{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VZCLPQBZMRXXJFPPB5JWX3NSNF","short_pith_number":"pith:VZCLPQBZ","canonical_record":{"source":{"id":"2602.11921","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-02-12T13:20:53Z","cross_cats_sorted":[],"title_canon_sha256":"e47f6acc3deee64c84d3689bcf7c35155deca90493508523fa82aa91785e3b9d","abstract_canon_sha256":"93805f41db1e97eab964b4088ea8024969992a304b8595b14f43f3ba87fb9747"},"schema_version":"1.0"},"canonical_sha256":"ae44b7c039646f7495ef0f536bedb2694644c5dc5533c8c81c09b08a448794d7","source":{"kind":"arxiv","id":"2602.11921","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.11921","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"2602.11921v3","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.11921","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"VZCLPQBZMRXX","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"VZCLPQBZMRXXJFPP","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"VZCLPQBZ","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VZCLPQBZMRXXJFPPB5JWX3NSNF","target":"record","payload":{"canonical_record":{"source":{"id":"2602.11921","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-02-12T13:20:53Z","cross_cats_sorted":[],"title_canon_sha256":"e47f6acc3deee64c84d3689bcf7c35155deca90493508523fa82aa91785e3b9d","abstract_canon_sha256":"93805f41db1e97eab964b4088ea8024969992a304b8595b14f43f3ba87fb9747"},"schema_version":"1.0"},"canonical_sha256":"ae44b7c039646f7495ef0f536bedb2694644c5dc5533c8c81c09b08a448794d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:05.281647Z","signature_b64":"JU6vMoxWD/oQ/tDuO4h54SSgL0mrk/VYMLelZhgG+DHnVdEw/ogsTq2EF2gDPFhGxgeujxzTm4Ff9v7Z6VUXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae44b7c039646f7495ef0f536bedb2694644c5dc5533c8c81c09b08a448794d7","last_reissued_at":"2026-05-18T02:45:05.281048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:05.281048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.11921","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kxWRERc2EdQ21KoP27Y5Qhd7CW29ILk/Pu+msNDUIbK2txTZYCplDi4Flco4UxRwreQZ1igesjieTUrHoRe9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T21:45:21.503652Z"},"content_sha256":"92dda62c983d5f7a3ed5b7975393842bdbfde3bcff991435d352191237d61654","schema_version":"1.0","event_id":"sha256:92dda62c983d5f7a3ed5b7975393842bdbfde3bcff991435d352191237d61654"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VZCLPQBZMRXXJFPPB5JWX3NSNF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relationship Between Controllability Scoring and Optimal Experimental Design","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Finite-time controllability scores in linear networks match D- and A-optimality criteria from optimal experimental design via additive Gramian decomposition.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kazuhiro Sato","submitted_at":"2026-02-12T13:20:53Z","abstract_excerpt":"Controllability scores provide control-theoretic centrality measures that quantify the relative importance of state nodes in networked dynamical systems. We establish a structural connection between finite-time controllability scoring and approximate optimal experimental design (OED): the finite-time controllability Gramian decomposes additively across nodes, yielding an affine matrix model of the same form as the information-matrix model in OED. This yields a direct correspondence between the volumetric controllability score (VCS) and D-optimality, and between the average energy controllabili"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish a structural connection between finite-time controllability scoring and approximate optimal experimental design (OED): the finite-time controllability Gramian decomposes additively across nodes, yielding an affine matrix model of the same form as the information-matrix model in OED.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The finite-time controllability Gramian admits an additive decomposition across nodes for linear networked systems, and source-like nodes without negative self-loops exhibit the stated long-horizon downweighting under AECS.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Finite-time controllability scoring matches approximate OED, with VCS corresponding to D-optimality and AECS to A-optimality, plus a unique optimizer and long-horizon node downweighting.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Finite-time controllability scores in linear networks match D- and A-optimality criteria from optimal experimental design via additive Gramian decomposition.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1bbded80f7d1900e126117841fcf8a2388b19da3ca651101566d85d9e8a360bb"},"source":{"id":"2602.11921","kind":"arxiv","version":3},"verdict":{"id":"02f8f3f8-d68a-471d-85e8-40a907cd2fe4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T02:43:37.956714Z","strongest_claim":"We establish a structural connection between finite-time controllability scoring and approximate optimal experimental design (OED): the finite-time controllability Gramian decomposes additively across nodes, yielding an affine matrix model of the same form as the information-matrix model in OED.","one_line_summary":"Finite-time controllability scoring matches approximate OED, with VCS corresponding to D-optimality and AECS to A-optimality, plus a unique optimizer and long-horizon node downweighting.