{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GKAJ5U7NYNVF3LQ2JYO4SLT4ML","short_pith_number":"pith:GKAJ5U7N","canonical_record":{"source":{"id":"1404.4113","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-16T00:04:14Z","cross_cats_sorted":["math-ph","math.MP","math.PR","quant-ph"],"title_canon_sha256":"0960d7ea455fc0af66d3bf97d55db607630d3b007fa2266e429a6f68cf8f68bb","abstract_canon_sha256":"2b0ca76f2f2fdf65a08bce5fbfea03164fdf8c44dcd856690cae48451f2b9b95"},"schema_version":"1.0"},"canonical_sha256":"32809ed3edc36a5dae1a4e1dc92e7c62c032f09ddbf7930692f9dc7d915032e9","source":{"kind":"arxiv","id":"1404.4113","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4113","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4113v4","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4113","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"pith_short_12","alias_value":"GKAJ5U7NYNVF","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GKAJ5U7NYNVF3LQ2","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GKAJ5U7N","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GKAJ5U7NYNVF3LQ2JYO4SLT4ML","target":"record","payload":{"canonical_record":{"source":{"id":"1404.4113","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-16T00:04:14Z","cross_cats_sorted":["math-ph","math.MP","math.PR","quant-ph"],"title_canon_sha256":"0960d7ea455fc0af66d3bf97d55db607630d3b007fa2266e429a6f68cf8f68bb","abstract_canon_sha256":"2b0ca76f2f2fdf65a08bce5fbfea03164fdf8c44dcd856690cae48451f2b9b95"},"schema_version":"1.0"},"canonical_sha256":"32809ed3edc36a5dae1a4e1dc92e7c62c032f09ddbf7930692f9dc7d915032e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:02.082663Z","signature_b64":"G+iXhSd4WVKOi0VBzAWI/Scfsve6iQgZ5bf6onSS/9w/6FKHvVi/t+Cn62zTEQgK6v4TmiMSE/akfj20G+MgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32809ed3edc36a5dae1a4e1dc92e7c62c032f09ddbf7930692f9dc7d915032e9","last_reissued_at":"2026-05-18T01:20:02.081956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:02.081956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.4113","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S3QMl5Z4YSGnxFwC3tvfObkDCyVJB9RnuOABLypNuvIeiDy5fr2ufuo2xAv3xVrnX55zN9uxDRyhIkyVhK+KBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:31:54.418073Z"},"content_sha256":"4fb20f7fb8b3c1d0e5ca14720131e94fb98e66a082a2d78ef7278e7d76efc2e3","schema_version":"1.0","event_id":"sha256:4fb20f7fb8b3c1d0e5ca14720131e94fb98e66a082a2d78ef7278e7d76efc2e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GKAJ5U7NYNVF3LQ2JYO4SLT4ML","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalue Attraction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","quant-ph"],"primary_cat":"math.SP","authors_text":"Ramis Movassagh","submitted_at":"2014-04-16T00:04:14Z","abstract_excerpt":"We prove that the complex conjugate (c.c.) eigenvalues of a smoothly varying real matrix attract (Eq. 15). We offer a dynamical perspective on the motion and interaction of the eigenvalues in the complex plane, derive their governing equations and discuss applications. C.c. pairs closest to the real axis, or those that are ill-conditioned, attract most strongly and can collide to become exactly real. As an application we consider random perturbations of a fixed matrix $M$. If $M$ is Normal, the total expected force on any eigenvalue is shown to be only the attraction of its c.c. (Eq. 24) and w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4113","kind":"arxiv","version":4},"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":"2026-05-18T01:20:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cD/B+z4k6eHL6jNmvfRLA7AzDDslFoY0QORdRShEszX3WoaIgLylz0T3n3EzjPy3g0ESf60yNOYhrwhfkxYsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:31:54.418776Z"},"content_sha256":"6ba461b6dd9af733273f695c8c06d7dd58fc877be2edced3542567b1ed0d2d55","schema_version":"1.0","event_id":"sha256:6ba461b6dd9af733273f695c8c06d7dd58fc877be2edced3542567b1ed0d2d55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKAJ5U7NYNVF3LQ2JYO4SLT4ML/bundle.json","state_url":"https://pith.science/pith/GKAJ5U7NYNVF3LQ2JYO4SLT4ML