{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RZ6VRIP72DZUSTHBGMHWDYFDHH","short_pith_number":"pith:RZ6VRIP7","schema_version":"1.0","canonical_sha256":"8e7d58a1ffd0f3494ce1330f61e0a339e59ba696e579922d51b6faea6c583ce2","source":{"kind":"arxiv","id":"1502.07688","version":2},"attestation_state":"computed","paper":{"title":"Sampling solutions of Schr\\\"odinger equations on combinatorial graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Isaac Z. Pesenson","submitted_at":"2015-02-12T13:28:08Z","abstract_excerpt":"We consider functions on a graph $G$ whose evolution in time $-\\infty<t<\\infty$ is governed by a Schr\\\"{o}dinger type equation with a combinatorial Laplace operator on the right side. For a given subset $S$ of vertices of $G$ we compute a cut-off frequency $\\omega>0$ such that solutions to a Cauchy problem with initial data in $PW_{\\omega}(G)$ are completely determined by their samples on $S\\times \\{k\\pi/\\omega\\},$ where $k\\in \\mathbf{N}$. It is shown that in the case of a bipartite graph our results are sharp."},"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":"1502.07688","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-02-12T13:28:08Z","cross_cats_sorted":[],"title_canon_sha256":"41950ea28613bb8e4ae62cb3fb2df56343124e748f5437e5a80c7f32182f6b85","abstract_canon_sha256":"0eb15657796e217e69b6911ca57d2f445c102ddbced02e91097802f2a2d9cadd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:23.944313Z","signature_b64":"xWHb0dp2IRmVJM1tbtcAdrhDVHegsi9RC2DdXulEpQE2Ar9JFyiMnD5dkHtsq/xnAAbQvtIzgK+yBo/xaVOHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e7d58a1ffd0f3494ce1330f61e0a339e59ba696e579922d51b6faea6c583ce2","last_reissued_at":"2026-05-18T02:17:23.943767Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:23.943767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sampling solutions of Schr\\\"odinger equations on combinatorial graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Isaac Z. Pesenson","submitted_at":"2015-02-12T13:28:08Z","abstract_excerpt":"We consider functions on a graph $G$ whose evolution in time $-\\infty<t<\\infty$ is governed by a Schr\\\"{o}dinger type equation with a combinatorial Laplace operator on the right side. For a given subset $S$ of vertices of $G$ we compute a cut-off frequency $\\omega>0$ such that solutions to a Cauchy problem with initial data in $PW_{\\omega}(G)$ are completely determined by their samples on $S\\times \\{k\\pi/\\omega\\},$ where $k\\in \\mathbf{N}$. It is shown that in the case of a bipartite graph our results are sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07688","kind":"arxiv","version":2},"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":"1502.07688","created_at":"2026-05-18T02:17:23.943858+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.07688v2","created_at":"2026-05-18T02:17:23.943858+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07688","created_at":"2026-05-18T02:17:23.943858+00:00"},{"alias_kind":"pith_short_12","alias_value":"RZ6VRIP72DZU","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RZ6VRIP72DZUSTHB","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RZ6VRIP7","created_at":"2026-05-18T12:29:39.896362+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/RZ6VRIP72DZUSTHBGMHWDYFDHH","json":"https://pith.science/pith/RZ6VRIP72DZUSTHBGMHWDYFDHH.json","graph_json":"https://pith.science/api/pith-number/RZ6VRIP72DZUSTHBGMHWDYFDHH/graph.json","events_json":"https://pith.science/api/pith-number/RZ6VRIP72DZUSTHBGMHWDYFDHH/events.json","paper":"https://pith.science/paper/RZ6VRIP7"},"agent_actions":{"view_html":"https://pith.science/pith/RZ6VRIP72DZUSTHBGMHWDYFDHH","download_json":"https://pith.science/pith/RZ6VRIP72DZUSTHBGMHWDYFDHH.json","view_paper":"https://pith.science/paper/RZ6VRIP7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.07688&json=true","fetch_graph":"https://pith.science/api/pith-number/RZ6VRIP72DZUSTHBGMHWDYFDHH/graph.json","fetch_events":"https://pith.science/api/pith-number/RZ6VRIP72DZUSTHBGMHWDYFDHH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RZ6VRIP72DZUSTHBGMHWDYFDHH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RZ6VRIP72DZUSTHBGMHWDYFDHH/action/storage_attestation","attest_author":"https://pith.science/pith/RZ6VRIP72DZUSTHBGMHWDYFDHH/action/author_attestation","sign_citation":"https://pith.science/pith/RZ6VRIP72DZUSTHBGMHWDYFDHH/action/citation_signature","submit_replication":"https://pith.science/pith/RZ6VRIP72DZUSTHBGMHWDYFDHH/action/replication_record"}},"created_at":"2026-05-18T02:17:23.943858+00:00","updated_at":"2026-05-18T02:17:23.943858+00:00"}