{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5RG6QPK2FBSBNQ2XUCCL62C3CY","short_pith_number":"pith:5RG6QPK2","canonical_record":{"source":{"id":"1612.00907","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-03T01:06:57Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"59cce09148ab9376361361f08413cb1581d1891d6ef940dad2659502f8f08028","abstract_canon_sha256":"a6d4372e42d54b25448ee8f378ff8f707e647d220e7568bd04896b84e8b9f5f1"},"schema_version":"1.0"},"canonical_sha256":"ec4de83d5a286416c357a084bf685b1636f7567a675c88b3a437996da2885986","source":{"kind":"arxiv","id":"1612.00907","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00907","created_at":"2026-05-18T00:55:06Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00907v1","created_at":"2026-05-18T00:55:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00907","created_at":"2026-05-18T00:55:06Z"},{"alias_kind":"pith_short_12","alias_value":"5RG6QPK2FBSB","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5RG6QPK2FBSBNQ2X","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5RG6QPK2","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5RG6QPK2FBSBNQ2XUCCL62C3CY","target":"record","payload":{"canonical_record":{"source":{"id":"1612.00907","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-03T01:06:57Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"59cce09148ab9376361361f08413cb1581d1891d6ef940dad2659502f8f08028","abstract_canon_sha256":"a6d4372e42d54b25448ee8f378ff8f707e647d220e7568bd04896b84e8b9f5f1"},"schema_version":"1.0"},"canonical_sha256":"ec4de83d5a286416c357a084bf685b1636f7567a675c88b3a437996da2885986","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:06.343254Z","signature_b64":"LLWIYGwbO/LqXT1f4u8kKnq915+7UfZmAbMzl9yD+KRi1CnqCXHfUQBSKGjXUTH+4iCD9Rxk2TbiRakKOd6vDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec4de83d5a286416c357a084bf685b1636f7567a675c88b3a437996da2885986","last_reissued_at":"2026-05-18T00:55:06.342507Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:06.342507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.00907","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":"2026-05-18T00:55:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AnGRTiii4u/KMVktEKNNcO+5LscuPRt+0M4X72nfhurtjKn6gIFmp9miXa7o2OT+6461a4EMOqs+UyYfhBwNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:33:21.996728Z"},"content_sha256":"2c18d86c0aa0691d242fe21b1f234f82f60972b2927d50aa39e9d01614921849","schema_version":"1.0","event_id":"sha256:2c18d86c0aa0691d242fe21b1f234f82f60972b2927d50aa39e9d01614921849"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5RG6QPK2FBSBNQ2XUCCL62C3CY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multigrid In Energy Preconditioner for Krylov Solvers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"G. G. Davidson, P. P. H. Wilson, R. N. Slaybaugh, T. M. Evans","submitted_at":"2016-12-03T01:06:57Z","abstract_excerpt":"We have added a new multigrid in energy (MGE) preconditioner to the Denovo discrete-ordinates radiation transport code. This preconditioner takes advantage of a new multilevel parallel decomposition. A multigroup Krylov subspace iterative solver that is decomposed in energy as well as space-angle forms the backbone of the transport solves in Denovo. The space-angle-energy decomposition facilitates scaling to hundreds of thousands of cores. The multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of Krylov iterations required for convergenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00907","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":"2026-05-18T00:55:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2otNFXBGrkj0fxb1wSQ2P+7c5qf6IeZ4D02vsKh5adx5wVTbqFADQKU6RkWtVx7Q2EnO82mGqAkdyXKGeXKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:33:21.997079Z"},"content_sha256":"677c9d73d14d4432053c1a73d4661248cf7903dc4f251179a3da39789da2aa16","schema_version":"1.0","event_id":"sha256:677c9d73d14d4432053c1a73d4661248cf7903dc4f251179a3da39789da2aa16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RG6QPK2FBSBNQ2XUCCL62C3CY/bundle.json","state_url":"https://pith.science