{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WMSCYBR5QL5EFJBID5LO7BNDS5","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":"b1f09b7833f638e8426f4b6ad492ef64649e1d69f6d769325f8c6717666eaa9f","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-06-15T13:52:13Z","title_canon_sha256":"96f3488ce97ca08ac0b2a91529c59aaaf29643616c31867ce774e6ce00e2feb5"},"schema_version":"1.0","source":{"id":"1706.04869","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04869","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04869v1","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04869","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"WMSCYBR5QL5E","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WMSCYBR5QL5EFJBI","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WMSCYBR5","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:28d0c16f635bea3de952e1dd1f4d8f8082cb839614fa71a9da53cab2c303f453","target":"graph","created_at":"2026-05-18T00:42:18Z","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":"Let $H$ be a Schr\\\"odinger operator defined on a noncompact Riemannian manifold $\\Omega$, and let $W\\in L^\\infty(\\Omega;\\mathbb{R})$. Suppose that the operator $H+W$ is critical in $\\Omega$, and let $\\varphi$ be the corresponding Agmon ground state. We prove that if $u$ is a generalized eigenfunction of $H$ satisfying $|u|\\leq \\varphi$ in $\\Omega$, then the corresponding eigenvalue is in the spectrum of $H$. The conclusion also holds true if for some $K\\Subset \\Omega$ the operator $H$ admits a positive solution in $\\tilde{\\Omega}=\\Omega\\setminus K$, and $|u|\\leq \\psi$ in $\\tilde{\\Omega}$, wher","authors_text":"Siegfried Beckus, Yehuda Pinchover","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-06-15T13:52:13Z","title":"Shnol-type theorem for the Agmon ground state"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04869","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":"sha256:975afcf7f453eab23d7eda0935747a5cadf9cb96d8a5bab8970ba2121e13d515","target":"record","created_at":"2026-05-18T00:42:18Z","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":"b1f09b7833f638e8426f4b6ad492ef64649e1d69f6d769325f8c6717666eaa9f","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-06-15T13:52:13Z","title_canon_sha256":"96f3488ce97ca08ac0b2a91529c59aaaf29643616c31867ce774e6ce00e2feb5"},"schema_version":"1.0","source":{"id":"1706.04869","kind":"arxiv","version":1}},"canonical_sha256":"b3242c063d82fa42a4281f56ef85a3977c4ed57a8af037ee1d75407c2a49a200","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3242c063d82fa42a4281f56ef85a3977c4ed57a8af037ee1d75407c2a49a200","first_computed_at":"2026-05-18T00:42:18.711983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:18.711983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b/esMHl82Cb3C+LpH4/EK7ncSdWNhWjSHPTwPI4jEWnYLQXrbSZU3KAyd0h4ynwqW+Dk1NThKzyyn7zwZ0/4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:18.712643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04869","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:975afcf7f453eab23d7eda0935747a5cadf9cb96d8a5bab8970ba2121e13d515","sha256:28d0c16f635bea3de952e1dd1f4d8f8082cb839614fa71a9da53cab2c303f453"],"state_sha256":"47056d2dfd28a3ba6bab55f41a315ce8eddeda48fb188ec71b0e43fdac5a5b40"}