{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NLMS3MDULN5EDIICIVTLNIB4YL","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":"c9811e6de07797553a9dfe42aeb179ca1b494e2c5bec12078340c10130686567","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2013-07-01T18:33:04Z","title_canon_sha256":"78d134f1e25936e256389ff831b19d0668abac0db4df3d2fa5d80e951be8ad08"},"schema_version":"1.0","source":{"id":"1307.0468","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0468","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0468v2","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0468","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"NLMS3MDULN5E","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NLMS3MDULN5EDIIC","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NLMS3MDU","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:779dea369f47113e360f36051b73697825f3ab8407773005b7b4914f4feb0ff9","target":"graph","created_at":"2026-05-18T03:06:54Z","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":"Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image signals, data in these domains are supported by arbitrary graphs. Signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs. This paper studies the concepts of low and high frequencies on graphs, and low-, high-, and band-pass graph filters. In traditional signal processing, there concepts are ","authors_text":"Aliaksei Sandryhaila, Jose M. F. Moura","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2013-07-01T18:33:04Z","title":"Discrete Signal Processing on Graphs: Frequency Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0468","kind":"arxiv","version":2},"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":"sha256:13f0f98cea8be5b6f2eb7bc4b9fda53e4af7db9760b1d5b9083b1120e28fc5ee","target":"record","created_at":"2026-05-18T03:06:54Z","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":"c9811e6de07797553a9dfe42aeb179ca1b494e2c5bec12078340c10130686567","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2013-07-01T18:33:04Z","title_canon_sha256":"78d134f1e25936e256389ff831b19d0668abac0db4df3d2fa5d80e951be8ad08"},"schema_version":"1.0","source":{"id":"1307.0468","kind":"arxiv","version":2}},"canonical_sha256":"6ad92db0745b7a41a1024566b6a03cc2ca3d8dc88cd2dc52fc589b58710b110b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ad92db0745b7a41a1024566b6a03cc2ca3d8dc88cd2dc52fc589b58710b110b","first_computed_at":"2026-05-18T03:06:54.839909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:54.839909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nAboCNPgjiCd9XQXPO1W5In9+xpSQvLIK3g9nSJM3rziklIN2w83dN6rvEoXLmLDE0UnKI9loKVsmeT+ZUkTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:54.840643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0468","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13f0f98cea8be5b6f2eb7bc4b9fda53e4af7db9760b1d5b9083b1120e28fc5ee","sha256:779dea369f47113e360f36051b73697825f3ab8407773005b7b4914f4feb0ff9"],"state_sha256":"30837a7f851cbc8672e69a20a51d861a87d501a4eb2a31f2a5d745f46dd59d96"}