{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VHHHZQ5CTUUBUORRS6R2G2EBIV","short_pith_number":"pith:VHHHZQ5C","canonical_record":{"source":{"id":"1703.02456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-03-04T16:48:27Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"91264abb25ebdd5f8f22ecaef30bd0a1fbbedffe22b7164e1d45b8e0825b7520","abstract_canon_sha256":"191d53f591b3cc0c86c9c57193ba1327485aa58141b45b7c138b5af979e80b89"},"schema_version":"1.0"},"canonical_sha256":"a9ce7cc3a29d281a3a3197a3a36881454ee2417961268eb1deea67a9c34868c6","source":{"kind":"arxiv","id":"1703.02456","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02456","created_at":"2026-06-04T18:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02456v2","created_at":"2026-06-04T18:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02456","created_at":"2026-06-04T18:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"VHHHZQ5CTUUB","created_at":"2026-06-04T18:10:33Z"},{"alias_kind":"pith_short_16","alias_value":"VHHHZQ5CTUUBUORR","created_at":"2026-06-04T18:10:33Z"},{"alias_kind":"pith_short_8","alias_value":"VHHHZQ5C","created_at":"2026-06-04T18:10:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VHHHZQ5CTUUBUORRS6R2G2EBIV","target":"record","payload":{"canonical_record":{"source":{"id":"1703.02456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-03-04T16:48:27Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"91264abb25ebdd5f8f22ecaef30bd0a1fbbedffe22b7164e1d45b8e0825b7520","abstract_canon_sha256":"191d53f591b3cc0c86c9c57193ba1327485aa58141b45b7c138b5af979e80b89"},"schema_version":"1.0"},"canonical_sha256":"a9ce7cc3a29d281a3a3197a3a36881454ee2417961268eb1deea67a9c34868c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T18:10:33.614601Z","signature_b64":"Heh70U1GlhpqZOJBERrm3LZjwGRUO2ym+lbStn4FWqkmU+blhGekA4zMypx4uq948A7w4p0heS0G4Dm5ngiqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9ce7cc3a29d281a3a3197a3a36881454ee2417961268eb1deea67a9c34868c6","last_reissued_at":"2026-06-04T18:10:33.614005Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T18:10:33.614005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.02456","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T18:10:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EnNIYVaNC1iMX9fPOcS6AT97dsqyADVcHluzQf95lgl1vwG5ObDCpljgVG7eZeBK2qKUuqkwltPovnf5Yl2PDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:12:40.795023Z"},"content_sha256":"fb84298a0cf456192370ebb1e6c832950cac1287f0df62b3fcabdd2409f38f77","schema_version":"1.0","event_id":"sha256:fb84298a0cf456192370ebb1e6c832950cac1287f0df62b3fcabdd2409f38f77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VHHHZQ5CTUUBUORRS6R2G2EBIV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A General Algorithm to Calculate the Inverse Principal $p$-th Root of Symmetric Positive Definite Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.RA","authors_text":"Andrea Walther, Christian Plessl, Dorothee Richters, Michael Lass, Thomas D. K\\\"uhne","submitted_at":"2017-03-04T16:48:27Z","abstract_excerpt":"We address the general mathematical problem of computing the inverse $p$-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary $p$-th roots and their inverses of symmetric positive definite matrices is presented. We show that the order of convergence is at least quadratic and that adaptively adjusting a parameter $q$ always leads to an even faster convergence. In this way, a better performance than with previously known iteration schemes is achieved. The efficiency of the iterative functions is demonstrated for various mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02456","kind":"arxiv","version":2},"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/1703.02456/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":"2026-06-04T18:10:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NVT0E0j5LuxBUUZIf25b3axxEGYCezhrd27FcONH3P+utUhWrP36d16Yivt7Rp5hhNap4bbOjnjFdO/l8UvMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:12:40.795401Z"},"content_sha256":"448eb69d504f9e4b3125830c77f90431bc2a71706b469f5ba541700fc11a22ab","schema_version":"1.0","event_id":"sha256:448eb69d504f9e4b3125830c77f90431bc2a71706b469f5ba541700fc11a22ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VHHHZQ5CTUUBUORRS6R2G2EBIV/bundle.json","state_url":"https://pith.science