{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UYO4TYTUMNA26YIE2E6JSFXVAH","short_pith_number":"pith:UYO4TYTU","schema_version":"1.0","canonical_sha256":"a61dc9e2746341af6104d13c9916f501dd7c7b813ac371e726037c4d2e9d0b75","source":{"kind":"arxiv","id":"1503.03291","version":2},"attestation_state":"computed","paper":{"title":"Toward An Uncertainty Principle For Weighted Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Bastien Pasdeloup, Michael Rabbat, R\\'eda Alami, Vincent Gripon","submitted_at":"2015-03-11T12:11:11Z","abstract_excerpt":"The uncertainty principle states that a signal cannot be localized both in time and frequency. With the aim of extending this result to signals on graphs, Agaskar&Lu introduce notions of graph and spectral spreads. They show that a graph uncertainty principle holds for some families of unweighted graphs. This principle states that a signal cannot be simultaneously localized both in graph and spectral domains. In this paper, we aim to extend their work to weighted graphs. We show that a naive extension of their definitions leads to inconsistent results such as discontinuity of the graph spread "},"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":"1503.03291","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-03-11T12:11:11Z","cross_cats_sorted":[],"title_canon_sha256":"570f725eeeda181cabc3ab16b6c5f5f8844b0f5a5134ff94dc90d04961b8993e","abstract_canon_sha256":"4f9ff8846cf100595fb0defaf82726c038fa7d6e0c93556cade2cd67c37fcdb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:06.168792Z","signature_b64":"eT7jweT9khA5GloOakoSqiqojrMpwbTo1MApq1ZicPQrt6mM5TX0Z8NBm0nSbCw38b7Zt+/HsVu0tHttdCsFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a61dc9e2746341af6104d13c9916f501dd7c7b813ac371e726037c4d2e9d0b75","last_reissued_at":"2026-05-18T01:19:06.168245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:06.168245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toward An Uncertainty Principle For Weighted Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Bastien Pasdeloup, Michael Rabbat, R\\'eda Alami, Vincent Gripon","submitted_at":"2015-03-11T12:11:11Z","abstract_excerpt":"The uncertainty principle states that a signal cannot be localized both in time and frequency. With the aim of extending this result to signals on graphs, Agaskar&Lu introduce notions of graph and spectral spreads. They show that a graph uncertainty principle holds for some families of unweighted graphs. This principle states that a signal cannot be simultaneously localized both in graph and spectral domains. In this paper, we aim to extend their work to weighted graphs. We show that a naive extension of their definitions leads to inconsistent results such as discontinuity of the graph spread "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03291","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":"1503.03291","created_at":"2026-05-18T01:19:06.168329+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.03291v2","created_at":"2026-05-18T01:19:06.168329+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03291","created_at":"2026-05-18T01:19:06.168329+00:00"},{"alias_kind":"pith_short_12","alias_value":"UYO4TYTUMNA2","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UYO4TYTUMNA26YIE","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UYO4TYTU","created_at":"2026-05-18T12:29:44.643036+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/UYO4TYTUMNA26YIE2E6JSFXVAH","json":"https://pith.science/pith/UYO4TYTUMNA26YIE2E6JSFXVAH.json","graph_json":"https://pith.science/api/pith-number/UYO4TYTUMNA26YIE2E6JSFXVAH/graph.json","events_json":"https://pith.science/api/pith-number/UYO4TYTUMNA26YIE2E6JSFXVAH/events.json","paper":"https://pith.science/paper/UYO4TYTU"},"agent_actions":{"view_html":"https://pith.science/pith/UYO4TYTUMNA26YIE2E6JSFXVAH","download_json":"https://pith.science/pith/UYO4TYTUMNA26YIE2E6JSFXVAH.json","view_paper":"https://pith.science/paper/UYO4TYTU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.03291&json=true","fetch_graph":"https://pith.science/api/pith-number/UYO4TYTUMNA26YIE2E6JSFXVAH/graph.json","fetch_events":"https://pith.science/api/pith-number/UYO4TYTUMNA26YIE2E6JSFXVAH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UYO4TYTUMNA26YIE2E6JSFXVAH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UYO4TYTUMNA26YIE2E6JSFXVAH/action/storage_attestation","attest_author":"https://pith.science/pith/UYO4TYTUMNA26YIE2E6JSFXVAH/action/author_attestation","sign_citation":"https://pith.science/pith/UYO4TYTUMNA26YIE2E6JSFXVAH/action/citation_signature","submit_replication":"https://pith.science/pith/UYO4TYTUMNA26YIE2E6JSFXVAH/action/replication_record"}},"created_at":"2026-05-18T01:19:06.168329+00:00","updated_at":"2026-05-18T01:19:06.168329+00:00"}