{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3SIRUHUVDGK564DRMMIBXKUWLZ","short_pith_number":"pith:3SIRUHUV","canonical_record":{"source":{"id":"2607.27852","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2026-07-30T08:31:20Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"1a9101aa333929a0a79aa55874347ccfefe6de51ab24022e127ec648b261bc9a","abstract_canon_sha256":"d0f775031e51cbbc57e19ac0470a40b088d6c8716a73e39e8b9e5fdc61f16e2b"},"schema_version":"1.0"},"canonical_sha256":"dc911a1e951995df707163101baa965e73052e12a926561b1c939d2538a8c0b6","source":{"kind":"arxiv","id":"2607.27852","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27852","created_at":"2026-07-31T01:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27852v1","created_at":"2026-07-31T01:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27852","created_at":"2026-07-31T01:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"3SIRUHUVDGK5","created_at":"2026-07-31T01:34:28Z"},{"alias_kind":"pith_short_16","alias_value":"3SIRUHUVDGK564DR","created_at":"2026-07-31T01:34:28Z"},{"alias_kind":"pith_short_8","alias_value":"3SIRUHUV","created_at":"2026-07-31T01:34:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3SIRUHUVDGK564DRMMIBXKUWLZ","target":"record","payload":{"canonical_record":{"source":{"id":"2607.27852","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2026-07-30T08:31:20Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"1a9101aa333929a0a79aa55874347ccfefe6de51ab24022e127ec648b261bc9a","abstract_canon_sha256":"d0f775031e51cbbc57e19ac0470a40b088d6c8716a73e39e8b9e5fdc61f16e2b"},"schema_version":"1.0"},"canonical_sha256":"dc911a1e951995df707163101baa965e73052e12a926561b1c939d2538a8c0b6","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc911a1e951995df707163101baa965e73052e12a926561b1c939d2538a8c0b6","last_reissued_at":"2026-07-31T01:34:28.972402Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:34:28.972402Z"},"source_kind":"arxiv","source_id":"2607.27852","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":"2026-07-31T01:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4ahQjLTxi++eN67F7AqI7+1wSzSr77DYD2kvhWdVmF7C5rNGOZL8K+mWLZcX/WuTrh8f4EQk6E5+wFF204QBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:52:43.302734Z"},"content_sha256":"3c2ac38b93fe1c04a087570da1a6f498f7c83d47c4933080ec619e6d358476ca","schema_version":"1.0","event_id":"sha256:3c2ac38b93fe1c04a087570da1a6f498f7c83d47c4933080ec619e6d358476ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3SIRUHUVDGK564DRMMIBXKUWLZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Strong Structural Controllability of Matrix-Weighted Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","math.OC"],"primary_cat":"eess.SY","authors_text":"Lanhao Zhao","submitted_at":"2026-07-30T08:31:20Z","abstract_excerpt":"This paper investigates the strong structural controllability of multi-agent networks. Based on the definition of equitable partitions, an upper bound for the strong structural controllable subspace (SSCS) is established. To reflect the physical significance of matrix weights where the state dimension is greater than one, the multi-agent system is modeled using higher-order dynamics. Furthermore, to address matrix singularity and asymmetric couplings, a matrix space basis decomposition method is proposed to transform the matrix-weighted network into layered scalar networks. Additionally, by ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27852","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.27852/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-31T01:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YQHorMODYmoyWhlrI8emN2WJmJ0zTISuFVxPAZsrBh7qvVhxAZ68nkRmU0B4KO7ahV0LTiBiiB0TmQuTGR/PCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:52:43.304471Z"},"content_sha256":"2d0e41826201a9afcf9e636b488c7e42985a69720b01a4de4beed013c57fd965","schema_version":"1.0","event_id":"sha256:2d0e41826201a9afcf9e636b488c7e42985a69720b01a4de4beed013c57fd965"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3SIRUHUVDGK564DRMMIBXKUWLZ/bundle.json","state