{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:YMLSXBDVM3CBHBHUBX2A5CWWCZ","short_pith_number":"pith:YMLSXBDV","canonical_record":{"source":{"id":"2008.00927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-08-03T15:03:17Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"d5f63f6097dfcf06b47683f721775793f4e4822aa5ab470db346af9450c2c752","abstract_canon_sha256":"15207fb995eb7e3e77fc1ca8cb86d5f815cd2d38dd9c27f201101eeb26085f95"},"schema_version":"1.0"},"canonical_sha256":"c3172b847566c41384f40df40e8ad6164b03a040684ebf048a3b29a447a6a587","source":{"kind":"arxiv","id":"2008.00927","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.00927","created_at":"2026-07-05T01:24:12Z"},{"alias_kind":"arxiv_version","alias_value":"2008.00927v1","created_at":"2026-07-05T01:24:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.00927","created_at":"2026-07-05T01:24:12Z"},{"alias_kind":"pith_short_12","alias_value":"YMLSXBDVM3CB","created_at":"2026-07-05T01:24:12Z"},{"alias_kind":"pith_short_16","alias_value":"YMLSXBDVM3CBHBHU","created_at":"2026-07-05T01:24:12Z"},{"alias_kind":"pith_short_8","alias_value":"YMLSXBDV","created_at":"2026-07-05T01:24:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:YMLSXBDVM3CBHBHUBX2A5CWWCZ","target":"record","payload":{"canonical_record":{"source":{"id":"2008.00927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-08-03T15:03:17Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"d5f63f6097dfcf06b47683f721775793f4e4822aa5ab470db346af9450c2c752","abstract_canon_sha256":"15207fb995eb7e3e77fc1ca8cb86d5f815cd2d38dd9c27f201101eeb26085f95"},"schema_version":"1.0"},"canonical_sha256":"c3172b847566c41384f40df40e8ad6164b03a040684ebf048a3b29a447a6a587","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:24:12.415669Z","signature_b64":"VAYBme7cHRkqM9A1vrpTHt3VCcQN5JfelWzQqYBFM2RNejY0jTK1NF0f0ktY/nBxHt8c3tlKN79mLNOiXIs0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3172b847566c41384f40df40e8ad6164b03a040684ebf048a3b29a447a6a587","last_reissued_at":"2026-07-05T01:24:12.415191Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:24:12.415191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.00927","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":"2026-07-05T01:24:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aw8fpd4gohreLENbU9X7Iyhtfpt8i8uOrRwVuM3myATipXfmFycN0vRZ/EldMaTgVhhP4MCV/YpQHr5ERcrjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:16:41.481478Z"},"content_sha256":"600905228a528e077a1e6b6ab314ea4c5d578f1791a72eced13642300fb5b400","schema_version":"1.0","event_id":"sha256:600905228a528e077a1e6b6ab314ea4c5d578f1791a72eced13642300fb5b400"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:YMLSXBDVM3CBHBHUBX2A5CWWCZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A parameter-dependent smoother for the multigrid method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Christian L\\\"obbert, Lars Grasedyck, Maren Klever, Tim A. Werthmann","submitted_at":"2020-08-03T15:03:17Z","abstract_excerpt":"The solution of parameter-dependent linear systems, by classical methods, leads to an arithmetic effort that grows exponentially in the number of parameters. This renders the multigrid method, which has a well understood convergence theory, infeasible. A parameter-dependent representation, e.g., a low-rank tensor format, can avoid this exponential dependence, but in these it is unknown how to calculate the inverse directly within the representation. The combination of these representations with the multigrid method requires a parameter-dependent version of the classical multigrid theory and a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.00927","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/2008.00927/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":"2026-07-05T01:24:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6Y0MAKpfuH7IN7ZID7TZY22aYzCjO0SZ9ixrkYfCMrGzXpZkfmQFqf/KjicIfagYdunHxXQY+rC7JMsyw47Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:16:41.482367Z"},"content_sha256":"b5baee1896eb80ce64ea7838162c520c5bef8a721f398377218c784b4f5c3367","schema_version":"1.0","event_id":"sha256:b5baee1896eb80ce64ea7838162c520c5bef8a721f398377218c784b4f5c3367"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YMLSXBDVM3CBHBHUBX2A5CWWCZ/bundle.json","state_url":"https://pith.science