{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:H3JYOYEMEAR2VFBXNZT5522Y5F","short_pith_number":"pith:H3JYOYEM","canonical_record":{"source":{"id":"1709.03364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-11T13:20:53Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"27789b4615b600a4f2b026e190cd856bc26aaaa9bb64d5b35587539d133e3887","abstract_canon_sha256":"49aeeb6b2bb66648268a573c6a283b433de01d1662f60f4ce8e2fd3bd2f3b39e"},"schema_version":"1.0"},"canonical_sha256":"3ed387608c2023aa94376e67deeb58e9422b6d5bb724fea779360372c78b9671","source":{"kind":"arxiv","id":"1709.03364","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03364","created_at":"2026-05-18T00:20:46Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03364v2","created_at":"2026-05-18T00:20:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03364","created_at":"2026-05-18T00:20:46Z"},{"alias_kind":"pith_short_12","alias_value":"H3JYOYEMEAR2","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H3JYOYEMEAR2VFBX","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H3JYOYEM","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:H3JYOYEMEAR2VFBXNZT5522Y5F","target":"record","payload":{"canonical_record":{"source":{"id":"1709.03364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-11T13:20:53Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"27789b4615b600a4f2b026e190cd856bc26aaaa9bb64d5b35587539d133e3887","abstract_canon_sha256":"49aeeb6b2bb66648268a573c6a283b433de01d1662f60f4ce8e2fd3bd2f3b39e"},"schema_version":"1.0"},"canonical_sha256":"3ed387608c2023aa94376e67deeb58e9422b6d5bb724fea779360372c78b9671","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:46.757588Z","signature_b64":"ZvNxfxYAZkemLtNDfTb901u3JjKXfzC24UJ9AE40/Uk3Mh7HIIUhDoiWcEMgTq7v4gajad9Pzcc2FNf/hGs6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ed387608c2023aa94376e67deeb58e9422b6d5bb724fea779360372c78b9671","last_reissued_at":"2026-05-18T00:20:46.757058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:46.757058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.03364","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":"2026-05-18T00:20:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mCAiwj0MD0PC6Z9MKO9UjnhhiL/J4kLl1FoMQc/kqFhdfF7OsBN23pUy/slP0iEISrb/adZBUoOgRZAY9xd1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:21:08.395206Z"},"content_sha256":"bfe5346dcc717525df30893b146c84e32cdaa2648f32d2287b55ef038443e562","schema_version":"1.0","event_id":"sha256:bfe5346dcc717525df30893b146c84e32cdaa2648f32d2287b55ef038443e562"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:H3JYOYEMEAR2VFBXNZT5522Y5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Detecting localized eigenstates of linear operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.NA","authors_text":"Jianfeng Lu, Stefan Steinerberger","submitted_at":"2017-09-11T13:20:53Z","abstract_excerpt":"We describe a way of detecting the location of localized eigenvectors of a linear system $Ax = \\lambda x$ for eigenvalues $\\lambda$ with $|\\lambda|$ comparatively large. We define the family of functions $f_{\\alpha}: \\left\\{1.2. \\dots, n\\right\\} \\rightarrow \\mathbb{R}_{}$ $$ f_{\\alpha}(k) = \\log \\left( \\| A^{\\alpha} e_k \\|_{\\ell^2} \\right),$$ where $\\alpha \\geq 0$ is a parameter and $e_k = (0,0,\\dots, 0,1,0, \\dots, 0)$ is the $k-$th standard basis vector. We prove that eigenvectors associated to eigenvalues with large absolute value localize around local maxima of $f_{\\alpha}$: the metastable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03364","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":""},"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":"2026-05-18T00:20:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/0W+72GOiROfX98BgGfaMnwAlH8a83+oU/dXKnIQ5oEBxbKE9Co+YMcbUDIeKZ1s9MslXV0sKemMdHTLE0dnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:21:08.395933Z"},"content_sha256":"e88bb4b59f9eb0d17dd12c3f63941f67f5a688b8aa7f93ef75269b7a45e07e38","schema_version":"1.0","event_id":"sha256:e88bb4b59f9eb0d17dd12c3f63941f67f5a688b8aa7f93ef75269b7a45e07e38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