{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2HH5BP4MV3BUHMBQ4HLGIPCQMQ","short_pith_number":"pith:2HH5BP4M","canonical_record":{"source":{"id":"1510.03947","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-14T02:15:35Z","cross_cats_sorted":["cs.SY","math.IT"],"title_canon_sha256":"4e84e7ae48df705e8ba6194d39a14cf51ecfcca1c4bac99c49a3319dc68df00c","abstract_canon_sha256":"2979538fda9e9de1d9bc958759767446a190400de8be0ac9b34206d5ca746a71"},"schema_version":"1.0"},"canonical_sha256":"d1cfd0bf8caec343b030e1d6643c5064119fd0fea42ae218a41824b6e577bc8e","source":{"kind":"arxiv","id":"1510.03947","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03947","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03947v2","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03947","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"pith_short_12","alias_value":"2HH5BP4MV3BU","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2HH5BP4MV3BUHMBQ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2HH5BP4M","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2HH5BP4MV3BUHMBQ4HLGIPCQMQ","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03947","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-14T02:15:35Z","cross_cats_sorted":["cs.SY","math.IT"],"title_canon_sha256":"4e84e7ae48df705e8ba6194d39a14cf51ecfcca1c4bac99c49a3319dc68df00c","abstract_canon_sha256":"2979538fda9e9de1d9bc958759767446a190400de8be0ac9b34206d5ca746a71"},"schema_version":"1.0"},"canonical_sha256":"d1cfd0bf8caec343b030e1d6643c5064119fd0fea42ae218a41824b6e577bc8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:09.964031Z","signature_b64":"Yg8c3gg8KmKCTxGtmCe6nNbhSUWiNawwOJ6xzgoZo120VklPSlylFUARvi5L4Svqfu6h0BsJFhe1hiE/NEMcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1cfd0bf8caec343b030e1d6643c5064119fd0fea42ae218a41824b6e577bc8e","last_reissued_at":"2026-05-18T00:44:09.963609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:09.963609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03947","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":"2026-05-18T00:44:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UzNKYDvjJHisvxWXRitKCsd+nPPTEvsS0Rgfz+hcosprUIrP2Y29zkuoMEaet7H9h9RkEbMVS6sMU9trw3F+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T22:48:07.717423Z"},"content_sha256":"541fc8ae9135e228ef51822ac21995395cfe7902b39e82179bcc209f9f3defd1","schema_version":"1.0","event_id":"sha256:541fc8ae9135e228ef51822ac21995395cfe7902b39e82179bcc209f9f3defd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2HH5BP4MV3BUHMBQ4HLGIPCQMQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributed Linear Network Operators using Graph Filters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.IT"],"primary_cat":"cs.IT","authors_text":"Alejandro Ribeiro, Antonio G. Marques, Santiago Segarra","submitted_at":"2015-10-14T02:15:35Z","abstract_excerpt":"We study the design of graph filters to implement arbitrary linear transformations between graph signals. Graph filters can be represented by matrix polynomials of the graph-shift operator, which captures the structure of the graph and is assumed to be given. Thus, graph-filter design consists in choosing the coefficients of these polynomials (known as filter coefficients) to resemble desired linear transformations. Due to the local structure of the graph-shift operator, graph filters can be implemented distributedly across nodes, making them suitable for networked settings. We determine spect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03947","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":"2026-05-18T00:44:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gM4r/tCV1OT+1SUPczsqLx7C1n15BABvWXTqS678aoRd2t8nJrhZdYLAgPxylr1MQf5/yB0+K2XdOXkoUnnKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T22:48:07.718077Z"},"content_sha256":"8385f73574de04b57c0082eef919b5fd0c7001dc186123fe1541d2e9281858eb","schema_version":"1.0","event_id":"sha256:8385f73574de04b57c0082eef919b5fd0c7001dc186123fe1541d2e9281858eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2HH5BP4MV3BUHMBQ4HLGIPCQMQ/bundle.json","state_url":"https://pith.science/pith/2HH5BP4MV3BUHMBQ4HLGIPCQMQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2HH5BP4MV3BUHMBQ4HLGIPCQMQ/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":"2026-05-29T22:48:07Z","links":{"resolver":"https://pith.science/pith/2HH5BP4MV3BUHMBQ4HLGIPCQMQ","bundle":"https://pith.science/pith/2HH5BP4MV3BUHMBQ4HLGIPCQMQ/bundle.json","state":"https://pith.science/pith/2HH5BP4MV3BUHMBQ4HLGIPCQMQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2HH5BP4MV3BUHMBQ4HLGIPCQMQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2HH5BP4MV3BUHMBQ4HLGIPCQMQ","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":"2979538fda9e9de1d9bc958759767446a190400de8be0ac9b34206d5ca746a71","cross_cats_sorted":["cs.SY","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-14T02:15:35Z","title_canon_sha256":"4e84e7ae48df705e8ba6194d39a14cf51ecfcca1c4bac99c49a3319dc68df00c"},"schema_version":"1.0","source":{"id":"1510.03947","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03947","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03947v2","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03947","created_at":"2026-05-18T00:44:09Z"},{"alias_kind":"pith_short_12","alias_value":"2HH5BP4MV3BU","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2HH5BP4MV3BUHMBQ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2HH5BP4M","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:8385f73574de04b57c0082eef919b5fd0c7001dc186123fe1541d2e9281858eb","target":"graph","created_at":"2026-05-18T00:44:09Z","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 study the design of graph filters to implement arbitrary linear transformations between graph signals. Graph filters can be represented by matrix polynomials of the graph-shift operator, which captures the structure of the graph and is assumed to be given. Thus, graph-filter design consists in choosing the coefficients of these polynomials (known as filter coefficients) to resemble desired linear transformations. Due to the local structure of the graph-shift operator, graph filters can be implemented distributedly across nodes, making them suitable for networked settings. We determine spect","authors_text":"Alejandro Ribeiro, Antonio G. Marques, Santiago Segarra","cross_cats":["cs.SY","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-14T02:15:35Z","title":"Distributed Linear Network Operators using Graph Filters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03947","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":"sha256:541fc8ae9135e228ef51822ac21995395cfe7902b39e82179bcc209f9f3defd1","target":"record","created_at":"2026-05-18T00:44:09Z","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":"2979538fda9e9de1d9bc958759767446a190400de8be0ac9b34206d5ca746a71","cross_cats_sorted":["cs.SY","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-14T02:15:35Z","title_canon_sha256":"4e84e7ae48df705e8ba6194d39a14cf51ecfcca1c4bac99c49a3319dc68df00c"},"schema_version":"1.0","source":{"id":"1510.03947","kind":"arxiv","version":2}},"canonical_sha256":"d1cfd0bf8caec343b030e1d6643c5064119fd0fea42ae218a41824b6e577bc8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1cfd0bf8caec343b030e1d6643c5064119fd0fea42ae218a41824b6e577bc8e","first_computed_at":"2026-05-18T00:44:09.963609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:09.963609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yg8c3gg8KmKCTxGtmCe6nNbhSUWiNawwOJ6xzgoZo120VklPSlylFUARvi5L4Svqfu6h0BsJFhe1hiE/NEMcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:09.964031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03947","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:541fc8ae9135e228ef51822ac21995395cfe7902b39e82179bcc209f9f3defd1","sha256:8385f73574de04b57c0082eef919b5fd0c7001dc186123fe1541d2e9281858eb"],"state_sha256":"ed8a91b0a16b22d8827c384c3159def3b34b00557b8ef851971cd6d1811eb27c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUGqBPOYUpLGcTIFKQ+LYPPQeqg4iDoiYsgyk7hfXNvHysN54pmb3Cr66I1aXAGd8tbhmNff0qLmVV0k+NxEAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T22:48:07.721297Z","bundle_sha256":"44a5d94d9677367eadc7442d2720a859a3e16e03dc0db099a2f1b272c54e51f5"}}