{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CIHMU2L36VHOW6IARVTMKQE44F","short_pith_number":"pith:CIHMU2L3","canonical_record":{"source":{"id":"1603.04917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-03-15T23:01:03Z","cross_cats_sorted":[],"title_canon_sha256":"6ac3a8ceb2dc1abc2721d934710a3c7cdf1fd4b26d27d946109cee98820c528d","abstract_canon_sha256":"2330d1da441de7de14523fb14198952043bdb9f7ad57719fc298e2440a1263d0"},"schema_version":"1.0"},"canonical_sha256":"120eca697bf54eeb79008d66c5409ce1751ef5879327a497cb21fdf9e7b89b70","source":{"kind":"arxiv","id":"1603.04917","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04917","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04917v2","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04917","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"CIHMU2L36VHO","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CIHMU2L36VHOW6IA","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CIHMU2L3","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CIHMU2L36VHOW6IARVTMKQE44F","target":"record","payload":{"canonical_record":{"source":{"id":"1603.04917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-03-15T23:01:03Z","cross_cats_sorted":[],"title_canon_sha256":"6ac3a8ceb2dc1abc2721d934710a3c7cdf1fd4b26d27d946109cee98820c528d","abstract_canon_sha256":"2330d1da441de7de14523fb14198952043bdb9f7ad57719fc298e2440a1263d0"},"schema_version":"1.0"},"canonical_sha256":"120eca697bf54eeb79008d66c5409ce1751ef5879327a497cb21fdf9e7b89b70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:21.459491Z","signature_b64":"ZNU/uhAKca33Y9WdZ5z0Zguy4k10ro0oAvJWpE/fiU3oqxh+vPKFuDIjNdP0LHxsijosK0ZO+bxeszUkBxu8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"120eca697bf54eeb79008d66c5409ce1751ef5879327a497cb21fdf9e7b89b70","last_reissued_at":"2026-05-18T00:32:21.458806Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:21.458806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.04917","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8KxFDyI0At5g2AvjrS7AlY4eMpVlVL1a++TM43wTKxU815q88Iq7PUwcDnbUwS4o2A0OT3MACX5VyjMlJZntCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:58:57.533461Z"},"content_sha256":"ca228b576ce24ddb44fb3aa7ac369eef6585653902a4e1dd1e199e5bce650091","schema_version":"1.0","event_id":"sha256:ca228b576ce24ddb44fb3aa7ac369eef6585653902a4e1dd1e199e5bce650091"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CIHMU2L36VHOW6IARVTMKQE44F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Splines and Wavelets on Circulant Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Madeleine S. Kotzagiannidis, Pier Luigi Dragotti","submitted_at":"2016-03-15T23:01:03Z","abstract_excerpt":"We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs. In this work, we leverage the inherent vanishing moment property of the circulant graph Laplacian operator, and by extension, the e-graph Laplacian, which is established as a parameterization of the former with respect to the degree per node, for the design of vertex-localized and critically-sampled higher-order graph (e-)spline wavelet filterbanks, which can reproduce and annihilate classes of (exponential) polynomial signals on circulant graphs. In ad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04917","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nv1OhPE+U4Qgvv7WXY14bS9fpsWOZiK69z8jGGeIw/IMXrO1VwOKvlSc4FaqFB+pvxjE8qFe5q6LVhaBR+e6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:58:57.533809Z"},"content_sha256":"ad3bd34cdbf65950f096f38e7d3c7e5ae681505b2bba8c97fc49e6ff5109e235","schema_version":"1.0","event_id":"sha256:ad3bd34cdbf65950f096f38e7d3c7e5ae681505b2bba8c97fc49e6ff5109e235"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CIHMU2L36VHOW6IARVTMKQE44F/bundle.json","state_url":"https://pith.science/pith/CIHMU2L36VHOW6IARVTMKQE44F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CIHMU2L36VHOW6IARVTMKQE44F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T03:58:57Z","links":{"resolver":"https://pith.science/pith/CIHMU2L36VHOW6IARVTMKQE44F","bundle":"https://pith.science/pith/CIHMU2L36VHOW6IARVTMKQE44F/bundle.json","state":"https://pith.science/pith/CIHMU2L36VHOW6IARVTMKQE44F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CIHMU2L36VHOW6IARVTMKQE44F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CIHMU2L36VHOW6IARVTMKQE44F","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":"2330d1da441de7de14523fb14198952043bdb9f7ad57719fc298e2440a1263d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-03-15T23:01:03Z","title_canon_sha256":"6ac3a8ceb2dc1abc2721d934710a3c7cdf1fd4b26d27d946109cee98820c528d"},"schema_version":"1.0","source":{"id":"1603.04917","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04917","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04917v2","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04917","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"CIHMU2L36VHO","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CIHMU2L36VHOW6IA","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CIHMU2L3","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:ad3bd34cdbf65950f096f38e7d3c7e5ae681505b2bba8c97fc49e6ff5109e235","target":"graph","created_at":"2026-05-18T00:32:21Z","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":"We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs. In this work, we leverage the inherent vanishing moment property of the circulant graph Laplacian operator, and by extension, the e-graph Laplacian, which is established as a parameterization of the former with respect to the degree per node, for the design of vertex-localized and critically-sampled higher-order graph (e-)spline wavelet filterbanks, which can reproduce and annihilate classes of (exponential) polynomial signals on circulant graphs. In ad","authors_text":"Madeleine S. Kotzagiannidis, Pier Luigi Dragotti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-03-15T23:01:03Z","title":"Splines and Wavelets on Circulant Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04917","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:ca228b576ce24ddb44fb3aa7ac369eef6585653902a4e1dd1e199e5bce650091","target":"record","created_at":"2026-05-18T00:32:21Z","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":"2330d1da441de7de14523fb14198952043bdb9f7ad57719fc298e2440a1263d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-03-15T23:01:03Z","title_canon_sha256":"6ac3a8ceb2dc1abc2721d934710a3c7cdf1fd4b26d27d946109cee98820c528d"},"schema_version":"1.0","source":{"id":"1603.04917","kind":"arxiv","version":2}},"canonical_sha256":"120eca697bf54eeb79008d66c5409ce1751ef5879327a497cb21fdf9e7b89b70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"120eca697bf54eeb79008d66c5409ce1751ef5879327a497cb21fdf9e7b89b70","first_computed_at":"2026-05-18T00:32:21.458806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:21.458806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZNU/uhAKca33Y9WdZ5z0Zguy4k10ro0oAvJWpE/fiU3oqxh+vPKFuDIjNdP0LHxsijosK0ZO+bxeszUkBxu8Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:21.459491Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04917","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca228b576ce24ddb44fb3aa7ac369eef6585653902a4e1dd1e199e5bce650091","sha256:ad3bd34cdbf65950f096f38e7d3c7e5ae681505b2bba8c97fc49e6ff5109e235"],"state_sha256":"add054a8c599d882d477789772e6f4f3dcf66908e7becf44682a09a066af3a9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EApQusQonDS1vFFgAVf+E0BSRZOFuYrYrnzeicAcC7SN5U3npOU6192lYuvD3fJPC/u4dhq+rRLURQOC6tV0AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:58:57.535740Z","bundle_sha256":"ce97832a3da79904342e29800c55e22eb41fe0ae7dd94642c8670e63434f3d86"}}