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The finite-time controllability Gramian admits an additive decomposition across nodes for linear networked systems, and source-like nodes without negative self-loops exhibit the stated long-horizon downweighting under AECS.","pith_extraction_headline":"Finite-time controllability scores in linear networks match D- and A-optimality criteria from optimal experimental design via additive Gramian decomposition."},"references":{"count":16,"sample":[{"doi":"","year":2017,"title":"On the role of network centrality in the controllability of complex networks,","work_id":"2f6da2c5-36a2-4d5c-920c-666b87e26cbd","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"Controllability of complex networks,","work_id":"3f283b0d-8a86-4ff6-afee-795316d4f26c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Controllability metrics, limitations and algorithms for complex networks,","work_id":"077e082e-3544-445f-aabc-7dc27c9b7b0b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"On submodularity and controllability in complex dynamical networks,","work_id":"f17933db-9cb9-4a2c-a595-60eb940cd572","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Controllability of large-scale networks: The control energy exponents,","work_id":"3244ec8f-c2bd-4736-9910-06f63551aee4","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":16,"snapshot_sha256":"b938f4b7b1dcca710ba41bbd433b82466a9ecbda4a9908775722961effe3b9f1","internal_anchors":1},"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":"02f8f3f8-d68a-471d-85e8-40a907cd2fe4"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xe3sF06ole3uKQN7INc5aMP7vYWS6Cpid1+Nx/i/pzS8ChYBaf7xqW5DzZnan+LS4J8P2zOjcC1tGsXqRm3UAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T21:45:21.504171Z"},"content_sha256":"913485f492ad86f42b17f7ecc96748dbe6ab2506d7e438f0089f506f955294ac","schema_version":"1.0","event_id":"sha256:913485f492ad86f42b17f7ecc96748dbe6ab2506d7e438f0089f506f955294ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZCLPQBZMRXXJFPPB5JWX3NSNF/bundle.json","state_url":"https://pith.science/pith/VZCLPQBZMRXXJFPPB5JWX3NSNF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZCLPQBZMRXXJFPPB5JWX3NSNF/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":"2026-05-21T21:45:21Z","links":{"resolver":"https://pith.science/pith/VZCLPQBZMRXXJFPPB5JWX3NSNF","bundle":"https://pith.science/pith/VZCLPQBZMRXXJFPPB5JWX3NSNF/bundle.json","state":"https://pith.science/pith/VZCLPQBZMRXXJFPPB5JWX3NSNF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZCLPQBZMRXXJFPPB5JWX3NSNF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VZCLPQBZMRXXJFPPB5JWX3NSNF","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":"93805f41db1e97eab964b4088ea8024969992a304b8595b14f43f3ba87fb9747","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-02-12T13:20:53Z","title_canon_sha256":"e47f6acc3deee64c84d3689bcf7c35155deca90493508523fa82aa91785e3b9d"},"schema_version":"1.0","source":{"id":"2602.11921","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.11921","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"2602.11921v3","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.11921","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"VZCLPQBZMRXX","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"VZCLPQBZMRXXJFPP","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"VZCLPQBZ","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:913485f492ad86f42b17f7ecc96748dbe6ab2506d7e438f0089f506f955294ac","target":"graph","created_at":"2026-05-18T02:45:05Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We establish a structural connection between finite-time controllability scoring and approximate optimal experimental design (OED): the finite-time controllability Gramian decomposes additively across nodes, yielding an affine matrix model of the same form as the information-matrix model in OED."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The finite-time controllability Gramian admits an additive decomposition across nodes for linear networked systems, and source-like nodes without negative self-loops exhibit the stated long-horizon downweighting under AECS."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Finite-time controllability scoring matches approximate OED, with VCS corresponding to D-optimality and AECS to A-optimality, plus a unique optimizer and long-horizon node downweighting."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Finite-time controllability scores in linear networks match D- and A-optimality criteria from optimal experimental design via additive Gramian decomposition."