{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:VVMYUR5XXZ6R6M6EO3FIM6TSRI","short_pith_number":"pith:VVMYUR5X","canonical_record":{"source":{"id":"2002.05001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-02-11T14:51:31Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"9c2528d4e2b50428454f00c339e662bca5291f206029a1fc4bfbdcbdbaafdc8e","abstract_canon_sha256":"07f0fe32a71bc3fc8a1cbb48c2e5f8183c2ed45e43c94c1f3a383098c85c08f9"},"schema_version":"1.0"},"canonical_sha256":"ad598a47b7be7d1f33c476ca867a728a14f70bf551ca0fcf59d45d5b0d1902ed","source":{"kind":"arxiv","id":"2002.05001","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.05001","created_at":"2026-07-05T04:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"2002.05001v2","created_at":"2026-07-05T04:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.05001","created_at":"2026-07-05T04:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"VVMYUR5XXZ6R","created_at":"2026-07-05T04:17:12Z"},{"alias_kind":"pith_short_16","alias_value":"VVMYUR5XXZ6R6M6E","created_at":"2026-07-05T04:17:12Z"},{"alias_kind":"pith_short_8","alias_value":"VVMYUR5X","created_at":"2026-07-05T04:17:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:VVMYUR5XXZ6R6M6EO3FIM6TSRI","target":"record","payload":{"canonical_record":{"source":{"id":"2002.05001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-02-11T14:51:31Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"9c2528d4e2b50428454f00c339e662bca5291f206029a1fc4bfbdcbdbaafdc8e","abstract_canon_sha256":"07f0fe32a71bc3fc8a1cbb48c2e5f8183c2ed45e43c94c1f3a383098c85c08f9"},"schema_version":"1.0"},"canonical_sha256":"ad598a47b7be7d1f33c476ca867a728a14f70bf551ca0fcf59d45d5b0d1902ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:17:12.084509Z","signature_b64":"DaVyee1cf18VSZdGju4/25bxz7GtY8COJsDX2erzkQmKVibdRwkR/hkbQc7Ejdl0WvCj+sIeBfTZNcskukPKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad598a47b7be7d1f33c476ca867a728a14f70bf551ca0fcf59d45d5b0d1902ed","last_reissued_at":"2026-07-05T04:17:12.084084Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:17:12.084084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.05001","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":"2026-07-05T04:17:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lvSSbw+72JQ2ph3tCeUWTFvxDSc1bl8qAEilkdPYl+GvxK2GA4zO7XATeaDAsfPfot3uK18tEyd8oycFappqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T13:46:01.836561Z"},"content_sha256":"2004262359304532319ab9fc5883e1d1e8c1fc2bb06c575f2a2310439f1f77d2","schema_version":"1.0","event_id":"sha256:2004262359304532319ab9fc5883e1d1e8c1fc2bb06c575f2a2310439f1f77d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:VVMYUR5XXZ6R6M6EO3FIM6TSRI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Tutorial on Matrix Perturbation Theory (using compact matrix notation)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"Bassam Bamieh","submitted_at":"2020-02-11T14:51:31Z","abstract_excerpt":"Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In this note, we give an introduction to this method that is independent of any physics notions, and relies purely on concepts from linear algebra. An additional feature of this presentation is that matrix notation and methods are used throughout. In particular, we formulate the equations for each term of the analytic expansions of eigenvalues and eigenvectors as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.05001","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/2002.05001/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":"2026-07-05T04:17:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gm/rVi+Kqxuh8mG1RyB7RFH8gWvtb5qi6E7+8cD50y8Zwc/oTLBIz6eXt3H9LdzlNxX/1q+nnIodv5qh+HUWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T13:46:01.837073Z"},"content_sha256":"326a4aa4c6cd0ee723cd0ab7abbc9febc1c32aa776068452e8b0bff852e12fed","schema_version":"1.0","event_id":"sha256:326a4aa4c6cd0ee723cd0ab7abbc9febc1c32aa776068452e8b0bff852e12fed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVMYUR5XXZ6R6M6EO3FIM6TSRI/bundle.json","state