{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2G27HGB5AOKFHF7QOHC33PKBFZ","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":"9dbb4bc2176d2051be7ed1d1079d4a845b14780bfc5afbefb4d9740921ddcff5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2022-03-25T17:20:52Z","title_canon_sha256":"f1c36288606147b0842eaece2b5f2636875a3f68491120739343ff29ffb92474"},"schema_version":"1.0","source":{"id":"2203.13791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.13791","created_at":"2026-07-05T04:08:36Z"},{"alias_kind":"arxiv_version","alias_value":"2203.13791v1","created_at":"2026-07-05T04:08:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.13791","created_at":"2026-07-05T04:08:36Z"},{"alias_kind":"pith_short_12","alias_value":"2G27HGB5AOKF","created_at":"2026-07-05T04:08:36Z"},{"alias_kind":"pith_short_16","alias_value":"2G27HGB5AOKFHF7Q","created_at":"2026-07-05T04:08:36Z"},{"alias_kind":"pith_short_8","alias_value":"2G27HGB5","created_at":"2026-07-05T04:08:36Z"}],"graph_snapshots":[{"event_id":"sha256:0e26907ca9e6f40d26d6b08d281ef19bcc5098a8d29a63d37e290110c49d44aa","target":"graph","created_at":"2026-07-05T04:08:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.13791/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces a $\\textit{canonical}$ graph signal model defined by a $\\textit{canonical}$ graph and a $\\textit{canonical}$ shift, the $\\textit{companion}$ graph and the $\\textit{companion}$ shift. These are canonical because, under standard conditions, we show that any graph signal processing (GSP) model can be transformed into the canonical model. The transform that obtains this is the graph $z$-transform ($\\textrm{G$z$T}$) that we introduce. The GSP canonical model comes closest to the discrete signal processing (DSP) time signal models: the structure of the companion shift decompose","authors_text":"John Shi, Jose M. F. Moura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2022-03-25T17:20:52Z","title":"The Companion Model -- a Canonical Model in Graph Signal Processing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.13791","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":"sha256:37aefba26419a78f89f598916030e0720caa6773be98371b8d6e1db18c56b602","target":"record","created_at":"2026-07-05T04:08:36Z","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":"9dbb4bc2176d2051be7ed1d1079d4a845b14780bfc5afbefb4d9740921ddcff5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2022-03-25T17:20:52Z","title_canon_sha256":"f1c36288606147b0842eaece2b5f2636875a3f68491120739343ff29ffb92474"},"schema_version":"1.0","source":{"id":"2203.13791","kind":"arxiv","version":1}},"canonical_sha256":"d1b5f3983d03945397f071c5bdbd412e6bf7fdac0dda02f1586fdea641ed4691","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1b5f3983d03945397f071c5bdbd412e6bf7fdac0dda02f1586fdea641ed4691","first_computed_at":"2026-07-05T04:08:36.227561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:08:36.227561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t0y0o7dxS8kMZ8HuGC1dlIr5NRhHRjnOL9FqnNbwRIL8DURjBT4R9ZYj65RfpXXf0yoMkRPgSY9YsuktJKexBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:08:36.227971Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.13791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37aefba26419a78f89f598916030e0720caa6773be98371b8d6e1db18c56b602","sha256:0e26907ca9e6f40d26d6b08d281ef19bcc5098a8d29a63d37e290110c49d44aa"],"state_sha256":"8458979971a4ac433ef1e173d2b520e662a902b1bbdf0582865715f99a973961"}