{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5DUS4JFLUYBACBCM646HQU3HZY","short_pith_number":"pith:5DUS4JFL","canonical_record":{"source":{"id":"2505.19929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-26T12:56:07Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a62c26dc6c8d6656ed8e4cfc64df592cc5de7f86e7e1f1a01ad86b303ed9234d","abstract_canon_sha256":"0ed90f3d906cb4c8e4dc18e29f149db2b2abd13a4714098d2724d6f3ef88e1a2"},"schema_version":"1.0"},"canonical_sha256":"e8e92e24aba60201044cf73c785367ce3d7ed3ab99caba97a5238dfc62e582dd","source":{"kind":"arxiv","id":"2505.19929","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.19929","created_at":"2026-07-05T11:09:50Z"},{"alias_kind":"arxiv_version","alias_value":"2505.19929v1","created_at":"2026-07-05T11:09:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.19929","created_at":"2026-07-05T11:09:50Z"},{"alias_kind":"pith_short_12","alias_value":"5DUS4JFLUYBA","created_at":"2026-07-05T11:09:50Z"},{"alias_kind":"pith_short_16","alias_value":"5DUS4JFLUYBACBCM","created_at":"2026-07-05T11:09:50Z"},{"alias_kind":"pith_short_8","alias_value":"5DUS4JFL","created_at":"2026-07-05T11:09:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5DUS4JFLUYBACBCM646HQU3HZY","target":"record","payload":{"canonical_record":{"source":{"id":"2505.19929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-26T12:56:07Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a62c26dc6c8d6656ed8e4cfc64df592cc5de7f86e7e1f1a01ad86b303ed9234d","abstract_canon_sha256":"0ed90f3d906cb4c8e4dc18e29f149db2b2abd13a4714098d2724d6f3ef88e1a2"},"schema_version":"1.0"},"canonical_sha256":"e8e92e24aba60201044cf73c785367ce3d7ed3ab99caba97a5238dfc62e582dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:09:50.034384Z","signature_b64":"ZTHRY0KtgUYgXq6oSN1sAmVCPGoTNWlXyOGJqj6/1fc4ha9QoOWndbnFIXhvN5DNSTqEjf3SxbNl9nOiVpw+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8e92e24aba60201044cf73c785367ce3d7ed3ab99caba97a5238dfc62e582dd","last_reissued_at":"2026-07-05T11:09:50.033839Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:09:50.033839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.19929","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":"2026-07-05T11:09:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3CZI+n5N1CuWYmfbbeYfWpdg9/oQ8VQbFsMdpyGeclFC7ug3HF4DgT1XQzERmwFiV9BNLsmsRXw8UCoOpuU+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:37:04.908850Z"},"content_sha256":"0063d7a6b74e43a1f1ff1f68dccdfbbb07939c413b58408c33c52642f3a1b91f","schema_version":"1.0","event_id":"sha256:0063d7a6b74e43a1f1ff1f68dccdfbbb07939c413b58408c33c52642f3a1b91f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5DUS4JFLUYBACBCM646HQU3HZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Galerkin Alternating Projection Method for Kinetic Equations in the Diffusive Limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Gianluca Ceruti, Lukas Einkemmer, Nicolas Crouseilles","submitted_at":"2025-05-26T12:56:07Z","abstract_excerpt":"The numerical approximation of high-dimensional evolution equations poses significant computational challenges, particularly in kinetic theory and radiative transfer. In this work, we introduce the Galerkin Alternating Projection (GAP) scheme, a novel integrator derived within the Dynamical Low-Rank Approximation (DLRA) framework. We perform a rigorous error analysis, establishing local and global accuracy using standard ODE techniques. Furthermore, we prove that GAP possesses the Asymptotic-Preserving (AP) property when applied to the Radiative Transfer Equation (RTE), ensuring consistent beh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19929","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.19929/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":"2026-07-05T11:09:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XjwKag4CcOdyOT1xpt1f1ZlrjaCEOL9LYdj+YLhCzl5NOOomFQyhx07CD9v65jBbSjSGxaseDe8WqWn/AMuODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:37:04.909425Z"},"content_sha256":"75c7289493cd030d63a22cd72525c271081e2727b90b25f6d37ac926ecad6a0b","schema_version":"1.0","event_id":"sha256:75c7289493cd030d63a22cd72525c271081e2727b90b25f6d37ac926ecad6a0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DUS4JFLUYBACBCM646HQU3HZY/bundle.json","state_url":"https://pith.science