{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4F23654LVULYSPFZYD5XA7YN7E","short_pith_number":"pith:4F23654L","canonical_record":{"source":{"id":"1408.5660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-08-25T04:35:25Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"00edfbe8f8bef0e0aa7346aae99d925241472be8d4527ed41f1ba1c4ffd77702","abstract_canon_sha256":"66d967e3bdbc109f3c78305d377453be18176611a978034a323ff9cc4dd4ff00"},"schema_version":"1.0"},"canonical_sha256":"e175bf778bad17893cb9c0fb707f0df918ed57c420ddf12187b6fec15dac0ada","source":{"kind":"arxiv","id":"1408.5660","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5660","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5660v1","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5660","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"4F23654LVULY","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4F23654LVULYSPFZ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4F23654L","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4F23654LVULYSPFZYD5XA7YN7E","target":"record","payload":{"canonical_record":{"source":{"id":"1408.5660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-08-25T04:35:25Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"00edfbe8f8bef0e0aa7346aae99d925241472be8d4527ed41f1ba1c4ffd77702","abstract_canon_sha256":"66d967e3bdbc109f3c78305d377453be18176611a978034a323ff9cc4dd4ff00"},"schema_version":"1.0"},"canonical_sha256":"e175bf778bad17893cb9c0fb707f0df918ed57c420ddf12187b6fec15dac0ada","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:24.613954Z","signature_b64":"ikQ9dZju9+ekncZkbYN5xg8uOjsjf816/lKoVI5q8ap6p1FA80fP+/eyLPicLMHJRzermbpKh3RhvpYw4YMLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e175bf778bad17893cb9c0fb707f0df918ed57c420ddf12187b6fec15dac0ada","last_reissued_at":"2026-05-18T02:44:24.613550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:24.613550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.5660","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0LX4AEXELR9PHsN3LK7XVNHRqczVDscme8wcTrIIXJjctaNyvBO1cyv0REzwbCUvDZ0vusHE9+ra/fM6iiTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:47:06.621940Z"},"content_sha256":"813d86544e72fd3ebc554d8befdbb34f7bffd80c34419756a31424b9711772fa","schema_version":"1.0","event_id":"sha256:813d86544e72fd3ebc554d8befdbb34f7bffd80c34419756a31424b9711772fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4F23654LVULYSPFZYD5XA7YN7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extended States for the Schr\\\"odinger Operator with Quasi-periodic Potential in Dimension Two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Roman Shterenberg, Yulia Karpeshina","submitted_at":"2014-08-25T04:35:25Z","abstract_excerpt":"We consider a Schr\\\"odinger operator $H=-\\Delta+V(\\vec x)$ in dimension two with a quasi-periodic potential $V(\\vec x)$. We prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves $e^{i\\langle \\vec \\varkappa,\\vec x\\rangle}$ at the high energy region. Second, the isoenergetic curves in the space of momenta $\\vec \\varkappa$ corresponding to these eigenfunctions have a form of slightly distorted circles with holes (C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5660","kind":"arxiv","version":1},"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":"2026-05-18T02:44:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TDeT2HsI3TgB8XOuqpRWwZe5jesSxEMChZcHcScnzzBqNa5ksMSC5jYXkbnndR88QZRt2vCdAOKn6biegkQeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:47:06.622343Z"},"content_sha256":"1bf75ebabc28600eb9394d5334fba92f325d2063f0ca1f26349589a48a1ad436","schema_version":"1.0","event_id":"sha256:1bf75ebabc28600eb9394d5334fba92f325d2063f0ca1f26349589a48a1ad436"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4F23654LVULYSPFZYD5XA7YN7E/bundle.json","state_url":"https://pith.science/pith/4F23654LVULYSPFZYD5XA7YN7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4F23654LVULYSPFZYD5XA7YN7E/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":"2026-05-27T14:47:06Z","links":{"resolver":"https://pith.science/pith/4F23654LVULYSPFZYD5XA7YN7E","bundle":"https://pith.science/pith/4F23654LVULYSPFZYD5XA7YN7E/bundle.json","state":"https://pith.science/pith/4F23654LVULYSPFZYD5XA7YN7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4F23654LVULYSPFZYD5XA7YN7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4F23654LVULYSPFZYD5XA7YN7E","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":"66d967e3bdbc109f3c78305d377453be18176611a978034a323ff9cc4dd4ff00","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-08-25T04:35:25Z","title_canon_sha256":"00edfbe8f8bef0e0aa7346aae99d925241472be8d4527ed41f1ba1c4ffd77702"},"schema_version":"1.0","source":{"id":"1408.5660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5660","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5660v1","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5660","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"4F23654LVULY","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4F23654LVULYSPFZ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4F23654L","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:1bf75ebabc28600eb9394d5334fba92f325d2063f0ca1f26349589a48a1ad436","target":"graph","created_at":"2026-05-18T02:44:24Z","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 consider a Schr\\\"odinger operator $H=-\\Delta+V(\\vec x)$ in dimension two with a quasi-periodic potential $V(\\vec x)$. We prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves $e^{i\\langle \\vec \\varkappa,\\vec x\\rangle}$ at the high energy region. Second, the isoenergetic curves in the space of momenta $\\vec \\varkappa$ corresponding to these eigenfunctions have a form of slightly distorted circles with holes (C","authors_text":"Roman Shterenberg, Yulia Karpeshina","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-08-25T04:35:25Z","title":"Extended States for the Schr\\\"odinger Operator with Quasi-periodic Potential in Dimension Two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5660","kind":"arxiv","version":1},"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":"sha256:813d86544e72fd3ebc554d8befdbb34f7bffd80c34419756a31424b9711772fa","target":"record","created_at":"2026-05-18T02:44:24Z","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":"66d967e3bdbc109f3c78305d377453be18176611a978034a323ff9cc4dd4ff00","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-08-25T04:35:25Z","title_canon_sha256":"00edfbe8f8bef0e0aa7346aae99d925241472be8d4527ed41f1ba1c4ffd77702"},"schema_version":"1.0","source":{"id":"1408.5660","kind":"arxiv","version":1}},"canonical_sha256":"e175bf778bad17893cb9c0fb707f0df918ed57c420ddf12187b6fec15dac0ada","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e175bf778bad17893cb9c0fb707f0df918ed57c420ddf12187b6fec15dac0ada","first_computed_at":"2026-05-18T02:44:24.613550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:24.613550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ikQ9dZju9+ekncZkbYN5xg8uOjsjf816/lKoVI5q8ap6p1FA80fP+/eyLPicLMHJRzermbpKh3RhvpYw4YMLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:24.613954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:813d86544e72fd3ebc554d8befdbb34f7bffd80c34419756a31424b9711772fa","sha256:1bf75ebabc28600eb9394d5334fba92f325d2063f0ca1f26349589a48a1ad436"],"state_sha256":"d01436bdbb8176a102c95a00ea976ce8ece3f7017d103caaf28877d28ed948bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/xvuBLX5nCBfjHYbyAvbWL4uhhii4R38noRIDJia0nHdtimOFXRA3Git0OZmsO/4wfxHQwVCMumDaVFvi7iCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:47:06.625607Z","bundle_sha256":"a737f8e257dbdbb1479451275093eed3996efebd982224833c90b66d68f1849d"}}