{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GE6FISNDHG4N6BP4T74PDCDMPX","short_pith_number":"pith:GE6FISND","schema_version":"1.0","canonical_sha256":"313c5449a339b8df05fc9ff8f1886c7deba8a58f36cc7893628253ef140e71b6","source":{"kind":"arxiv","id":"1211.3891","version":1},"attestation_state":"computed","paper":{"title":"Localization for alloy-type models with non-monotone potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Martin Tautenhahn","submitted_at":"2012-11-16T13:55:06Z","abstract_excerpt":"We consider a family of self-adjoint operators [H_\\omega = - \\Delta + \\lambda V_\\omega, \\quad \\omega \\in \\Omega = \\bigtimes_{k \\in \\ZZ^d} \\RR,] on the Hilbert space $\\ell^2 (\\ZZ^d)$ or $L^2 (\\RR^d)$. Here $\\Delta$ denotes the Laplace operator (discrete or continuous), $V_\\omega$ is a multiplication operator given by the function $$V_\\omega (x) = \\sum_{k \\in \\ZZ^d} \\omega_k u(x-k) on $\\ZZ^d$, or \\quad V_\\omega (x) = \\sum_{k \\in \\ZZ^d} \\omega_k U(x-k) on $\\RR^d$,$$ and $\\lambda > 0$ is a real parameter modeling the strength of the disorder present in the model. The functions $u:\\ZZ^d \\to \\RR$ an"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1211.3891","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-11-16T13:55:06Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"0c6674200a31da4ee088a86c71cf1fa154ac662b74410916d44e8cbb4edc0812","abstract_canon_sha256":"a68e6f1eff33fb8ae12d2e3f528772f8d96b51cfda02851f76330d5a56a03184"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:37.694762Z","signature_b64":"rshwvQtHr8XLatV3cNtENf7xoVulPD9cLsJ/bKGbJv2Z6nw2JkUd6s10jKlQRK3ZymdDQU3uhOFJsGQxT6D7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"313c5449a339b8df05fc9ff8f1886c7deba8a58f36cc7893628253ef140e71b6","last_reissued_at":"2026-05-18T03:40:37.693951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:37.693951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Localization for alloy-type models with non-monotone potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Martin Tautenhahn","submitted_at":"2012-11-16T13:55:06Z","abstract_excerpt":"We consider a family of self-adjoint operators [H_\\omega = - \\Delta + \\lambda V_\\omega, \\quad \\omega \\in \\Omega = \\bigtimes_{k \\in \\ZZ^d} \\RR,] on the Hilbert space $\\ell^2 (\\ZZ^d)$ or $L^2 (\\RR^d)$. Here $\\Delta$ denotes the Laplace operator (discrete or continuous), $V_\\omega$ is a multiplication operator given by the function $$V_\\omega (x) = \\sum_{k \\in \\ZZ^d} \\omega_k u(x-k) on $\\ZZ^d$, or \\quad V_\\omega (x) = \\sum_{k \\in \\ZZ^d} \\omega_k U(x-k) on $\\RR^d$,$$ and $\\lambda > 0$ is a real parameter modeling the strength of the disorder present in the model. The functions $u:\\ZZ^d \\to \\RR$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3891","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.3891","created_at":"2026-05-18T03:40:37.694092+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.3891v1","created_at":"2026-05-18T03:40:37.694092+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3891","created_at":"2026-05-18T03:40:37.694092+00:00"},{"alias_kind":"pith_short_12","alias_value":"GE6FISNDHG4N","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GE6FISNDHG4N6BP4","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GE6FISND","created_at":"2026-05-18T12:27:06.952714+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GE6FISNDHG4N6BP4T74PDCDMPX","json":"https://pith.science/pith/GE6FISNDHG4N6BP4T74PDCDMPX.json","graph_json":"https://pith.science/api/pith-number/GE6FISNDHG4N6BP4T74PDCDMPX/graph.json","events_json":"https://pith.science/api/pith-number/GE6FISNDHG4N6BP4T74PDCDMPX/events.json","paper":"https://pith.science/paper/GE6FISND"},"agent_actions":{"view_html":"https://pith.science/pith/GE6FISNDHG4N6BP4T74PDCDMPX","download_json":"https://pith.science/pith/GE6FISNDHG4N6BP4T74PDCDMPX.json","view_paper":"https://pith.science/paper/GE6FISND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.3891&json=true","fetch_graph":"https://pith.science/api/pith-number/GE6FISNDHG4N6BP4T74PDCDMPX/graph.json","fetch_events":"https://pith.science/api/pith-number/GE6FISNDHG4N6BP4T74PDCDMPX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GE6FISNDHG4N6BP4T74PDCDMPX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GE6FISNDHG4N6BP4T74PDCDMPX/action/storage_attestation","attest_author":"https://pith.science/pith/GE6FISNDHG4N6BP4T74PDCDMPX/action/author_attestation","sign_citation":"https://pith.science/pith/GE6FISNDHG4N6BP4T74PDCDMPX/action/citation_signature","submit_replication":"https://pith.science/pith/GE6FISNDHG4N6BP4T74PDCDMPX/action/replication_record"}},"created_at":"2026-05-18T03:40:37.694092+00:00","updated_at":"2026-05-18T03:40:37.694092+00:00"}