/pith/VHHHZQ5CTUUBUORRS6R2G2EBIV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VHHHZQ5CTUUBUORRS6R2G2EBIV/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":"2026-07-07T14:12:40Z","links":{"resolver":"https://pith.science/pith/VHHHZQ5CTUUBUORRS6R2G2EBIV","bundle":"https://pith.science/pith/VHHHZQ5CTUUBUORRS6R2G2EBIV/bundle.json","state":"https://pith.science/pith/VHHHZQ5CTUUBUORRS6R2G2EBIV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VHHHZQ5CTUUBUORRS6R2G2EBIV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VHHHZQ5CTUUBUORRS6R2G2EBIV","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":"191d53f591b3cc0c86c9c57193ba1327485aa58141b45b7c138b5af979e80b89","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-03-04T16:48:27Z","title_canon_sha256":"91264abb25ebdd5f8f22ecaef30bd0a1fbbedffe22b7164e1d45b8e0825b7520"},"schema_version":"1.0","source":{"id":"1703.02456","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02456","created_at":"2026-06-04T18:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02456v2","created_at":"2026-06-04T18:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02456","created_at":"2026-06-04T18:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"VHHHZQ5CTUUB","created_at":"2026-06-04T18:10:33Z"},{"alias_kind":"pith_short_16","alias_value":"VHHHZQ5CTUUBUORR","created_at":"2026-06-04T18:10:33Z"},{"alias_kind":"pith_short_8","alias_value":"VHHHZQ5C","created_at":"2026-06-04T18:10:33Z"}],"graph_snapshots":[{"event_id":"sha256:448eb69d504f9e4b3125830c77f90431bc2a71706b469f5ba541700fc11a22ab","target":"graph","created_at":"2026-06-04T18:10:33Z","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/1703.02456/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We address the general mathematical problem of computing the inverse $p$-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary $p$-th roots and their inverses of symmetric positive definite matrices is presented. We show that the order of convergence is at least quadratic and that adaptively adjusting a parameter $q$ always leads to an even faster convergence. In this way, a better performance than with previously known iteration schemes is achieved. The efficiency of the iterative functions is demonstrated for various mat","authors_text":"Andrea Walther, Christian Plessl, Dorothee Richters, Michael Lass, Thomas D. K\\\"uhne","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-03-04T16:48:27Z","title":"A General Algorithm to Calculate the Inverse Principal $p$-th Root of Symmetric Positive Definite Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02456","kind":"arxiv","version":2},"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:fb84298a0cf456192370ebb1e6c832950cac1287f0df62b3fcabdd2409f38f77","target":"record","created_at":"2026-06-04T18:10:33Z","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":"191d53f591b3cc0c86c9c57193ba1327485aa58141b45b7c138b5af979e80b89","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-03-04T16:48:27Z","title_canon_sha256":"91264abb25ebdd5f8f22ecaef30bd0a1fbbedffe22b7164e1d45b8e0825b7520"},"schema_version":"1.0","source":{"id":"1703.02456","kind":"arxiv","version":2}},"canonical_sha256":"a9ce7cc3a29d281a3a3197a3a36881454ee2417961268eb1deea67a9c34868c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9ce7cc3a29d281a3a3197a3a36881454ee2417961268eb1deea67a9c34868c6","first_computed_at":"2026-06-04T18:10:33.614005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T18:10:33.614005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Heh70U1GlhpqZOJBERrm3LZjwGRUO2ym+lbStn4FWqkmU+blhGekA4zMypx4uq948A7w4p0heS0G4Dm5ngiqBA==","signature_status":"signed_v1","signed_at":"2026-06-04T18:10:33.614601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.02456","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb84298a0cf456192370ebb1e6c832950cac1287f0df62b3fcabdd2409f38f77","sha256:448eb69d504f9e4b3125830c77f90431bc2a71706b469f5ba541700fc11a22ab"],"state_sha256":"20acb5e58443a71e2f4f160f195e2f72d19ddb763e16fa9cf17fb95f1b8e723f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5jfpJXgltn7HtwqrsDOUzM5eMCsbbhQcqGSvmNp9nTv5mnE2nZt3lANEI2w/hAF6Fb5sPXaMWUd39w5Uk+0LAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T14:12:40.797343Z","bundle_sha256":"6e695c1acfdfe5a7102874402767f0e3d59f8398fe651d4c2fd27d6bbef629dc"}}