{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:V3I4O37HDNUPH5KFBX52WLPVFJ","short_pith_number":"pith:V3I4O37H","canonical_record":{"source":{"id":"2204.01722","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MS","submitted_at":"2022-04-04T04:41:24Z","cross_cats_sorted":["cs.CE","cs.DC","cs.NA","math.NA"],"title_canon_sha256":"36eb200db9b747165b18a98259469f371abf9aa7a6ba2a26193d32cb76b27459","abstract_canon_sha256":"f4db72de1881f74de8b2392af251b724c89e47bce2da9227b38a2855fe42e47c"},"schema_version":"1.0"},"canonical_sha256":"aed1c76fe71b68f3f5450dfbab2df52a7281c6855d3da385bf00979f7416a0e6","source":{"kind":"arxiv","id":"2204.01722","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.01722","created_at":"2026-07-05T04:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"2204.01722v3","created_at":"2026-07-05T04:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.01722","created_at":"2026-07-05T04:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"V3I4O37HDNUP","created_at":"2026-07-05T04:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"V3I4O37HDNUPH5KF","created_at":"2026-07-05T04:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"V3I4O37H","created_at":"2026-07-05T04:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:V3I4O37HDNUPH5KFBX52WLPVFJ","target":"record","payload":{"canonical_record":{"source":{"id":"2204.01722","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MS","submitted_at":"2022-04-04T04:41:24Z","cross_cats_sorted":["cs.CE","cs.DC","cs.NA","math.NA"],"title_canon_sha256":"36eb200db9b747165b18a98259469f371abf9aa7a6ba2a26193d32cb76b27459","abstract_canon_sha256":"f4db72de1881f74de8b2392af251b724c89e47bce2da9227b38a2855fe42e47c"},"schema_version":"1.0"},"canonical_sha256":"aed1c76fe71b68f3f5450dfbab2df52a7281c6855d3da385bf00979f7416a0e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:26:00.508335Z","signature_b64":"DQHV3l3cs2k3dG6M5+amgZoPv4M76SM4QBYZDfJ6tJUT6eA900bYD4SLsj6BycQWBm48NrLQnFjnNvblj3ubDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aed1c76fe71b68f3f5450dfbab2df52a7281c6855d3da385bf00979f7416a0e6","last_reissued_at":"2026-07-05T04:26:00.507849Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:26:00.507849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.01722","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":"2026-07-05T04:26:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"39xK0ma7yebyYFItsr4/FRdHAZl24TA9E3kDnU4xCi9hyViPmXH/YRhBpSpezF9XC14MapYElvgyrv8gMssnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:28:21.559689Z"},"content_sha256":"16714a330af78b7e18dc452808344def104d76cf0d0ae092aa5e77bb4c503785","schema_version":"1.0","event_id":"sha256:16714a330af78b7e18dc452808344def104d76cf0d0ae092aa5e77bb4c503785"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:V3I4O37HDNUPH5KFBX52WLPVFJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CE","cs.DC","cs.NA","math.NA"],"primary_cat":"cs.MS","authors_text":"Jed Brown, Jeremy L. Thompson, Junchao Zhang, Karen Stengel, Leila Ghaffari, Matthew Knepley, Natalie Beams, Rezgar Shakeri, Valeria Barra, William Moses","submitted_at":"2022-04-04T04:41:24Z","abstract_excerpt":"Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models and numerical experiments to demonstrate that high-order methods greatly reduce the costs to reach engineering tolerances while enabling effective use of GPUs; these data structures also offer up to 2x benefit for linear elements. We demonstrate the reliability, efficiency, and scalability of matrix-free $p$-multigrid methods with algebraic multigrid coarse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.01722","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.01722/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":"2026-07-05T04:26:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sVBdhQFOaQtnSYyFcIXZisWEfuNKuGhCblAkfCyyDLvNXdtT6dApry5+RuUFyb5/a8Er/Y7HSFr9SXKRPFAqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:28:21.560675Z"},"content_sha256":"2389c7ac4eb384289b2dbae1ea5159d4c1c45c5bfb1112b614cf40bc453aa92c","schema_version":"1.0","event_id":"sha256:2389c7ac4eb384289b2dbae1ea5159d4c1c45c5bfb1112b614cf40bc453aa92c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V3I4O37HDNUPH5KFBX52WLPVFJ/bundle.json","state_url":"https://pith.science/pith