{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WCRDBFFGJEXSM4QMLBQ4ECTACR","short_pith_number":"pith:WCRDBFFG","canonical_record":{"source":{"id":"1606.03241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-06-10T09:21:41Z","cross_cats_sorted":[],"title_canon_sha256":"56e806224d0e9b3e281cd9e815828faca3417069ac14a3aa3d09c56795276fdb","abstract_canon_sha256":"b4dcdf614327017841724fd6834d1d2bee9345c2934c039581cb3f2ae4a11827"},"schema_version":"1.0"},"canonical_sha256":"b0a23094a6492f26720c5861c20a6014636b3d091e9243fc80ab2c3abe37960d","source":{"kind":"arxiv","id":"1606.03241","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03241","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03241v2","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03241","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"WCRDBFFGJEXS","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WCRDBFFGJEXSM4QM","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WCRDBFFG","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WCRDBFFGJEXSM4QMLBQ4ECTACR","target":"record","payload":{"canonical_record":{"source":{"id":"1606.03241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-06-10T09:21:41Z","cross_cats_sorted":[],"title_canon_sha256":"56e806224d0e9b3e281cd9e815828faca3417069ac14a3aa3d09c56795276fdb","abstract_canon_sha256":"b4dcdf614327017841724fd6834d1d2bee9345c2934c039581cb3f2ae4a11827"},"schema_version":"1.0"},"canonical_sha256":"b0a23094a6492f26720c5861c20a6014636b3d091e9243fc80ab2c3abe37960d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:37.205399Z","signature_b64":"qwRByA/f9P46fTqF6BeCkQV84R0GdOf1VU94H94QnVaGqhgyj6b8BgmcKm+1O4hgHAwdkxWientSVG0vbCu7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0a23094a6492f26720c5861c20a6014636b3d091e9243fc80ab2c3abe37960d","last_reissued_at":"2026-05-18T01:04:37.204704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:37.204704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.03241","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":"2026-05-18T01:04:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ldhtewuS/WibIh20x9eq+XY6TmzNfeOiFUa/h09zrGtoh8hvDOWzMNtmnJeRJ0DsDmsIbTUqzj4FXXxNScS7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T16:49:10.738210Z"},"content_sha256":"1901f13d03983e60e8cd1abe9598cc719e6e161042a0dba8db1c09a9e4c04931","schema_version":"1.0","event_id":"sha256:1901f13d03983e60e8cd1abe9598cc719e6e161042a0dba8db1c09a9e4c04931"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WCRDBFFGJEXSM4QMLBQ4ECTACR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Cecile Monthus","submitted_at":"2016-06-10T09:21:41Z","abstract_excerpt":"For random L\\'evy matrices of size $N \\times N$, where matrix elements are drawn with some heavy-tailed distribution $P(H_{ij}) \\propto N^{-1} |H_{ij} |^{-1-\\mu}$ with $0<\\mu<2$ (infinite variance), there exists an extensive number of finite eigenvalues $E=O(1)$, while the maximal eigenvalue grows as $E_{max} \\sim N^{\\frac{1}{\\mu}}$. Here we study the localization properties of the corresponding eigenvectors via some strong disorder perturbative expansion that remains consistent within the localized phase and that yields their Inverse Participation Ratios (I.P.R.) $Y_q$ as a function of the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03241","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":"2026-05-18T01:04:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DqrvGgVox2xHcbtWhNKzVgNw9rCYhJVLiXbpbWzpNrcRgoXSWxZoLLgRjfZS9zA0A4+fLTgtrUNh57frlX/ABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T16:49:10.738573Z"},"content_sha256":"a5e1aa3bebd056f2798fb5e17ec193b603e1fe99f91efb522be2a6fd7a235176","schema_version":"1.0","event_id":"sha256:a5e1aa3bebd056f2798fb5e17ec193b603e1fe99f91efb522be2a6fd7a235176"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WCRDBFFGJEXSM4QMLBQ4ECTACR/bundle.json","state_url":"https://pith.science/pith/WCRDBFFGJEXSM4QMLBQ4ECTACR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WCRDBFFGJEXSM4QMLBQ4ECTACR/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":"2026-06-04T16:49:10Z","links":{"resolver":"https://pith.science/pith/WCRDBFFGJEXSM4QMLBQ4ECTACR","bundle":"https://pith.science/pith/WCRDBFFGJEXSM4QMLBQ4ECTACR/bundle.json","state":"https://pith.science/pith/WCRDBFFGJEXSM4QMLBQ4ECTACR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WCRDBFFGJEXSM4QMLBQ4ECTACR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WCRDBFFGJEXSM4QMLBQ4ECTACR","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":"b4dcdf614327017841724fd6834d1d2bee9345c2934c039581cb3f2ae4a11827","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-06-10T09:21:41Z","title_canon_sha256":"56e806224d0e9b3e281cd9e815828faca3417069ac14a3aa3d09c56795276fdb"},"schema_version":"1.0","source":{"id":"1606.03241","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03241","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03241v2","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03241","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"WCRDBFFGJEXS","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WCRDBFFGJEXSM4QM","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WCRDBFFG","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:a5e1aa3bebd056f2798fb5e17ec193b603e1fe99f91efb522be2a6fd7a235176","target":"graph","created_at":"2026-05-18T01:04:37Z","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":"For random L\\'evy matrices of size $N \\times N$, where matrix elements are drawn with some heavy-tailed distribution $P(H_{ij}) \\propto N^{-1} |H_{ij} |^{-1-\\mu}$ with $0<\\mu<2$ (infinite variance), there exists an extensive number of finite eigenvalues $E=O(1)$, while the maximal eigenvalue grows as $E_{max} \\sim N^{\\frac{1}{\\mu}}$. Here we study the localization properties of the corresponding eigenvectors via some strong disorder perturbative expansion that remains consistent within the localized phase and that yields their Inverse Participation Ratios (I.P.R.) $Y_q$ as a function of the co","authors_text":"Cecile Monthus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-06-10T09:21:41Z","title":"Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03241","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":"sha256:1901f13d03983e60e8cd1abe9598cc719e6e161042a0dba8db1c09a9e4c04931","target":"record","created_at":"2026-05-18T01:04:37Z","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":"b4dcdf614327017841724fd6834d1d2bee9345c2934c039581cb3f2ae4a11827","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-06-10T09:21:41Z","title_canon_sha256":"56e806224d0e9b3e281cd9e815828faca3417069ac14a3aa3d09c56795276fdb"},"schema_version":"1.0","source":{"id":"1606.03241","kind":"arxiv","version":2}},"canonical_sha256":"b0a23094a6492f26720c5861c20a6014636b3d091e9243fc80ab2c3abe37960d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0a23094a6492f26720c5861c20a6014636b3d091e9243fc80ab2c3abe37960d","first_computed_at":"2026-05-18T01:04:37.204704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:37.204704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qwRByA/f9P46fTqF6BeCkQV84R0GdOf1VU94H94QnVaGqhgyj6b8BgmcKm+1O4hgHAwdkxWientSVG0vbCu7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:37.205399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03241","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1901f13d03983e60e8cd1abe9598cc719e6e161042a0dba8db1c09a9e4c04931","sha256:a5e1aa3bebd056f2798fb5e17ec193b603e1fe99f91efb522be2a6fd7a235176"],"state_sha256":"eaed564cfb94aedf946af2bfd1e44a2fd5bbf55aaeb279bc32042fbd7664f9fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPomTxh79TJffqlvUiJWXLNkRbMWWbr8334l86fxDzzpC3FRleI4/Hr4R7V9JXW5oPhQhWMEnWQV4h04GsMTDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T16:49:10.740615Z","bundle_sha256":"7523161f357dfcc9e7c0cf731ad2f56f5ebcccbb11fb663a9f531e8b3bcf8251"}}