{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YUUFUA7IRPXPHMVAWB2Z34M6SI","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":"f2f91bafaf5992f987a19515b370059cf18e0d4a4453e4d88f35adc4b8688ef2","cross_cats_sorted":["cs.NA","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-09T17:36:33Z","title_canon_sha256":"89b6e7a76e0a5d4eb7cfc2516b631ddb821be970e555131b8daa1b2766f08017"},"schema_version":"1.0","source":{"id":"1811.04033","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04033","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04033v1","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04033","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"YUUFUA7IRPXP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YUUFUA7IRPXPHMVA","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YUUFUA7I","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:2a8082b9761baaaa67e2778e5e358ba262e616b7823288dd61e867417d7789b7","target":"graph","created_at":"2026-05-18T00:01:11Z","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":"The discrete cosine transform is a valuable tool in analysis of data on undirected rectangular grids, like images. In this paper it is shown how one can define an analogue of the discrete cosine transform on triangles. This is done by combining algebraic signal processing theory with a specific kind of multivariate Chebyshev polynomials. Using a multivariate Christoffel-Darboux formula it is shown how to derive an orthogonal version of the transform.","authors_text":"Bastian Seifert, Knut H\\\"uper","cross_cats":["cs.NA","eess.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-09T17:36:33Z","title":"The discrete cosine transform on triangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04033","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":"sha256:6d73d37b71f608a6dda41b21a8e5a66a56d15b9da12e914ac395b57156bfd2b7","target":"record","created_at":"2026-05-18T00:01:11Z","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":"f2f91bafaf5992f987a19515b370059cf18e0d4a4453e4d88f35adc4b8688ef2","cross_cats_sorted":["cs.NA","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-09T17:36:33Z","title_canon_sha256":"89b6e7a76e0a5d4eb7cfc2516b631ddb821be970e555131b8daa1b2766f08017"},"schema_version":"1.0","source":{"id":"1811.04033","kind":"arxiv","version":1}},"canonical_sha256":"c5285a03e88beef3b2a0b0759df19e92380c13d4b9c09f4b7d64941ef5944cc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5285a03e88beef3b2a0b0759df19e92380c13d4b9c09f4b7d64941ef5944cc8","first_computed_at":"2026-05-18T00:01:11.245886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:11.245886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VOMho+tTST2vaZQwyfe0Vu4rEvH/0Rj9hf8tju51WgSj5O0PXFKF+J7BmpJVP5+Kqi/SdWvLkLm7ukDtNm0HBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:11.246536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04033","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d73d37b71f608a6dda41b21a8e5a66a56d15b9da12e914ac395b57156bfd2b7","sha256:2a8082b9761baaaa67e2778e5e358ba262e616b7823288dd61e867417d7789b7"],"state_sha256":"6077119d8ab1cf228df79bd49e6551bb151e0a687312fb2638d574ba3e65a7a1"}