{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:CDJUJ7F322FPBFEYJVFNXH4DRY","short_pith_number":"pith:CDJUJ7F3","canonical_record":{"source":{"id":"1003.1695","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-03-08T18:22:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6b75e77ace2ab94a43e2ae7f75ef32ebd41be0f3d542c695511eb71f97d7c7ac","abstract_canon_sha256":"99d7e61c0d5c4ecbd91b8900fb408fd9075444341f1bd0dc4f065a9ef45bc84a"},"schema_version":"1.0"},"canonical_sha256":"10d344fcbbd68af094984d4adb9f838e1d1a0387ae0dd504257f3cb5a2348b13","source":{"kind":"arxiv","id":"1003.1695","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1695","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1695v3","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1695","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"CDJUJ7F322FP","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CDJUJ7F322FPBFEY","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CDJUJ7F3","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:CDJUJ7F322FPBFEYJVFNXH4DRY","target":"record","payload":{"canonical_record":{"source":{"id":"1003.1695","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-03-08T18:22:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6b75e77ace2ab94a43e2ae7f75ef32ebd41be0f3d542c695511eb71f97d7c7ac","abstract_canon_sha256":"99d7e61c0d5c4ecbd91b8900fb408fd9075444341f1bd0dc4f065a9ef45bc84a"},"schema_version":"1.0"},"canonical_sha256":"10d344fcbbd68af094984d4adb9f838e1d1a0387ae0dd504257f3cb5a2348b13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:16.123156Z","signature_b64":"Ee0p/i2/oPP+WK+bcR4g3GDiwTVyfU6ntUGdXVwrEwVkjx8OAC/vbZX4jzpnOHB41r3g0Mtv9EzqJHD8Jv4LBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10d344fcbbd68af094984d4adb9f838e1d1a0387ae0dd504257f3cb5a2348b13","last_reissued_at":"2026-05-18T02:30:16.122780Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:16.122780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.1695","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":"2026-05-18T02:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DzG6k1zMpMMP99WFMAN2LZLlquaU93wfrBFJxsNRnk1jFjpgLKyCX9RjeCxh0rH2rC1QsT2+qtYlnjGBGsUUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:34:53.299226Z"},"content_sha256":"acaa148bef876a5c7bd276b582126594d8bc469fd691c879aa640c959d51b4cf","schema_version":"1.0","event_id":"sha256:acaa148bef876a5c7bd276b582126594d8bc469fd691c879aa640c959d51b4cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:CDJUJ7F322FPBFEYJVFNXH4DRY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit-Periodic Schr\\\"odinger Operators With Uniformly Localized Eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"David Damanik, Zheng Gan","submitted_at":"2010-03-08T18:22:31Z","abstract_excerpt":"We exhibit limit-periodic Schr\\\"odinger operators that are uniformly localized in the strongest sense possible. That is, for these operators there are uniform exponential decay rates such that every element of the hull has a complete set of eigenvectors that decay exponentially off their centers of localization at least as fast as prescribed by the uniform decay rate. Consequently, these operators exhibit uniform dynamical localization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1695","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":""},"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":"2026-05-18T02:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7t5YI99mnYH7i1Qyc/A/QTcAxLSPQag0GgF3ruhJ2bNtqZB7oAlljoVppxw1KG6pzedbeYIFnfdC1wwnk5q3Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:34:53.299582Z"},"content_sha256":"4b2dcbe7b6114f668d7b6d98bbeaea8f2e2b5562064c2777cf21abaebd4db282","schema_version":"1.0","event_id":"sha256:4b2dcbe7b6114f668d7b6d98bbeaea8f2e2b5562064c2777cf21abaebd4db282"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CDJUJ7F322FPBFEYJVFNXH4DRY/bundle.json","state_url":"https://pith.science/pith/CDJUJ7F322FPBFEYJVFNXH4DRY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CDJUJ7F322FPBFEYJVFNXH4DRY/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":"2026-06-02T18:34:53Z","links":{"resolver":"https://pith.science/pith/CDJUJ7F322FPBFEYJVFNXH4DRY","bundle":"https://pith.science/pith/CDJUJ7F322FPBFEYJVFNXH4DRY/bundle.json","state":"https://pith.science/pith/CDJUJ7F322FPBFEYJVFNXH4DRY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CDJUJ7F322FPBFEYJVFNXH4DRY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CDJUJ7F322FPBFEYJVFNXH4DRY","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":"99d7e61c0d5c4ecbd91b8900fb408fd9075444341f1bd0dc4f065a9ef45bc84a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-03-08T18:22:31Z","title_canon_sha256":"6b75e77ace2ab94a43e2ae7f75ef32ebd41be0f3d542c695511eb71f97d7c7ac"},"schema_version":"1.0","source":{"id":"1003.1695","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1695","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1695v3","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1695","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"CDJUJ7F322FP","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CDJUJ7F322FPBFEY","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CDJUJ7F3","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:4b2dcbe7b6114f668d7b6d98bbeaea8f2e2b5562064c2777cf21abaebd4db282","target":"graph","created_at":"2026-05-18T02:30:16Z","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 exhibit limit-periodic Schr\\\"odinger operators that are uniformly localized in the strongest sense possible. That is, for these operators there are uniform exponential decay rates such that every element of the hull has a complete set of eigenvectors that decay exponentially off their centers of localization at least as fast as prescribed by the uniform decay rate. Consequently, these operators exhibit uniform dynamical localization.","authors_text":"David Damanik, Zheng Gan","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-03-08T18:22:31Z","title":"Limit-Periodic Schr\\\"odinger Operators With Uniformly Localized Eigenfunctions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1695","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:acaa148bef876a5c7bd276b582126594d8bc469fd691c879aa640c959d51b4cf","target":"record","created_at":"2026-05-18T02:30:16Z","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":"99d7e61c0d5c4ecbd91b8900fb408fd9075444341f1bd0dc4f065a9ef45bc84a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-03-08T18:22:31Z","title_canon_sha256":"6b75e77ace2ab94a43e2ae7f75ef32ebd41be0f3d542c695511eb71f97d7c7ac"},"schema_version":"1.0","source":{"id":"1003.1695","kind":"arxiv","version":3}},"canonical_sha256":"10d344fcbbd68af094984d4adb9f838e1d1a0387ae0dd504257f3cb5a2348b13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10d344fcbbd68af094984d4adb9f838e1d1a0387ae0dd504257f3cb5a2348b13","first_computed_at":"2026-05-18T02:30:16.122780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:16.122780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ee0p/i2/oPP+WK+bcR4g3GDiwTVyfU6ntUGdXVwrEwVkjx8OAC/vbZX4jzpnOHB41r3g0Mtv9EzqJHD8Jv4LBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:16.123156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.1695","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acaa148bef876a5c7bd276b582126594d8bc469fd691c879aa640c959d51b4cf","sha256:4b2dcbe7b6114f668d7b6d98bbeaea8f2e2b5562064c2777cf21abaebd4db282"],"state_sha256":"2a19644275b88fb0c522efc36cb964de7fed89c57e0d44fcce85c67f65c8ea94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZYGlKBttHWVVmSHr/1dPPSrTmQWHBeXn+i+pDD/4rnsq3EcKntc3d23y9eQdzGCaf+QvGWLYWMU/RZsyGn7wBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:34:53.301510Z","bundle_sha256":"c4243178562a1687b621b43d15f750d9356c40f95c50c87f2d1d0d2ec15a4982"}}