{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OH4ZLNME4VSKUZJHC64W7RL3W6","short_pith_number":"pith:OH4ZLNME","canonical_record":{"source":{"id":"1603.05534","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T15:16:14Z","cross_cats_sorted":["math.AP","physics.med-ph"],"title_canon_sha256":"9e1e84ca85e77b672902534e4dbec46785ced3d3d37d1c40dabcf6c17d6f099a","abstract_canon_sha256":"6acf35a34194ce7e3fe97375c89f491bd78f342d14bb1300b1878f545f5f5fe9"},"schema_version":"1.0"},"canonical_sha256":"71f995b584e564aa652717b96fc57bb78577ad6cc5827bbfd9aff7e542be9ba1","source":{"kind":"arxiv","id":"1603.05534","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05534","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05534v3","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05534","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"OH4ZLNME4VSK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OH4ZLNME4VSKUZJH","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OH4ZLNME","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OH4ZLNME4VSKUZJHC64W7RL3W6","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05534","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T15:16:14Z","cross_cats_sorted":["math.AP","physics.med-ph"],"title_canon_sha256":"9e1e84ca85e77b672902534e4dbec46785ced3d3d37d1c40dabcf6c17d6f099a","abstract_canon_sha256":"6acf35a34194ce7e3fe97375c89f491bd78f342d14bb1300b1878f545f5f5fe9"},"schema_version":"1.0"},"canonical_sha256":"71f995b584e564aa652717b96fc57bb78577ad6cc5827bbfd9aff7e542be9ba1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:14.322938Z","signature_b64":"AOcC8qGQlQo6S44gqicwoYHWbYOmB7xdnuz2FS+pqyvT+/UgTTxPNAsayCffR2sI6bxZ/+jvBYE2LIMsgyLNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71f995b584e564aa652717b96fc57bb78577ad6cc5827bbfd9aff7e542be9ba1","last_reissued_at":"2026-05-18T00:19:14.322281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:14.322281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05534","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":"2026-05-18T00:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3XNE64RmGjg/5WU3SdddISTD1TPn9+rMH18sISNlS9F21U7XkETQK4Nt3nOOkGVmQ3jXo/jmC6lZUlmzJI+9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:16:24.284860Z"},"content_sha256":"2303e159db7d4469232470adb8875acfaf8328051f79850240769f96e9c3fe6c","schema_version":"1.0","event_id":"sha256:2303e159db7d4469232470adb8875acfaf8328051f79850240769f96e9c3fe6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OH4ZLNME4VSKUZJHC64W7RL3W6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Existence of $L^2$-solutions of Coupled Boltzmann Continuous Slowing Down Transport Equation System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","physics.med-ph"],"primary_cat":"math.OC","authors_text":"J. Tervo, M. Frank, M. Herty, P. Kokkonen","submitted_at":"2016-03-17T15:16:14Z","abstract_excerpt":"The paper considers a coupled system of linear Boltzmann transport equations (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in radiation therapy. The evolution of charged particles (e.g. electrons and positrons) are in practice often modelled using the CSDA version of BTE because of the so-called forward peakedness of scattering events contributing to the particle fluencies (or particle densities), which causes severe problems in numerical methods. We shall find, after the prelimina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05534","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":""},"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":"2026-05-18T00:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TIytG+YbJFIkcy5VDValweLOR3yK0aKued9wdwVvdOQTWxTX8jV00OdfWnfGnJr7iP6F2oshC80657OSIw+eAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:16:24.285510Z"},"content_sha256":"7eae3b8a963f0a7a6dac49288392a104a84c1f7236ff8bf4967d9b5cd0c553e8","schema_version":"1.0","event_id":"sha256:7eae3b8a963f0a7a6dac49288392a104a84c1f7236ff8bf4967d9b5cd0c553e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OH4ZLNME4VSKUZJHC64W7RL3W6/bundle.json","state_url":"https://pith