{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:BGYYYFSTXO5VYMNXMAQDOLPLWR","short_pith_number":"pith:BGYYYFST","canonical_record":{"source":{"id":"2109.11143","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-09-23T05:00:32Z","cross_cats_sorted":[],"title_canon_sha256":"78f7b0e6e24bf7404dab961c7148457f355129c58c2526669be3c3a91818ddfd","abstract_canon_sha256":"23206bfb8bd779f2bb4a29cddef3d3565d469051746838fbeed634cf2e6dfba1"},"schema_version":"1.0"},"canonical_sha256":"09b18c1653bbbb5c31b76020372debb44b6868fee8a51fbdae9e68eb8074f9a3","source":{"kind":"arxiv","id":"2109.11143","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11143","created_at":"2026-07-05T04:45:47Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11143v3","created_at":"2026-07-05T04:45:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11143","created_at":"2026-07-05T04:45:47Z"},{"alias_kind":"pith_short_12","alias_value":"BGYYYFSTXO5V","created_at":"2026-07-05T04:45:47Z"},{"alias_kind":"pith_short_16","alias_value":"BGYYYFSTXO5VYMNX","created_at":"2026-07-05T04:45:47Z"},{"alias_kind":"pith_short_8","alias_value":"BGYYYFST","created_at":"2026-07-05T04:45:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:BGYYYFSTXO5VYMNXMAQDOLPLWR","target":"record","payload":{"canonical_record":{"source":{"id":"2109.11143","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-09-23T05:00:32Z","cross_cats_sorted":[],"title_canon_sha256":"78f7b0e6e24bf7404dab961c7148457f355129c58c2526669be3c3a91818ddfd","abstract_canon_sha256":"23206bfb8bd779f2bb4a29cddef3d3565d469051746838fbeed634cf2e6dfba1"},"schema_version":"1.0"},"canonical_sha256":"09b18c1653bbbb5c31b76020372debb44b6868fee8a51fbdae9e68eb8074f9a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:45:47.301951Z","signature_b64":"EfUctCaJzCqeHj93/nqgRXPu5FsXsUYY/Q8LLSWbMvot8PIvmLLt23Xt2HOJCrznxzbWZMJO/M1Up70g05nrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09b18c1653bbbb5c31b76020372debb44b6868fee8a51fbdae9e68eb8074f9a3","last_reissued_at":"2026-07-05T04:45:47.301544Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:45:47.301544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.11143","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:45:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MwVpZmDHEVAZXWZCdhxwZkM5ylb+rVqrJFI2xhj17fKXIGFkNuoXUrvEavvHKGgXfj+roqd6YTEcNQOC/zNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T22:56:29.198134Z"},"content_sha256":"40ee2b35ca24538b44f0e356cd2d6a8f75a010e32d7aeef8033202a1b40b26cf","schema_version":"1.0","event_id":"sha256:40ee2b35ca24538b44f0e356cd2d6a8f75a010e32d7aeef8033202a1b40b26cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:BGYYYFSTXO5VYMNXMAQDOLPLWR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hau-Tieng Wu, Stefan Steinerberger","submitted_at":"2021-09-23T05:00:32Z","abstract_excerpt":"We consider the eigenvalue problem $Ax = \\lambda x$ where $A \\in \\mathbb{R}^{n \\times n}$ and the eigenvalue is also real $\\lambda \\in \\mathbb{R}$. If we are given $A$, $\\lambda$ and, additionally, the absolute value of the entries of $x$ (the vector $(|x_i|)_{i=1}^n$), is there a fast way to recover $x$? In particular, can this be done quicker than computing $x$ from scratch? This may be understood as a special case of the phase retrieval problem. We present a randomized algorithm which provably converges in expectation whenever $\\lambda$ is a simple eigenvalue. The problem should become easi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11143","kind":"arxiv","version":3},"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/2109.11143/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":"2026-07-05T04:45:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RCKzbWMhYJTewVF4ypY50gUwXyU4GxrnXmjF5oamkB3fQGhZjAZonB+hAeN7tBsq75frs9fNNiMvj3p4pJAgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T22:56:29.198664Z"},"content_sha256":"0009f6767adfa85ca17c18508b47a5dd866682fde4341267e10a260cff80db0f","schema_version":"1.0","event_id":"sha256:0009f6767adfa85ca17c18508b47a5dd866682fde4341267e10a260cff80db0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BGYYYFSTXO5VYMNXMAQDOLPLWR/bundle.json","state_url":"https://pith.science/pith/BGYYYFSTXO5VYMNXMAQDOLPLWR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BGYYYFSTXO5VYMNXMAQDOLPLWR/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":"2026-08-04T22:56:29Z","links":{"resolver":"https://pith.science/pith/BGYYYFSTXO5VYMNXMAQDOLPLWR","bundle":"https://pith.science/pith/BGYYYFSTXO5VYMNXMAQDOLPLWR/bundle.json","state":"https://pith.science/pith/BGYYYFSTXO5VYMNXMAQDOLPLWR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BGYYYFSTXO5VYMNXMAQDOLPLWR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BGYYYFSTXO5VYMNXMAQDOLPLWR","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":"23206bfb8bd779f2bb4a29cddef3d3565d469051746838fbeed634cf2e6dfba1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-09-23T05:00:32Z","title_canon_sha256":"78f7b0e6e24bf7404dab961c7148457f355129c58c2526669be3c3a91818ddfd"},"schema_version":"1.0","source":{"id":"2109.11143","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11143","created_at":"2026-07-05T04:45:47Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11143v3","created_at":"2026-07-05T04:45:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11143","created_at":"2026-07-05T04:45:47Z"},{"alias_kind":"pith_short_12","alias_value":"BGYYYFSTXO5V","created_at":"2026-07-05T04:45:47Z"},{"alias_kind":"pith_short_16","alias_value":"BGYYYFSTXO5VYMNX","created_at":"2026-07-05T04:45:47Z"},{"alias_kind":"pith_short_8","alias_value":"BGYYYFST","created_at":"2026-07-05T04:45:47Z"}],"graph_snapshots":[{"event_id":"sha256:0009f6767adfa85ca17c18508b47a5dd866682fde4341267e10a260cff80db0f","target":"graph","created_at":"2026-07-05T04:45:47Z","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/2109.11143/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the eigenvalue problem $Ax = \\lambda x$ where $A \\in \\mathbb{R}^{n \\times n}$ and the eigenvalue is also real $\\lambda \\in \\mathbb{R}$. If we are given $A$, $\\lambda$ and, additionally, the absolute value of the entries of $x$ (the vector $(|x_i|)_{i=1}^n$), is there a fast way to recover $x$? In particular, can this be done quicker than computing $x$ from scratch? This may be understood as a special case of the phase retrieval problem. We present a randomized algorithm which provably converges in expectation whenever $\\lambda$ is a simple eigenvalue. The problem should become easi","authors_text":"Hau-Tieng Wu, Stefan Steinerberger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-09-23T05:00:32Z","title":"Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11143","kind":"arxiv","version":3},"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":"sha256:40ee2b35ca24538b44f0e356cd2d6a8f75a010e32d7aeef8033202a1b40b26cf","target":"record","created_at":"2026-07-05T04:45:47Z","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":"23206bfb8bd779f2bb4a29cddef3d3565d469051746838fbeed634cf2e6dfba1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-09-23T05:00:32Z","title_canon_sha256":"78f7b0e6e24bf7404dab961c7148457f355129c58c2526669be3c3a91818ddfd"},"schema_version":"1.0","source":{"id":"2109.11143","kind":"arxiv","version":3}},"canonical_sha256":"09b18c1653bbbb5c31b76020372debb44b6868fee8a51fbdae9e68eb8074f9a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09b18c1653bbbb5c31b76020372debb44b6868fee8a51fbdae9e68eb8074f9a3","first_computed_at":"2026-07-05T04:45:47.301544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:45:47.301544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EfUctCaJzCqeHj93/nqgRXPu5FsXsUYY/Q8LLSWbMvot8PIvmLLt23Xt2HOJCrznxzbWZMJO/M1Up70g05nrBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:45:47.301951Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.11143","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40ee2b35ca24538b44f0e356cd2d6a8f75a010e32d7aeef8033202a1b40b26cf","sha256:0009f6767adfa85ca17c18508b47a5dd866682fde4341267e10a260cff80db0f"],"state_sha256":"8f6197ee44918b069882489ea502615d7506ae0c5d893e8fb4a6d50228599043"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6KaKVZoER0o8DlSE6dF72P+qHs2iRGtz5sZh5XTt4FLpvesoEbBjQgS2XJSDJdd15htu8v67R5aI4kmfafoUAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T22:56:29.203962Z","bundle_sha256":"4d87c771f9d89dd2fe2a5d98720674d1393885c694b3b0a23b4e095af009928f"}}