/pith/5RG6QPK2FBSBNQ2XUCCL62C3CY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RG6QPK2FBSBNQ2XUCCL62C3CY/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":"2026-05-28T13:33:21Z","links":{"resolver":"https://pith.science/pith/5RG6QPK2FBSBNQ2XUCCL62C3CY","bundle":"https://pith.science/pith/5RG6QPK2FBSBNQ2XUCCL62C3CY/bundle.json","state":"https://pith.science/pith/5RG6QPK2FBSBNQ2XUCCL62C3CY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RG6QPK2FBSBNQ2XUCCL62C3CY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5RG6QPK2FBSBNQ2XUCCL62C3CY","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":"a6d4372e42d54b25448ee8f378ff8f707e647d220e7568bd04896b84e8b9f5f1","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-03T01:06:57Z","title_canon_sha256":"59cce09148ab9376361361f08413cb1581d1891d6ef940dad2659502f8f08028"},"schema_version":"1.0","source":{"id":"1612.00907","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00907","created_at":"2026-05-18T00:55:06Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00907v1","created_at":"2026-05-18T00:55:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00907","created_at":"2026-05-18T00:55:06Z"},{"alias_kind":"pith_short_12","alias_value":"5RG6QPK2FBSB","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5RG6QPK2FBSBNQ2X","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5RG6QPK2","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:677c9d73d14d4432053c1a73d4661248cf7903dc4f251179a3da39789da2aa16","target":"graph","created_at":"2026-05-18T00:55:06Z","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 have added a new multigrid in energy (MGE) preconditioner to the Denovo discrete-ordinates radiation transport code. This preconditioner takes advantage of a new multilevel parallel decomposition. A multigroup Krylov subspace iterative solver that is decomposed in energy as well as space-angle forms the backbone of the transport solves in Denovo. The space-angle-energy decomposition facilitates scaling to hundreds of thousands of cores. The multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of Krylov iterations required for convergenc","authors_text":"G. G. Davidson, P. P. H. Wilson, R. N. Slaybaugh, T. M. Evans","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-03T01:06:57Z","title":"Multigrid In Energy Preconditioner for Krylov Solvers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00907","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":"sha256:2c18d86c0aa0691d242fe21b1f234f82f60972b2927d50aa39e9d01614921849","target":"record","created_at":"2026-05-18T00:55:06Z","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":"a6d4372e42d54b25448ee8f378ff8f707e647d220e7568bd04896b84e8b9f5f1","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-03T01:06:57Z","title_canon_sha256":"59cce09148ab9376361361f08413cb1581d1891d6ef940dad2659502f8f08028"},"schema_version":"1.0","source":{"id":"1612.00907","kind":"arxiv","version":1}},"canonical_sha256":"ec4de83d5a286416c357a084bf685b1636f7567a675c88b3a437996da2885986","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec4de83d5a286416c357a084bf685b1636f7567a675c88b3a437996da2885986","first_computed_at":"2026-05-18T00:55:06.342507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:06.342507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LLWIYGwbO/LqXT1f4u8kKnq915+7UfZmAbMzl9yD+KRi1CnqCXHfUQBSKGjXUTH+4iCD9Rxk2TbiRakKOd6vDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:06.343254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00907","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c18d86c0aa0691d242fe21b1f234f82f60972b2927d50aa39e9d01614921849","sha256:677c9d73d14d4432053c1a73d4661248cf7903dc4f251179a3da39789da2aa16"],"state_sha256":"ffbf8f62c2bf165d76cc093885c5dbb261df66221557aebfc8baba902b8e870a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FxjKwjC1KcjjbKzSrbnqj1mTcc2VkfDOwHsXvGFvJHqUE170St8NNRNknPCj47RZO/lI+lNFb3lm9KiDrxMLCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:33:21.999113Z","bundle_sha256":"96c7943e5ca604fc969db1a5363d1fc83d6a4ae2f51d790e0faface376a3435b"}}