.science/pith/OH4ZLNME4VSKUZJHC64W7RL3W6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OH4ZLNME4VSKUZJHC64W7RL3W6/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":"2026-05-30T11:16:24Z","links":{"resolver":"https://pith.science/pith/OH4ZLNME4VSKUZJHC64W7RL3W6","bundle":"https://pith.science/pith/OH4ZLNME4VSKUZJHC64W7RL3W6/bundle.json","state":"https://pith.science/pith/OH4ZLNME4VSKUZJHC64W7RL3W6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OH4ZLNME4VSKUZJHC64W7RL3W6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OH4ZLNME4VSKUZJHC64W7RL3W6","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":"6acf35a34194ce7e3fe97375c89f491bd78f342d14bb1300b1878f545f5f5fe9","cross_cats_sorted":["math.AP","physics.med-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T15:16:14Z","title_canon_sha256":"9e1e84ca85e77b672902534e4dbec46785ced3d3d37d1c40dabcf6c17d6f099a"},"schema_version":"1.0","source":{"id":"1603.05534","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05534","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05534v3","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05534","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"OH4ZLNME4VSK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OH4ZLNME4VSKUZJH","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OH4ZLNME","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:7eae3b8a963f0a7a6dac49288392a104a84c1f7236ff8bf4967d9b5cd0c553e8","target":"graph","created_at":"2026-05-18T00:19:14Z","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":"The paper considers a coupled system of linear Boltzmann transport equations (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in radiation therapy. The evolution of charged particles (e.g. electrons and positrons) are in practice often modelled using the CSDA version of BTE because of the so-called forward peakedness of scattering events contributing to the particle fluencies (or particle densities), which causes severe problems in numerical methods. We shall find, after the prelimina","authors_text":"J. Tervo, M. Frank, M. Herty, P. Kokkonen","cross_cats":["math.AP","physics.med-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T15:16:14Z","title":"On Existence of $L^2$-solutions of Coupled Boltzmann Continuous Slowing Down Transport Equation System"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05534","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":"sha256:2303e159db7d4469232470adb8875acfaf8328051f79850240769f96e9c3fe6c","target":"record","created_at":"2026-05-18T00:19:14Z","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":"6acf35a34194ce7e3fe97375c89f491bd78f342d14bb1300b1878f545f5f5fe9","cross_cats_sorted":["math.AP","physics.med-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T15:16:14Z","title_canon_sha256":"9e1e84ca85e77b672902534e4dbec46785ced3d3d37d1c40dabcf6c17d6f099a"},"schema_version":"1.0","source":{"id":"1603.05534","kind":"arxiv","version":3}},"canonical_sha256":"71f995b584e564aa652717b96fc57bb78577ad6cc5827bbfd9aff7e542be9ba1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71f995b584e564aa652717b96fc57bb78577ad6cc5827bbfd9aff7e542be9ba1","first_computed_at":"2026-05-18T00:19:14.322281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:14.322281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AOcC8qGQlQo6S44gqicwoYHWbYOmB7xdnuz2FS+pqyvT+/UgTTxPNAsayCffR2sI6bxZ/+jvBYE2LIMsgyLNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:14.322938Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05534","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2303e159db7d4469232470adb8875acfaf8328051f79850240769f96e9c3fe6c","sha256:7eae3b8a963f0a7a6dac49288392a104a84c1f7236ff8bf4967d9b5cd0c553e8"],"state_sha256":"baef9f6feacfcf2391dc02d77d18b08d3096df154f1603d7d3407d664f7186ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nIb6+1TTyah6GS4td83R2D27U/5bzRdnsXfWNdWmHh025N6SmrMCXIDAx9JKU4VYoVu4QZjV/w/lyWMiywkFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:16:24.288527Z","bundle_sha256":"d99610f63f05c5d46a2367f64ca42b36de597cb057b05a41fea32ad76b681fa0"}}