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We assume that the graph has a \"web-like\" structure, i.e, it consists of an inner part, formed by a finite number of vertices, and some threads attach to it.\nWe prove that such solution $u(t"},"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":"1611.05381","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-16T17:39:04Z","cross_cats_sorted":[],"title_canon_sha256":"41e6714c7823803a6233fc45fe3b8e7b57e84bd01d19ccead4f50a0750991594","abstract_canon_sha256":"3090a1215808b637a7882269973afe4fef7095848df0d9be438d027b285f9cf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:20.297490Z","signature_b64":"53TzYhz1r+fWjIoSn55bBCBvCI6ovcQPMwUbqmUS5u9tqKDXjrO6LubkqlRVyMGVUSjGj4WKo+6eVTrhM/hoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2bd605824006c36198aba7d28734937c24a55b649135c84d63992f9aad89f04","last_reissued_at":"2026-05-18T00:55:20.296732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:20.296732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uncertainty principle for discrete Schr\\\"odinger evolution on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Isaac Alvarez-Romero","submitted_at":"2016-11-16T17:39:04Z","abstract_excerpt":"We consider the Schr\\\"odinger evolution on graph, i.e. solution to the equation $\\partial_tu(t,\\alpha)=i\\sum_{\\beta\\in\\mathcal{A}}L(\\alpha,\\beta)u(t,\\beta)$, here $\\mathcal{A}$ is the set of vertices of the graph and the matrix $(L(\\alpha,\\beta))_{\\alpha,\\beta\\in\\mathcal{A}}$ describes interaction between the vertices, in particular two vertices $\\alpha$ and $\\beta$ are connected if $L(\\alpha,\\beta)\\neq0$. We assume that the graph has a \"web-like\" structure, i.e, it consists of an inner part, formed by a finite number of vertices, and some threads attach to it.\nWe prove that such solution $u(t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05381","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":"1611.05381","created_at":"2026-05-18T00:55:20.296861+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.05381v2","created_at":"2026-05-18T00:55:20.296861+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05381","created_at":"2026-05-18T00:55:20.296861+00:00"},{"alias_kind":"pith_short_12","alias_value":"WK6WAWBEABWD","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"WK6WAWBEABWDMGMK","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"WK6WAWBE","created_at":"2026-05-18T12:30:48.956258+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/WK6WAWBEABWDMGMKXJ6SQ42JG7","json":"https://pith.science/pith/WK6WAWBEABWDMGMKXJ6SQ42JG7.json","graph_json":"https://pith.science/api/pith-number/WK6WAWBEABWDMGMKXJ6SQ42JG7/graph.json","events_json":"https://pith.science/api/pith-number/WK6WAWBEABWDMGMKXJ6SQ42JG7/events.json","paper":"https://pith.science/paper/WK6WAWBE"},"agent_actions":{"view_html":"https://pith.science/pith/WK6WAWBEABWDMGMKXJ6SQ42JG7","download_json":"https://pith.science/pith/WK6WAWBEABWDMGMKXJ6SQ42JG7.json","view_paper":"https://pith.science/paper/WK6WAWBE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.05381&json=true","fetch_graph":"https://pith.science/api/pith-number/WK6WAWBEABWDMGMKXJ6SQ42JG7/graph.json","fetch_events":"https://pith.science/api/pith-number/WK6WAWBEABWDMGMKXJ6SQ42JG7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WK6WAWBEABWDMGMKXJ6SQ42JG7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WK6WAWBEABWDMGMKXJ6SQ42JG7/action/storage_attestation","attest_author":"https://pith.science/pith/WK6WAWBEABWDMGMKXJ6SQ42JG7/action/author_attestation","sign_citation":"https://pith.science/pith/WK6WAWBEABWDMGMKXJ6SQ42JG7/action/citation_signature","submit_replication":"https://pith.science/pith/WK6WAWBEABWDMGMKXJ6SQ42JG7/action/replication_record"}},"created_at":"2026-05-18T00:55:20.296861+00:00","updated_at":"2026-05-18T00:55:20.296861+00:00"}