H3JYOYEMEAR2VFBXNZT5522Y5F/bundle.json","state_url":"https://pith.science/pith/H3JYOYEMEAR2VFBXNZT5522Y5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H3JYOYEMEAR2VFBXNZT5522Y5F/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":"2026-05-25T18:21:08Z","links":{"resolver":"https://pith.science/pith/H3JYOYEMEAR2VFBXNZT5522Y5F","bundle":"https://pith.science/pith/H3JYOYEMEAR2VFBXNZT5522Y5F/bundle.json","state":"https://pith.science/pith/H3JYOYEMEAR2VFBXNZT5522Y5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H3JYOYEMEAR2VFBXNZT5522Y5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H3JYOYEMEAR2VFBXNZT5522Y5F","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":"49aeeb6b2bb66648268a573c6a283b433de01d1662f60f4ce8e2fd3bd2f3b39e","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-11T13:20:53Z","title_canon_sha256":"27789b4615b600a4f2b026e190cd856bc26aaaa9bb64d5b35587539d133e3887"},"schema_version":"1.0","source":{"id":"1709.03364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03364","created_at":"2026-05-18T00:20:46Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03364v2","created_at":"2026-05-18T00:20:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03364","created_at":"2026-05-18T00:20:46Z"},{"alias_kind":"pith_short_12","alias_value":"H3JYOYEMEAR2","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H3JYOYEMEAR2VFBX","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H3JYOYEM","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:e88bb4b59f9eb0d17dd12c3f63941f67f5a688b8aa7f93ef75269b7a45e07e38","target":"graph","created_at":"2026-05-18T00:20:46Z","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 describe a way of detecting the location of localized eigenvectors of a linear system $Ax = \\lambda x$ for eigenvalues $\\lambda$ with $|\\lambda|$ comparatively large. We define the family of functions $f_{\\alpha}: \\left\\{1.2. \\dots, n\\right\\} \\rightarrow \\mathbb{R}_{}$ $$ f_{\\alpha}(k) = \\log \\left( \\| A^{\\alpha} e_k \\|_{\\ell^2} \\right),$$ where $\\alpha \\geq 0$ is a parameter and $e_k = (0,0,\\dots, 0,1,0, \\dots, 0)$ is the $k-$th standard basis vector. We prove that eigenvectors associated to eigenvalues with large absolute value localize around local maxima of $f_{\\alpha}$: the metastable ","authors_text":"Jianfeng Lu, Stefan Steinerberger","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-11T13:20:53Z","title":"Detecting localized eigenstates of linear operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03364","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:bfe5346dcc717525df30893b146c84e32cdaa2648f32d2287b55ef038443e562","target":"record","created_at":"2026-05-18T00:20:46Z","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":"49aeeb6b2bb66648268a573c6a283b433de01d1662f60f4ce8e2fd3bd2f3b39e","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-11T13:20:53Z","title_canon_sha256":"27789b4615b600a4f2b026e190cd856bc26aaaa9bb64d5b35587539d133e3887"},"schema_version":"1.0","source":{"id":"1709.03364","kind":"arxiv","version":2}},"canonical_sha256":"3ed387608c2023aa94376e67deeb58e9422b6d5bb724fea779360372c78b9671","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ed387608c2023aa94376e67deeb58e9422b6d5bb724fea779360372c78b9671","first_computed_at":"2026-05-18T00:20:46.757058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:46.757058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZvNxfxYAZkemLtNDfTb901u3JjKXfzC24UJ9AE40/Uk3Mh7HIIUhDoiWcEMgTq7v4gajad9Pzcc2FNf/hGs6AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:46.757588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfe5346dcc717525df30893b146c84e32cdaa2648f32d2287b55ef038443e562","sha256:e88bb4b59f9eb0d17dd12c3f63941f67f5a688b8aa7f93ef75269b7a45e07e38"],"state_sha256":"655e3f706ff9b8f9aaae3f67c7b12bf63ff59b21096ecd97d9b67aebb2c810db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ahKMh0AHGdbjbSHtby/uqefZxhQYwkR1yxTLaCvQYj8OdRqCIl4wRBQDGSSSDpF4tudP+x2kNxiPxwcbq9AlAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:21:08.399399Z","bundle_sha256":"28f4deb40e53d50c409b1b1209d28b81313679a60d5f2e3d5707b96e049a860f"}}