/pith/YMLSXBDVM3CBHBHUBX2A5CWWCZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YMLSXBDVM3CBHBHUBX2A5CWWCZ/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":"2026-08-12T13:16:41Z","links":{"resolver":"https://pith.science/pith/YMLSXBDVM3CBHBHUBX2A5CWWCZ","bundle":"https://pith.science/pith/YMLSXBDVM3CBHBHUBX2A5CWWCZ/bundle.json","state":"https://pith.science/pith/YMLSXBDVM3CBHBHUBX2A5CWWCZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YMLSXBDVM3CBHBHUBX2A5CWWCZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:YMLSXBDVM3CBHBHUBX2A5CWWCZ","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":"15207fb995eb7e3e77fc1ca8cb86d5f815cd2d38dd9c27f201101eeb26085f95","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-08-03T15:03:17Z","title_canon_sha256":"d5f63f6097dfcf06b47683f721775793f4e4822aa5ab470db346af9450c2c752"},"schema_version":"1.0","source":{"id":"2008.00927","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.00927","created_at":"2026-07-05T01:24:12Z"},{"alias_kind":"arxiv_version","alias_value":"2008.00927v1","created_at":"2026-07-05T01:24:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.00927","created_at":"2026-07-05T01:24:12Z"},{"alias_kind":"pith_short_12","alias_value":"YMLSXBDVM3CB","created_at":"2026-07-05T01:24:12Z"},{"alias_kind":"pith_short_16","alias_value":"YMLSXBDVM3CBHBHU","created_at":"2026-07-05T01:24:12Z"},{"alias_kind":"pith_short_8","alias_value":"YMLSXBDV","created_at":"2026-07-05T01:24:12Z"}],"graph_snapshots":[{"event_id":"sha256:b5baee1896eb80ce64ea7838162c520c5bef8a721f398377218c784b4f5c3367","target":"graph","created_at":"2026-07-05T01:24:12Z","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/2008.00927/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The solution of parameter-dependent linear systems, by classical methods, leads to an arithmetic effort that grows exponentially in the number of parameters. This renders the multigrid method, which has a well understood convergence theory, infeasible. A parameter-dependent representation, e.g., a low-rank tensor format, can avoid this exponential dependence, but in these it is unknown how to calculate the inverse directly within the representation. The combination of these representations with the multigrid method requires a parameter-dependent version of the classical multigrid theory and a ","authors_text":"Christian L\\\"obbert, Lars Grasedyck, Maren Klever, Tim A. Werthmann","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-08-03T15:03:17Z","title":"A parameter-dependent smoother for the multigrid method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.00927","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":"sha256:600905228a528e077a1e6b6ab314ea4c5d578f1791a72eced13642300fb5b400","target":"record","created_at":"2026-07-05T01:24:12Z","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":"15207fb995eb7e3e77fc1ca8cb86d5f815cd2d38dd9c27f201101eeb26085f95","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-08-03T15:03:17Z","title_canon_sha256":"d5f63f6097dfcf06b47683f721775793f4e4822aa5ab470db346af9450c2c752"},"schema_version":"1.0","source":{"id":"2008.00927","kind":"arxiv","version":1}},"canonical_sha256":"c3172b847566c41384f40df40e8ad6164b03a040684ebf048a3b29a447a6a587","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3172b847566c41384f40df40e8ad6164b03a040684ebf048a3b29a447a6a587","first_computed_at":"2026-07-05T01:24:12.415191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:24:12.415191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VAYBme7cHRkqM9A1vrpTHt3VCcQN5JfelWzQqYBFM2RNejY0jTK1NF0f0ktY/nBxHt8c3tlKN79mLNOiXIs0Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:24:12.415669Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.00927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:600905228a528e077a1e6b6ab314ea4c5d578f1791a72eced13642300fb5b400","sha256:b5baee1896eb80ce64ea7838162c520c5bef8a721f398377218c784b4f5c3367"],"state_sha256":"83da79105260c1ca1da77cdcaba1a6af15d6adb639413be59e413e99824fa58c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OVSUvvZhiNfWHlcO5hiGa8+rldCDy8Vq2PBJ8oiwCkWJwcQNls918BU7FGBP4blPxz1NzOvmxbPrKQE2bmdBAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T13:16:41.489515Z","bundle_sha256":"5083622ad6b77ad2ec865fa7a03681620054a8ef8261ee9ff0e17bb9304928a8"}}