_url":"https://pith.science/pith/VVMYUR5XXZ6R6M6EO3FIM6TSRI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVMYUR5XXZ6R6M6EO3FIM6TSRI/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":"2026-08-10T13:46:01Z","links":{"resolver":"https://pith.science/pith/VVMYUR5XXZ6R6M6EO3FIM6TSRI","bundle":"https://pith.science/pith/VVMYUR5XXZ6R6M6EO3FIM6TSRI/bundle.json","state":"https://pith.science/pith/VVMYUR5XXZ6R6M6EO3FIM6TSRI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVMYUR5XXZ6R6M6EO3FIM6TSRI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:VVMYUR5XXZ6R6M6EO3FIM6TSRI","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":"07f0fe32a71bc3fc8a1cbb48c2e5f8183c2ed45e43c94c1f3a383098c85c08f9","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-02-11T14:51:31Z","title_canon_sha256":"9c2528d4e2b50428454f00c339e662bca5291f206029a1fc4bfbdcbdbaafdc8e"},"schema_version":"1.0","source":{"id":"2002.05001","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.05001","created_at":"2026-07-05T04:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"2002.05001v2","created_at":"2026-07-05T04:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.05001","created_at":"2026-07-05T04:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"VVMYUR5XXZ6R","created_at":"2026-07-05T04:17:12Z"},{"alias_kind":"pith_short_16","alias_value":"VVMYUR5XXZ6R6M6E","created_at":"2026-07-05T04:17:12Z"},{"alias_kind":"pith_short_8","alias_value":"VVMYUR5X","created_at":"2026-07-05T04:17:12Z"}],"graph_snapshots":[{"event_id":"sha256:326a4aa4c6cd0ee723cd0ab7abbc9febc1c32aa776068452e8b0bff852e12fed","target":"graph","created_at":"2026-07-05T04:17:12Z","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/2002.05001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In this note, we give an introduction to this method that is independent of any physics notions, and relies purely on concepts from linear algebra. An additional feature of this presentation is that matrix notation and methods are used throughout. In particular, we formulate the equations for each term of the analytic expansions of eigenvalues and eigenvectors as ","authors_text":"Bassam Bamieh","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-02-11T14:51:31Z","title":"A Tutorial on Matrix Perturbation Theory (using compact matrix notation)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.05001","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":"sha256:2004262359304532319ab9fc5883e1d1e8c1fc2bb06c575f2a2310439f1f77d2","target":"record","created_at":"2026-07-05T04:17:12Z","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":"07f0fe32a71bc3fc8a1cbb48c2e5f8183c2ed45e43c94c1f3a383098c85c08f9","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-02-11T14:51:31Z","title_canon_sha256":"9c2528d4e2b50428454f00c339e662bca5291f206029a1fc4bfbdcbdbaafdc8e"},"schema_version":"1.0","source":{"id":"2002.05001","kind":"arxiv","version":2}},"canonical_sha256":"ad598a47b7be7d1f33c476ca867a728a14f70bf551ca0fcf59d45d5b0d1902ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad598a47b7be7d1f33c476ca867a728a14f70bf551ca0fcf59d45d5b0d1902ed","first_computed_at":"2026-07-05T04:17:12.084084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:17:12.084084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DaVyee1cf18VSZdGju4/25bxz7GtY8COJsDX2erzkQmKVibdRwkR/hkbQc7Ejdl0WvCj+sIeBfTZNcskukPKAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:17:12.084509Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.05001","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2004262359304532319ab9fc5883e1d1e8c1fc2bb06c575f2a2310439f1f77d2","sha256:326a4aa4c6cd0ee723cd0ab7abbc9febc1c32aa776068452e8b0bff852e12fed"],"state_sha256":"a494c31abca2661f96ab906af4b0a99679b0a230cce344fdd5a09923e352a790"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J6wNWSli0U0rcgjKGq72sg0B8NNko5H8blpcYKVGoZJfpPhvysR0zwg5XeXaP5n7POzFo3LrVmI7LcLjzhycAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T13:46:01.841516Z","bundle_sha256":"661aaf5c94b3f73fe28fd2db615addafe5fd5029a01f3682de6e7dd635e3c6aa"}}