{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5OEVK4KL3KWJSZC2QMVGKF7KCY","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":"b4999810e2926656ec8120ddaefd41efd87b9dbe85e2b36f16ef3219c168cb58","cross_cats_sorted":["cs.DM","math.IT","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-02T17:02:24Z","title_canon_sha256":"9f121e3ddf6e9d86d2bd3d9e045cf7b1cfe09eec40c7158fe6f51ebf5cc29fb6"},"schema_version":"1.0","source":{"id":"1512.00775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00775","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00775v1","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00775","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"5OEVK4KL3KWJ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5OEVK4KL3KWJSZC2","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5OEVK4KL","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:16f5b9c2a2a6a217be686ca84c12e6847bde9c43770c3ef2dd0115e1487bb9fd","target":"graph","created_at":"2026-05-18T01:25:25Z","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":"In many applications, from sensor to social networks, gene regulatory networks or big data, observations can be represented as a signal defined over the vertices of a graph. Building on the recently introduced Graph Fourier Transform, the first contribution of this paper is to provide an uncertainty principle for signals on graph. As a by-product of this theory, we show how to build a dictionary of maximally concentrated signals on vertex/frequency domains. Then, we establish a direct relation between uncertainty principle and sampling, which forms the basis for a sampling theorem of signals d","authors_text":"Mikhail Tsitsvero, Paolo Di Lorenzo, Sergio Barbarossa","cross_cats":["cs.DM","math.IT","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-02T17:02:24Z","title":"Uncertainty Principle and Sampling of Signals Defined on Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00775","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:e7632e888e1b28e10f294eef77d278d44856aed29c2ae8928c79ecc102f78b6f","target":"record","created_at":"2026-05-18T01:25:25Z","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":"b4999810e2926656ec8120ddaefd41efd87b9dbe85e2b36f16ef3219c168cb58","cross_cats_sorted":["cs.DM","math.IT","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-02T17:02:24Z","title_canon_sha256":"9f121e3ddf6e9d86d2bd3d9e045cf7b1cfe09eec40c7158fe6f51ebf5cc29fb6"},"schema_version":"1.0","source":{"id":"1512.00775","kind":"arxiv","version":1}},"canonical_sha256":"eb8955714bdaac99645a832a6517ea1625d3bc977a70a35d4eab77ac9dbba848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb8955714bdaac99645a832a6517ea1625d3bc977a70a35d4eab77ac9dbba848","first_computed_at":"2026-05-18T01:25:25.125661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:25.125661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BU1dl/gBpK383C6gjzpwKDX06Atr42wdq5ctpVfRIJ9FzIXv+Wj47kbS4cZBT0Eynzcq90NS5tEoJGnFskQiDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:25.126144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7632e888e1b28e10f294eef77d278d44856aed29c2ae8928c79ecc102f78b6f","sha256:16f5b9c2a2a6a217be686ca84c12e6847bde9c43770c3ef2dd0115e1487bb9fd"],"state_sha256":"3df20306c94859c472945a63c4f2d1caaab9bfd7cd9dbd15f46a92310ed03c72"}