{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3SEOJDS3LXNOEHWVH4LUBKDRVE","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":"4d31639ef56d755d959c0dcbfc22a7f1c57ccf92fd02fa8b9272c8064278c655","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-18T13:33:11Z","title_canon_sha256":"5ec6eddf0bb7e931763100c05979e1b611497d2a1f1178956998f7051da48189"},"schema_version":"1.0","source":{"id":"1212.4346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4346","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4346v1","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4346","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"3SEOJDS3LXNO","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3SEOJDS3LXNOEHWV","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3SEOJDS3","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:bd9a316640d1e09eb4f4d83da2d56fe3f293c3c41fb7daa86c4020984bd86c05","target":"graph","created_at":"2026-05-18T03:38:13Z","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":"In this paper, we introduce the notion of reproducing kernel Hilbert spaces for graphs and the Gram matrices associated with them. Our aim is to investigate the Gram matrices of reproducing kernel Hilbert spaces. We provide several bounds on the entries of the Gram matrices of reproducing kernel Hilbert spaces and characterize the graphs which attain our bounds.","authors_text":"Michio Seto, Sho Suda, Tetsuji Taniguchi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-18T13:33:11Z","title":"Gram matrices of reproducing kernel Hilbert spaces over graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4346","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:f2557a6adb340bf67190c4a220f1f7cf18db065e91fd0520aa81746cd2c1ddb4","target":"record","created_at":"2026-05-18T03:38:13Z","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":"4d31639ef56d755d959c0dcbfc22a7f1c57ccf92fd02fa8b9272c8064278c655","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-18T13:33:11Z","title_canon_sha256":"5ec6eddf0bb7e931763100c05979e1b611497d2a1f1178956998f7051da48189"},"schema_version":"1.0","source":{"id":"1212.4346","kind":"arxiv","version":1}},"canonical_sha256":"dc88e48e5b5ddae21ed53f1740a871a9171e372960da7d002bc013875e1b51a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc88e48e5b5ddae21ed53f1740a871a9171e372960da7d002bc013875e1b51a2","first_computed_at":"2026-05-18T03:38:13.263732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:13.263732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BHl1MuuTTHSjQxf/fBArCcWM/rUJZY2c+59Ioik9L+rC/2yItk9EoR/DGSPFJNz9cLcFnSNLD1IAyMrGSElRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:13.264151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2557a6adb340bf67190c4a220f1f7cf18db065e91fd0520aa81746cd2c1ddb4","sha256:bd9a316640d1e09eb4f4d83da2d56fe3f293c3c41fb7daa86c4020984bd86c05"],"state_sha256":"4a444a357c53ed6292420183629707050035bb795e308d3d938000aab72748d3"}