_url":"https://pith.science/pith/3SIRUHUVDGK564DRMMIBXKUWLZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3SIRUHUVDGK564DRMMIBXKUWLZ/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":"2026-08-03T18:52:43Z","links":{"resolver":"https://pith.science/pith/3SIRUHUVDGK564DRMMIBXKUWLZ","bundle":"https://pith.science/pith/3SIRUHUVDGK564DRMMIBXKUWLZ/bundle.json","state":"https://pith.science/pith/3SIRUHUVDGK564DRMMIBXKUWLZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3SIRUHUVDGK564DRMMIBXKUWLZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3SIRUHUVDGK564DRMMIBXKUWLZ","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":"d0f775031e51cbbc57e19ac0470a40b088d6c8716a73e39e8b9e5fdc61f16e2b","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2026-07-30T08:31:20Z","title_canon_sha256":"1a9101aa333929a0a79aa55874347ccfefe6de51ab24022e127ec648b261bc9a"},"schema_version":"1.0","source":{"id":"2607.27852","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27852","created_at":"2026-07-31T01:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27852v1","created_at":"2026-07-31T01:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27852","created_at":"2026-07-31T01:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"3SIRUHUVDGK5","created_at":"2026-07-31T01:34:28Z"},{"alias_kind":"pith_short_16","alias_value":"3SIRUHUVDGK564DR","created_at":"2026-07-31T01:34:28Z"},{"alias_kind":"pith_short_8","alias_value":"3SIRUHUV","created_at":"2026-07-31T01:34:28Z"}],"graph_snapshots":[{"event_id":"sha256:2d0e41826201a9afcf9e636b488c7e42985a69720b01a4de4beed013c57fd965","target":"graph","created_at":"2026-07-31T01:34:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.27852/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates the strong structural controllability of multi-agent networks. Based on the definition of equitable partitions, an upper bound for the strong structural controllable subspace (SSCS) is established. To reflect the physical significance of matrix weights where the state dimension is greater than one, the multi-agent system is modeled using higher-order dynamics. Furthermore, to address matrix singularity and asymmetric couplings, a matrix space basis decomposition method is proposed to transform the matrix-weighted network into layered scalar networks. Additionally, by ex","authors_text":"Lanhao Zhao","cross_cats":["cs.SY","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2026-07-30T08:31:20Z","title":"On the Strong Structural Controllability of Matrix-Weighted Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27852","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":"sha256:3c2ac38b93fe1c04a087570da1a6f498f7c83d47c4933080ec619e6d358476ca","target":"record","created_at":"2026-07-31T01:34:28Z","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":"d0f775031e51cbbc57e19ac0470a40b088d6c8716a73e39e8b9e5fdc61f16e2b","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2026-07-30T08:31:20Z","title_canon_sha256":"1a9101aa333929a0a79aa55874347ccfefe6de51ab24022e127ec648b261bc9a"},"schema_version":"1.0","source":{"id":"2607.27852","kind":"arxiv","version":1}},"canonical_sha256":"dc911a1e951995df707163101baa965e73052e12a926561b1c939d2538a8c0b6","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc911a1e951995df707163101baa965e73052e12a926561b1c939d2538a8c0b6","first_computed_at":"2026-07-31T01:34:28.972402Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:34:28.972402Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.27852","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c2ac38b93fe1c04a087570da1a6f498f7c83d47c4933080ec619e6d358476ca","sha256:2d0e41826201a9afcf9e636b488c7e42985a69720b01a4de4beed013c57fd965"],"state_sha256":"9619c71aee71beade9fc3d993b790b0a213eb6f9b6c737a44476ee794a3f45b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"60M0PocByN/kV4ehnKrxy+YCbXa/D1dRLiP8LL5nJHCp7ZKyvnZX8X120UtCdjb415H7xQ8LvwfKFhNxYrCYBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T18:52:43.310425Z","bundle_sha256":"0fbaa9f5a553b8020029c2892bf48785402cac0d1b0064fda44b33ef08ee2e9e"}}