKwEEfd2H3sXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T22:03:49.926181Z"},"content_sha256":"9b3aec1fe041223d0c2090e447ad61362613a8d511706bf92ed118cdf55fde28","schema_version":"1.0","event_id":"sha256:9b3aec1fe041223d0c2090e447ad61362613a8d511706bf92ed118cdf55fde28"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TW7EVKAMQJMDL5YVPVRATJRQPG/bundle.json","state_url":"https://pith.science/pith/TW7EVKAMQJMDL5YVPVRATJRQPG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TW7EVKAMQJMDL5YVPVRATJRQPG/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":"2026-05-20T22:03:49Z","links":{"resolver":"https://pith.science/pith/TW7EVKAMQJMDL5YVPVRATJRQPG","bundle":"https://pith.science/pith/TW7EVKAMQJMDL5YVPVRATJRQPG/bundle.json","state":"https://pith.science/pith/TW7EVKAMQJMDL5YVPVRATJRQPG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TW7EVKAMQJMDL5YVPVRATJRQPG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TW7EVKAMQJMDL5YVPVRATJRQPG","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":"fb46ccbc84410103595116dd89dc1f21e7ae8bcc2ef9afc9048c40e1f632a9cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-01T23:04:17Z","title_canon_sha256":"f91353c43546fa320a7ac7c4b7968ae78acc26db7af00f0ee3df0cb6b369b6ee"},"schema_version":"1.0","source":{"id":"1211.0327","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0327","created_at":"2026-05-18T03:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0327v1","created_at":"2026-05-18T03:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0327","created_at":"2026-05-18T03:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"TW7EVKAMQJMD","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TW7EVKAMQJMDL5YV","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TW7EVKAM","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:9b3aec1fe041223d0c2090e447ad61362613a8d511706bf92ed118cdf55fde28","target":"graph","created_at":"2026-05-18T03:41:41Z","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 present new results building on the conservative deterministic spectral method for the space homogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the Boltzmann equation, and uses the machinery of the Fourier transform to reformulate the collisional integral into a weighted convolution in Fourier space. A constrained optimization problem is solved to preserve the mass, momentum, and energy of the resulting distribution.\n  Within this framework we have extended the formulation to the case of more general case ","authors_text":"Irene M. Gamba, Jeffrey R. Haack","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-01T23:04:17Z","title":"Conservative Deterministic Spectral Boltzmann Solver Near the Grazing Collisions Limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0327","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":"sha256:59c274e39b05cdbbb31e5d42e1f394f1277d8cb36d3fd5e2515ae750092bfc49","target":"record","created_at":"2026-05-18T03:41:41Z","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":"fb46ccbc84410103595116dd89dc1f21e7ae8bcc2ef9afc9048c40e1f632a9cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-01T23:04:17Z","title_canon_sha256":"f91353c43546fa320a7ac7c4b7968ae78acc26db7af00f0ee3df0cb6b369b6ee"},"schema_version":"1.0","source":{"id":"1211.0327","kind":"arxiv","version":1}},"canonical_sha256":"9dbe4aa80c825835f7157d6209a6307994efce0a26c3f180418eb33181b23eda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dbe4aa80c825835f7157d6209a6307994efce0a26c3f180418eb33181b23eda","first_computed_at":"2026-05-18T03:41:41.548919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:41.548919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KCAATrHSmvAYMBzHMJ4nGNQgAEvexcxLH8kWhtVPlO5BAYabtP6uLsKX23QkRPMVT6o8nImAgOusaS0cCwBPAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:41.549842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0327","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59c274e39b05cdbbb31e5d42e1f394f1277d8cb36d3fd5e2515ae750092bfc49","sha256:9b3aec1fe041223d0c2090e447ad61362613a8d511706bf92ed118cdf55fde28"],"state_sha256":"5710db6797529404195eb362fb8626a6247dd8497ae07115f2cfda5119d10945"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ceDK5luIR2H04jR9PZmBfUEEQtIm3SIAkX3SlqTjwxiqVgffw8Q9php4nM7d+Li5Gh86XJNtUA+sTjVVthrgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T22:03:49.929341Z","bundle_sha256":"8b096179c213b7f1bfd8d1281b76608d6fa52e30d7301966be0296b846d18239"}}