{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EVY45Z6V3UTELX3P4WSTUEO3XC","short_pith_number":"pith:EVY45Z6V","canonical_record":{"source":{"id":"1810.01464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-02T19:19:26Z","cross_cats_sorted":[],"title_canon_sha256":"4724ec62f651fe04f1ac1fa66a1c53d153eca8cec27910313976ff22b021fb3f","abstract_canon_sha256":"992d1645c9ce5893cea4f6f7e3e033e15998738a0c4703603f972abb7d64d969"},"schema_version":"1.0"},"canonical_sha256":"2571cee7d5dd2645df6fe5a53a11dbb88e5c30ee4f85c230377e4a31c2e589c4","source":{"kind":"arxiv","id":"1810.01464","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01464","created_at":"2026-05-18T00:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01464v1","created_at":"2026-05-18T00:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01464","created_at":"2026-05-18T00:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"EVY45Z6V3UTE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EVY45Z6V3UTELX3P","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EVY45Z6V","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EVY45Z6V3UTELX3P4WSTUEO3XC","target":"record","payload":{"canonical_record":{"source":{"id":"1810.01464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-02T19:19:26Z","cross_cats_sorted":[],"title_canon_sha256":"4724ec62f651fe04f1ac1fa66a1c53d153eca8cec27910313976ff22b021fb3f","abstract_canon_sha256":"992d1645c9ce5893cea4f6f7e3e033e15998738a0c4703603f972abb7d64d969"},"schema_version":"1.0"},"canonical_sha256":"2571cee7d5dd2645df6fe5a53a11dbb88e5c30ee4f85c230377e4a31c2e589c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:12.157015Z","signature_b64":"UXTYFktNOH1GFdYGiZ2xzQ9vmJXNw1XFVYtyPdideneqrJFO3fXpInseZNOpOYqB9pYhtsD4pT6I3HyJYnHxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2571cee7d5dd2645df6fe5a53a11dbb88e5c30ee4f85c230377e4a31c2e589c4","last_reissued_at":"2026-05-18T00:04:12.156224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:12.156224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.01464","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":"2026-05-18T00:04:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H7butYsppPj5Kdsjbft7lxO2X+Uv/yo2O5qiRJvS5JgNGYrJ3Sxiq+bL+aOXg1CEM/ZLZE4uctAA46/quKA+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:16:57.156600Z"},"content_sha256":"5e3c0be0bb8dcfc41f3723a57176fd13b4f28075bb8cd32d3fe180427cd4525e","schema_version":"1.0","event_id":"sha256:5e3c0be0bb8dcfc41f3723a57176fd13b4f28075bb8cd32d3fe180427cd4525e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EVY45Z6V3UTELX3P4WSTUEO3XC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbation theory for the matrix square root and matrix modulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marcus Carlsson","submitted_at":"2018-10-02T19:19:26Z","abstract_excerpt":"We provide first order perturbation formulas for the matrix square root (in the positive semi-definite case) and the matrix modulus (in the general case). The results are new for singular matrices, and extend previously known Fr\\'{e}chet differentiability formulas provided by the Daleckii-Krein theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01464","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":"2026-05-18T00:04:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZqQ8dYTCZIe5dGvlI2R3zLmv2gO1HmFTfevGs5HyLZQ4zBsLZ7WQ+IKqxBCYwmX0oCn3WG5gb1Sl1ym8K2P5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:16:57.157308Z"},"content_sha256":"74af3f1e6ee3168cb2e685e4f21c8d6a23c28a2d7bf60c48d30b58bfe3eab127","schema_version":"1.0","event_id":"sha256:74af3f1e6ee3168cb2e685e4f21c8d6a23c28a2d7bf60c48d30b58bfe3eab127"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EVY45Z6V3UTELX3P4WSTUEO3XC/bundle.json","state_url":"https://pith.science/pith/EVY45Z6V3UTELX3P4WSTUEO3XC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EVY45Z6V3UTELX3P4WSTUEO3XC/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":"2026-06-06T15:16:57Z","links":{"resolver":"https://pith.science/pith/EVY45Z6V3UTELX3P4WSTUEO3XC","bundle":"https://pith.science/pith/EVY45Z6V3UTELX3P4WSTUEO3XC/bundle.json","state":"https://pith.science/pith/EVY45Z6V3UTELX3P4WSTUEO3XC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EVY45Z6V3UTELX3P4WSTUEO3XC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EVY45Z6V3UTELX3P4WSTUEO3XC","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":"992d1645c9ce5893cea4f6f7e3e033e15998738a0c4703603f972abb7d64d969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-02T19:19:26Z","title_canon_sha256":"4724ec62f651fe04f1ac1fa66a1c53d153eca8cec27910313976ff22b021fb3f"},"schema_version":"1.0","source":{"id":"1810.01464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01464","created_at":"2026-05-18T00:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01464v1","created_at":"2026-05-18T00:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01464","created_at":"2026-05-18T00:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"EVY45Z6V3UTE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EVY45Z6V3UTELX3P","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EVY45Z6V","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:74af3f1e6ee3168cb2e685e4f21c8d6a23c28a2d7bf60c48d30b58bfe3eab127","target":"graph","created_at":"2026-05-18T00:04:12Z","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"},"paper":{"abstract_excerpt":"We provide first order perturbation formulas for the matrix square root (in the positive semi-definite case) and the matrix modulus (in the general case). The results are new for singular matrices, and extend previously known Fr\\'{e}chet differentiability formulas provided by the Daleckii-Krein theorem.","authors_text":"Marcus Carlsson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-02T19:19:26Z","title":"Perturbation theory for the matrix square root and matrix modulus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01464","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":"sha256:5e3c0be0bb8dcfc41f3723a57176fd13b4f28075bb8cd32d3fe180427cd4525e","target":"record","created_at":"2026-05-18T00:04:12Z","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":"992d1645c9ce5893cea4f6f7e3e033e15998738a0c4703603f972abb7d64d969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-02T19:19:26Z","title_canon_sha256":"4724ec62f651fe04f1ac1fa66a1c53d153eca8cec27910313976ff22b021fb3f"},"schema_version":"1.0","source":{"id":"1810.01464","kind":"arxiv","version":1}},"canonical_sha256":"2571cee7d5dd2645df6fe5a53a11dbb88e5c30ee4f85c230377e4a31c2e589c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2571cee7d5dd2645df6fe5a53a11dbb88e5c30ee4f85c230377e4a31c2e589c4","first_computed_at":"2026-05-18T00:04:12.156224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:12.156224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UXTYFktNOH1GFdYGiZ2xzQ9vmJXNw1XFVYtyPdideneqrJFO3fXpInseZNOpOYqB9pYhtsD4pT6I3HyJYnHxBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:12.157015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.01464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e3c0be0bb8dcfc41f3723a57176fd13b4f28075bb8cd32d3fe180427cd4525e","sha256:74af3f1e6ee3168cb2e685e4f21c8d6a23c28a2d7bf60c48d30b58bfe3eab127"],"state_sha256":"8ed1756f965a8be313cd268a520ed5b9545e59ff393e10d52c2341896c0555dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQtizj0WrrQ2NqjZTx9qHO8u9upbq02pJe9bTXn18hMVejpb4mtuvfPQ0ldma80omwric9Co5/7+yW0BPXdJBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:16:57.160515Z","bundle_sha256":"4fc5753a22eaae40d51d25789fc103f489aaed0cec531f13a64d83de5dcedac5"}}