{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:Z6Y2VDLXHPONPPHAW7YGH3FXS3","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":"72804bd70e99862f6beaceacdd9c827b4cc0cd8b3bcff21a3d368f0768e3b367","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-19T13:20:17Z","title_canon_sha256":"d831d0f141a2f4b5330f99c776bb2d6a9882a4f7e7c49c2333ee33c16532fe71"},"schema_version":"1.0","source":{"id":"0901.2843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.2843","created_at":"2026-05-18T02:14:56Z"},{"alias_kind":"arxiv_version","alias_value":"0901.2843v1","created_at":"2026-05-18T02:14:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.2843","created_at":"2026-05-18T02:14:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z6Y2VDLXHPON","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"Z6Y2VDLXHPONPPHA","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"Z6Y2VDLX","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:e37e66c8d38e311fe9b72880d4c74f77c74c0da2ce0d760c02681fe1c302e7c2","target":"graph","created_at":"2026-05-18T02:14:56Z","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":"This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\\\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunc","authors_text":"Steffen Roch, Vladimir Rabinovich","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-19T13:20:17Z","title":"Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.2843","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":"sha256:0dbad9ff25705889b3c99a9fbf41bce966280c3c64134fbc3b8ec65fa90c4a34","target":"record","created_at":"2026-05-18T02:14:56Z","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":"72804bd70e99862f6beaceacdd9c827b4cc0cd8b3bcff21a3d368f0768e3b367","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-19T13:20:17Z","title_canon_sha256":"d831d0f141a2f4b5330f99c776bb2d6a9882a4f7e7c49c2333ee33c16532fe71"},"schema_version":"1.0","source":{"id":"0901.2843","kind":"arxiv","version":1}},"canonical_sha256":"cfb1aa8d773bdcd7bce0b7f063ecb796d7a5ac8989a46b706c5d4f6d21152eaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfb1aa8d773bdcd7bce0b7f063ecb796d7a5ac8989a46b706c5d4f6d21152eaf","first_computed_at":"2026-05-18T02:14:56.814602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:56.814602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oYLoTVeG+S3cj9tVWcyZe1XAjGmOFDw6sp+3CU1TpAOmUqFc74F5ukDilupxmMRczuUHxlkt+fs5InHxkSK1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:56.815146Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.2843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dbad9ff25705889b3c99a9fbf41bce966280c3c64134fbc3b8ec65fa90c4a34","sha256:e37e66c8d38e311fe9b72880d4c74f77c74c0da2ce0d760c02681fe1c302e7c2"],"state_sha256":"207f950d090b98abe9b09bd273f4b313d1380278f2ea345f7ba64620d776eec1"}