/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKAJ5U7NYNVF3LQ2JYO4SLT4ML/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":"2026-05-26T04:31:54Z","links":{"resolver":"https://pith.science/pith/GKAJ5U7NYNVF3LQ2JYO4SLT4ML","bundle":"https://pith.science/pith/GKAJ5U7NYNVF3LQ2JYO4SLT4ML/bundle.json","state":"https://pith.science/pith/GKAJ5U7NYNVF3LQ2JYO4SLT4ML/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKAJ5U7NYNVF3LQ2JYO4SLT4ML/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GKAJ5U7NYNVF3LQ2JYO4SLT4ML","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":"2b0ca76f2f2fdf65a08bce5fbfea03164fdf8c44dcd856690cae48451f2b9b95","cross_cats_sorted":["math-ph","math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-16T00:04:14Z","title_canon_sha256":"0960d7ea455fc0af66d3bf97d55db607630d3b007fa2266e429a6f68cf8f68bb"},"schema_version":"1.0","source":{"id":"1404.4113","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4113","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4113v4","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4113","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"pith_short_12","alias_value":"GKAJ5U7NYNVF","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GKAJ5U7NYNVF3LQ2","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GKAJ5U7N","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:6ba461b6dd9af733273f695c8c06d7dd58fc877be2edced3542567b1ed0d2d55","target":"graph","created_at":"2026-05-18T01:20:02Z","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 prove that the complex conjugate (c.c.) eigenvalues of a smoothly varying real matrix attract (Eq. 15). We offer a dynamical perspective on the motion and interaction of the eigenvalues in the complex plane, derive their governing equations and discuss applications. C.c. pairs closest to the real axis, or those that are ill-conditioned, attract most strongly and can collide to become exactly real. As an application we consider random perturbations of a fixed matrix $M$. If $M$ is Normal, the total expected force on any eigenvalue is shown to be only the attraction of its c.c. (Eq. 24) and w","authors_text":"Ramis Movassagh","cross_cats":["math-ph","math.MP","math.PR","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-16T00:04:14Z","title":"Eigenvalue Attraction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4113","kind":"arxiv","version":4},"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":"sha256:4fb20f7fb8b3c1d0e5ca14720131e94fb98e66a082a2d78ef7278e7d76efc2e3","target":"record","created_at":"2026-05-18T01:20:02Z","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":"2b0ca76f2f2fdf65a08bce5fbfea03164fdf8c44dcd856690cae48451f2b9b95","cross_cats_sorted":["math-ph","math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-16T00:04:14Z","title_canon_sha256":"0960d7ea455fc0af66d3bf97d55db607630d3b007fa2266e429a6f68cf8f68bb"},"schema_version":"1.0","source":{"id":"1404.4113","kind":"arxiv","version":4}},"canonical_sha256":"32809ed3edc36a5dae1a4e1dc92e7c62c032f09ddbf7930692f9dc7d915032e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32809ed3edc36a5dae1a4e1dc92e7c62c032f09ddbf7930692f9dc7d915032e9","first_computed_at":"2026-05-18T01:20:02.081956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:02.081956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G+iXhSd4WVKOi0VBzAWI/Scfsve6iQgZ5bf6onSS/9w/6FKHvVi/t+Cn62zTEQgK6v4TmiMSE/akfj20G+MgAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:02.082663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4113","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fb20f7fb8b3c1d0e5ca14720131e94fb98e66a082a2d78ef7278e7d76efc2e3","sha256:6ba461b6dd9af733273f695c8c06d7dd58fc877be2edced3542567b1ed0d2d55"],"state_sha256":"694b17e5774490bb4f26fbfc56ae258f42c404ce700829f0c99eb27f6d4fc8be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x0G5imWsdHrteEi230PcQJvq60QGQ7Y2S+Y593TnQ2XRlVM7tflFFPB9RjeuIGYGNyiWucS/dvJrYKDtSnlJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:31:54.422229Z","bundle_sha256":"0ede7b3bac9e11124f91e659540e759d2c51eaa16be1596d0092a96d002e854a"}}