{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LH7HITNWIPIMPUVTJIXKADMRYN","short_pith_number":"pith:LH7HITNW","canonical_record":{"source":{"id":"1606.06962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-06-22T14:33:15Z","cross_cats_sorted":["cs.SI","stat.ML"],"title_canon_sha256":"b2ce62cc35e82cf4e1f4dc587ec992068cb6cdcb09b0d07ffa90976ce3c21795","abstract_canon_sha256":"fa83538b96f87c51872505770792eb7b1e42acd174e3d858a579bf28361f0554"},"schema_version":"1.0"},"canonical_sha256":"59fe744db643d0c7d2b34a2ea00d91c35ec1e75f9ab5f9ccf43d369c86496a93","source":{"kind":"arxiv","id":"1606.06962","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06962","created_at":"2026-05-18T01:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06962v1","created_at":"2026-05-18T01:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06962","created_at":"2026-05-18T01:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"LH7HITNWIPIM","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LH7HITNWIPIMPUVT","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LH7HITNW","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LH7HITNWIPIMPUVTJIXKADMRYN","target":"record","payload":{"canonical_record":{"source":{"id":"1606.06962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-06-22T14:33:15Z","cross_cats_sorted":["cs.SI","stat.ML"],"title_canon_sha256":"b2ce62cc35e82cf4e1f4dc587ec992068cb6cdcb09b0d07ffa90976ce3c21795","abstract_canon_sha256":"fa83538b96f87c51872505770792eb7b1e42acd174e3d858a579bf28361f0554"},"schema_version":"1.0"},"canonical_sha256":"59fe744db643d0c7d2b34a2ea00d91c35ec1e75f9ab5f9ccf43d369c86496a93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:00.830465Z","signature_b64":"ynsLmkNSyvimdCK8dETazvyg9oCAkEsYe5rScOovFT93ohe97dKUzzlsKnyoDhn1k14WI963KnLDOVXrMml2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59fe744db643d0c7d2b34a2ea00d91c35ec1e75f9ab5f9ccf43d369c86496a93","last_reissued_at":"2026-05-18T01:12:00.830126Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:00.830126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.06962","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KMsrXtAIi8rVsq28OKYwNzZY900vQrR2Lf2Bxz4AyhsaaHmf8O/Drv6FvECK0b4HOilRfTw3CuarGiLcxXFlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:02:28.918606Z"},"content_sha256":"a33ee9afb34797c529717ab540e7482d09fff9434494f7faa4bb6631077fd51c","schema_version":"1.0","event_id":"sha256:a33ee9afb34797c529717ab540e7482d09fff9434494f7faa4bb6631077fd51c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LH7HITNWIPIMPUVTJIXKADMRYN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards stationary time-vertex signal processing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andreas Loukas, Francesco Grassi, Nathanael Perraudin, Pierre Vandergheynst","submitted_at":"2016-06-22T14:33:15Z","abstract_excerpt":"Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods for signal processing on graphs ignore the dimension of time, treating successive graph signals independently or taking a global average. To address this shortcoming, this paper considers the statistical analysis of time-varying graph signals. We introduce a novel definition of joint (time-vertex) stationarity, which generalizes the classical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06962","kind":"arxiv","version":1},"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":"2026-05-18T01:12:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPhI9cJyYJRNee1KHvqvIFOLo8gRzy/Jy3HmRnwQG8Fn0x+/9L5HqvcWgshrrp4VUT5/4vf8baP6iJ4a5ZWyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:02:28.918957Z"},"content_sha256":"f0e5af08f34743a9bcb7000cc6dabdfb3f8d55e11c9c7b0c8c66784acc3260ea","schema_version":"1.0","event_id":"sha256:f0e5af08f34743a9bcb7000cc6dabdfb3f8d55e11c9c7b0c8c66784acc3260ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LH7HITNWIPIMPUVTJIXKADMRYN/bundle.json","state_url":"https://pith.science/pith/LH7HITNWIPIMPUVTJIXKADMRYN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LH7HITNWIPIMPUVTJIXKADMRYN/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":"2026-06-26T07:02:28Z","links":{"resolver":"https://pith.science/pith/LH7HITNWIPIMPUVTJIXKADMRYN","bundle":"https://pith.science/pith/LH7HITNWIPIMPUVTJIXKADMRYN/bundle.json","state":"https://pith.science/pith/LH7HITNWIPIMPUVTJIXKADMRYN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LH7HITNWIPIMPUVTJIXKADMRYN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LH7HITNWIPIMPUVTJIXKADMRYN","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":"fa83538b96f87c51872505770792eb7b1e42acd174e3d858a579bf28361f0554","cross_cats_sorted":["cs.SI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-06-22T14:33:15Z","title_canon_sha256":"b2ce62cc35e82cf4e1f4dc587ec992068cb6cdcb09b0d07ffa90976ce3c21795"},"schema_version":"1.0","source":{"id":"1606.06962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06962","created_at":"2026-05-18T01:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06962v1","created_at":"2026-05-18T01:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06962","created_at":"2026-05-18T01:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"LH7HITNWIPIM","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LH7HITNWIPIMPUVT","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LH7HITNW","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:f0e5af08f34743a9bcb7000cc6dabdfb3f8d55e11c9c7b0c8c66784acc3260ea","target":"graph","created_at":"2026-05-18T01:12:00Z","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":"Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods for signal processing on graphs ignore the dimension of time, treating successive graph signals independently or taking a global average. To address this shortcoming, this paper considers the statistical analysis of time-varying graph signals. We introduce a novel definition of joint (time-vertex) stationarity, which generalizes the classical","authors_text":"Andreas Loukas, Francesco Grassi, Nathanael Perraudin, Pierre Vandergheynst","cross_cats":["cs.SI","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-06-22T14:33:15Z","title":"Towards stationary time-vertex signal processing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06962","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:a33ee9afb34797c529717ab540e7482d09fff9434494f7faa4bb6631077fd51c","target":"record","created_at":"2026-05-18T01:12:00Z","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":"fa83538b96f87c51872505770792eb7b1e42acd174e3d858a579bf28361f0554","cross_cats_sorted":["cs.SI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-06-22T14:33:15Z","title_canon_sha256":"b2ce62cc35e82cf4e1f4dc587ec992068cb6cdcb09b0d07ffa90976ce3c21795"},"schema_version":"1.0","source":{"id":"1606.06962","kind":"arxiv","version":1}},"canonical_sha256":"59fe744db643d0c7d2b34a2ea00d91c35ec1e75f9ab5f9ccf43d369c86496a93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59fe744db643d0c7d2b34a2ea00d91c35ec1e75f9ab5f9ccf43d369c86496a93","first_computed_at":"2026-05-18T01:12:00.830126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:00.830126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ynsLmkNSyvimdCK8dETazvyg9oCAkEsYe5rScOovFT93ohe97dKUzzlsKnyoDhn1k14WI963KnLDOVXrMml2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:00.830465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a33ee9afb34797c529717ab540e7482d09fff9434494f7faa4bb6631077fd51c","sha256:f0e5af08f34743a9bcb7000cc6dabdfb3f8d55e11c9c7b0c8c66784acc3260ea"],"state_sha256":"3679b81b37391b271b8cc8e36a8f73e4ec391a9a6781d52cae7ce42f03a6ba29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vbjqk+eDv/hbk8bmNlVXXn/MbDJ7GfYGlcWuoQHpjwawN64Wbrk4toi27/jh2JEx4TZk1t4EMEhxjztaG+55Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T07:02:28.920950Z","bundle_sha256":"8fd2ecd01af81230715f6ccb1fffce491536bd3bbdaddcfa2deab3a83ff48c68"}}