}],"snapshot_sha256":"1bbded80f7d1900e126117841fcf8a2388b19da3ca651101566d85d9e8a360bb"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Controllability scores provide control-theoretic centrality measures that quantify the relative importance of state nodes in networked dynamical systems. We establish a structural connection between finite-time controllability scoring and approximate optimal experimental design (OED): the finite-time controllability Gramian decomposes additively across nodes, yielding an affine matrix model of the same form as the information-matrix model in OED. This yields a direct correspondence between the volumetric controllability score (VCS) and D-optimality, and between the average energy controllabili","authors_text":"Kazuhiro Sato","cross_cats":[],"headline":"Finite-time controllability scores in linear networks match D- and A-optimality criteria from optimal experimental design via additive Gramian decomposition.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-02-12T13:20:53Z","title":"Relationship Between Controllability Scoring and Optimal Experimental Design"},"references":{"count":16,"internal_anchors":1,"resolved_work":16,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"On the role of network centrality in the controllability of complex networks,","work_id":"2f6da2c5-36a2-4d5c-920c-666b87e26cbd","year":2017},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Controllability of complex networks,","work_id":"3f283b0d-8a86-4ff6-afee-795316d4f26c","year":2011},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Controllability metrics, limitations and algorithms for complex networks,","work_id":"077e082e-3544-445f-aabc-7dc27c9b7b0b","year":2014},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"On submodularity and controllability in complex dynamical networks,","work_id":"f17933db-9cb9-4a2c-a595-60eb940cd572","year":2016},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Controllability of large-scale networks: The control energy exponents,","work_id":"3244ec8f-c2bd-4736-9910-06f63551aee4","year":2024}],"snapshot_sha256":"b938f4b7b1dcca710ba41bbd433b82466a9ecbda4a9908775722961effe3b9f1"},"source":{"id":"2602.11921","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-16T02:43:37.956714Z","id":"02f8f3f8-d68a-471d-85e8-40a907cd2fe4","model_set":{"reader":"grok-4.3"},"one_line_summary":"Finite-time controllability scoring matches approximate OED, with VCS corresponding to D-optimality and AECS to A-optimality, plus a unique optimizer and long-horizon node downweighting.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Finite-time controllability scores in linear networks match D- and A-optimality criteria from optimal experimental design via additive Gramian decomposition.","strongest_claim":"We establish a structural connection between finite-time controllability scoring and approximate optimal experimental design (OED): the finite-time controllability Gramian decomposes additively across nodes, yielding an affine matrix model of the same form as the information-matrix model in OED.","weakest_assumption":"The finite-time controllability Gramian admits an additive decomposition across nodes for linear networked systems, and source-like nodes without negative self-loops exhibit the stated long-horizon downweighting under AECS."}},"verdict_id":"02f8f3f8-d68a-471d-85e8-40a907cd2fe4"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:92dda62c983d5f7a3ed5b7975393842bdbfde3bcff991435d352191237d61654","target":"record","created_at":"2026-05-18T02:45:05Z","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":"93805f41db1e97eab964b4088ea8024969992a304b8595b14f43f3ba87fb9747","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-02-12T13:20:53Z","title_canon_sha256":"e47f6acc3deee64c84d3689bcf7c35155deca90493508523fa82aa91785e3b9d"},"schema_version":"1.0","source":{"id":"2602.11921","kind":"arxiv","version":3}},"canonical_sha256":"ae44b7c039646f7495ef0f536bedb2694644c5dc5533c8c81c09b08a448794d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae44b7c039646f7495ef0f536bedb2694644c5dc5533c8c81c09b08a448794d7","first_computed_at":"2026-05-18T02:45:05.281048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:05.281048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JU6vMoxWD/oQ/tDuO4h54SSgL0mrk/VYMLelZhgG+DHnVdEw/ogsTq2EF2gDPFhGxgeujxzTm4Ff9v7Z6VUXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:05.281647Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.11921","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92dda62c983d5f7a3ed5b7975393842bdbfde3bcff991435d352191237d61654","sha256:913485f492ad86f42b17f7ecc96748dbe6ab2506d7e438f0089f506f955294ac"],"state_sha256":"76b7aaa859280e2786ea87d3eafe686b8dcec3b8f96bdcb023ed459c157bdacd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G2ZilStOwozjv9uNAh83uRQFBBTaFddWbkHU4oFuXhGNrl2ZpPMf640PB2SQfAAFFprIiQQVa1ZjXDDjj3JyCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T21:45:21.506796Z","bundle_sha256":"1dbfcbd32b38dcef817a53b569fed07ecb351b82fe90f4596dd60d8b44066afd"}}