/pith/5DUS4JFLUYBACBCM646HQU3HZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DUS4JFLUYBACBCM646HQU3HZY/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":"2026-08-09T06:37:04Z","links":{"resolver":"https://pith.science/pith/5DUS4JFLUYBACBCM646HQU3HZY","bundle":"https://pith.science/pith/5DUS4JFLUYBACBCM646HQU3HZY/bundle.json","state":"https://pith.science/pith/5DUS4JFLUYBACBCM646HQU3HZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DUS4JFLUYBACBCM646HQU3HZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5DUS4JFLUYBACBCM646HQU3HZY","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":"0ed90f3d906cb4c8e4dc18e29f149db2b2abd13a4714098d2724d6f3ef88e1a2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-26T12:56:07Z","title_canon_sha256":"a62c26dc6c8d6656ed8e4cfc64df592cc5de7f86e7e1f1a01ad86b303ed9234d"},"schema_version":"1.0","source":{"id":"2505.19929","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.19929","created_at":"2026-07-05T11:09:50Z"},{"alias_kind":"arxiv_version","alias_value":"2505.19929v1","created_at":"2026-07-05T11:09:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.19929","created_at":"2026-07-05T11:09:50Z"},{"alias_kind":"pith_short_12","alias_value":"5DUS4JFLUYBA","created_at":"2026-07-05T11:09:50Z"},{"alias_kind":"pith_short_16","alias_value":"5DUS4JFLUYBACBCM","created_at":"2026-07-05T11:09:50Z"},{"alias_kind":"pith_short_8","alias_value":"5DUS4JFL","created_at":"2026-07-05T11:09:50Z"}],"graph_snapshots":[{"event_id":"sha256:75c7289493cd030d63a22cd72525c271081e2727b90b25f6d37ac926ecad6a0b","target":"graph","created_at":"2026-07-05T11:09:50Z","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/2505.19929/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The numerical approximation of high-dimensional evolution equations poses significant computational challenges, particularly in kinetic theory and radiative transfer. In this work, we introduce the Galerkin Alternating Projection (GAP) scheme, a novel integrator derived within the Dynamical Low-Rank Approximation (DLRA) framework. We perform a rigorous error analysis, establishing local and global accuracy using standard ODE techniques. Furthermore, we prove that GAP possesses the Asymptotic-Preserving (AP) property when applied to the Radiative Transfer Equation (RTE), ensuring consistent beh","authors_text":"Gianluca Ceruti, Lukas Einkemmer, Nicolas Crouseilles","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-26T12:56:07Z","title":"A Galerkin Alternating Projection Method for Kinetic Equations in the Diffusive Limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19929","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":"sha256:0063d7a6b74e43a1f1ff1f68dccdfbbb07939c413b58408c33c52642f3a1b91f","target":"record","created_at":"2026-07-05T11:09:50Z","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":"0ed90f3d906cb4c8e4dc18e29f149db2b2abd13a4714098d2724d6f3ef88e1a2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-26T12:56:07Z","title_canon_sha256":"a62c26dc6c8d6656ed8e4cfc64df592cc5de7f86e7e1f1a01ad86b303ed9234d"},"schema_version":"1.0","source":{"id":"2505.19929","kind":"arxiv","version":1}},"canonical_sha256":"e8e92e24aba60201044cf73c785367ce3d7ed3ab99caba97a5238dfc62e582dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8e92e24aba60201044cf73c785367ce3d7ed3ab99caba97a5238dfc62e582dd","first_computed_at":"2026-07-05T11:09:50.033839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:09:50.033839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZTHRY0KtgUYgXq6oSN1sAmVCPGoTNWlXyOGJqj6/1fc4ha9QoOWndbnFIXhvN5DNSTqEjf3SxbNl9nOiVpw+BA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:09:50.034384Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.19929","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0063d7a6b74e43a1f1ff1f68dccdfbbb07939c413b58408c33c52642f3a1b91f","sha256:75c7289493cd030d63a22cd72525c271081e2727b90b25f6d37ac926ecad6a0b"],"state_sha256":"5db678c329011cceebc2b93bef268e4f68c18bfe161169685061795df761282a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+mmhpr1uf74GkgnNW39ZcFOXUsQsSjuDfstXuIwxWTXCUChvcfu0hTA+jWXcepV/fIVXc66m0s2/fOerA24BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T06:37:04.913183Z","bundle_sha256":"83c4c9a04bf801679e9f7cc35b9cf1260aace567cfdcaadafae89118832a462a"}}