/V3I4O37HDNUPH5KFBX52WLPVFJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V3I4O37HDNUPH5KFBX52WLPVFJ/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":"2026-08-09T09:28:21Z","links":{"resolver":"https://pith.science/pith/V3I4O37HDNUPH5KFBX52WLPVFJ","bundle":"https://pith.science/pith/V3I4O37HDNUPH5KFBX52WLPVFJ/bundle.json","state":"https://pith.science/pith/V3I4O37HDNUPH5KFBX52WLPVFJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V3I4O37HDNUPH5KFBX52WLPVFJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:V3I4O37HDNUPH5KFBX52WLPVFJ","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":"f4db72de1881f74de8b2392af251b724c89e47bce2da9227b38a2855fe42e47c","cross_cats_sorted":["cs.CE","cs.DC","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MS","submitted_at":"2022-04-04T04:41:24Z","title_canon_sha256":"36eb200db9b747165b18a98259469f371abf9aa7a6ba2a26193d32cb76b27459"},"schema_version":"1.0","source":{"id":"2204.01722","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.01722","created_at":"2026-07-05T04:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"2204.01722v3","created_at":"2026-07-05T04:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.01722","created_at":"2026-07-05T04:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"V3I4O37HDNUP","created_at":"2026-07-05T04:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"V3I4O37HDNUPH5KF","created_at":"2026-07-05T04:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"V3I4O37H","created_at":"2026-07-05T04:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:2389c7ac4eb384289b2dbae1ea5159d4c1c45c5bfb1112b614cf40bc453aa92c","target":"graph","created_at":"2026-07-05T04:26:00Z","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/2204.01722/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models and numerical experiments to demonstrate that high-order methods greatly reduce the costs to reach engineering tolerances while enabling effective use of GPUs; these data structures also offer up to 2x benefit for linear elements. We demonstrate the reliability, efficiency, and scalability of matrix-free $p$-multigrid methods with algebraic multigrid coarse","authors_text":"Jed Brown, Jeremy L. Thompson, Junchao Zhang, Karen Stengel, Leila Ghaffari, Matthew Knepley, Natalie Beams, Rezgar Shakeri, Valeria Barra, William Moses","cross_cats":["cs.CE","cs.DC","cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MS","submitted_at":"2022-04-04T04:41:24Z","title":"Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.01722","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":"sha256:16714a330af78b7e18dc452808344def104d76cf0d0ae092aa5e77bb4c503785","target":"record","created_at":"2026-07-05T04:26:00Z","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":"f4db72de1881f74de8b2392af251b724c89e47bce2da9227b38a2855fe42e47c","cross_cats_sorted":["cs.CE","cs.DC","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MS","submitted_at":"2022-04-04T04:41:24Z","title_canon_sha256":"36eb200db9b747165b18a98259469f371abf9aa7a6ba2a26193d32cb76b27459"},"schema_version":"1.0","source":{"id":"2204.01722","kind":"arxiv","version":3}},"canonical_sha256":"aed1c76fe71b68f3f5450dfbab2df52a7281c6855d3da385bf00979f7416a0e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aed1c76fe71b68f3f5450dfbab2df52a7281c6855d3da385bf00979f7416a0e6","first_computed_at":"2026-07-05T04:26:00.507849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:26:00.507849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DQHV3l3cs2k3dG6M5+amgZoPv4M76SM4QBYZDfJ6tJUT6eA900bYD4SLsj6BycQWBm48NrLQnFjnNvblj3ubDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:26:00.508335Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.01722","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16714a330af78b7e18dc452808344def104d76cf0d0ae092aa5e77bb4c503785","sha256:2389c7ac4eb384289b2dbae1ea5159d4c1c45c5bfb1112b614cf40bc453aa92c"],"state_sha256":"872eab02ea16c86405e2bec2b47ccb31f52fc2cbbacb4977cdb8dedec71581b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82CrWHs8A2vIWhg/fGzraGGvZ+Irf8NAHbKNYEy8vC49YHaQ7CYCq+znk+8AnbbIEbaA4XiuwfSLGLdgSDoCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T09:28:21.567877Z","bundle_sha256":"5c960a2526fbaa1117b98ad5f3476dedb2c63912545264742557ea2d0d52e178"}}