{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TOUPYKMZEVTHVBHPWZSLICI7X2","short_pith_number":"pith:TOUPYKMZ","canonical_record":{"source":{"id":"1412.6792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-21T14:52:36Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9b6c47284861493350e96e180eb97a1928c93745aae67f84360887757be37bac","abstract_canon_sha256":"17b227a17cd5a69a55cd82d0235ac87abe2c0eae557073c06f7f65a9fcfd200d"},"schema_version":"1.0"},"canonical_sha256":"9ba8fc299925667a84efb664b4091fbe80b13ffbeaa667512575fc44cdcc9c54","source":{"kind":"arxiv","id":"1412.6792","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6792","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6792v1","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6792","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"TOUPYKMZEVTH","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TOUPYKMZEVTHVBHP","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TOUPYKMZ","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TOUPYKMZEVTHVBHPWZSLICI7X2","target":"record","payload":{"canonical_record":{"source":{"id":"1412.6792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-21T14:52:36Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9b6c47284861493350e96e180eb97a1928c93745aae67f84360887757be37bac","abstract_canon_sha256":"17b227a17cd5a69a55cd82d0235ac87abe2c0eae557073c06f7f65a9fcfd200d"},"schema_version":"1.0"},"canonical_sha256":"9ba8fc299925667a84efb664b4091fbe80b13ffbeaa667512575fc44cdcc9c54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:51.226110Z","signature_b64":"FSEApD6yb3qUfQgo0JaEG/HtM3N/KZlXJ8f2OL9xEoZClp1TKeAAmJXbYs9ILGJGMGym09vwmLpoGeJ7fE3FCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ba8fc299925667a84efb664b4091fbe80b13ffbeaa667512575fc44cdcc9c54","last_reissued_at":"2026-05-18T00:57:51.225432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:51.225432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.6792","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":"2026-05-18T00:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q9No6NIp80OD/KY/uU0xSi9yOgnajWyJ3vd+4pqR7BIatlCC3vtCrjRhsl9gVnzCCE6Zdj62v7E8DyIYBPLnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:08:56.265455Z"},"content_sha256":"3764380ed79186a5a987b68408f50411477efe8963a56010ccba7f041a803445","schema_version":"1.0","event_id":"sha256:3764380ed79186a5a987b68408f50411477efe8963a56010ccba7f041a803445"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TOUPYKMZEVTHVBHPWZSLICI7X2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A linear time algorithm to verify strong structural controllability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Alexander Weber, Ferdinand Svaricek, Gunther Reissig","submitted_at":"2014-12-21T14:52:36Z","abstract_excerpt":"We prove that strong structural controllability of a pair of structural matrices $(\\mathcal{A},\\mathcal{B})$ can be verified in time linear in $n + r + \\nu$, where $\\mathcal{A}$ is square, $n$ and $r$ denote the number of columns of $\\mathcal{A}$ and $\\mathcal{B}$, respectively, and $\\nu$ is the number of non-zero entries in $(\\mathcal{A},\\mathcal{B})$. We also present an algorithm realizing this bound, which depends on a recent, high-level method to verify strong structural controllability and uses sparse matrix data structures. Linear time complexity is actually achieved by separately storin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6792","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":"2026-05-18T00:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKFU1QK17OS1uZ4pXFStfTdRviN4e8N8tZ4zzs/sEfbT8uvxW8v7LLDzYskellZkffHK9PkE6LoVuwBoDDQpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:08:56.265808Z"},"content_sha256":"88e2cd797f4d0d8a2d345c011643a1ab1f7f5884bf98a1451769b5938423e7fd","schema_version":"1.0","event_id":"sha256:88e2cd797f4d0d8a2d345c011643a1ab1f7f5884bf98a1451769b5938423e7fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TOUPYKMZEVTHVBHPWZSLICI7X2/bundle.json","state_url":"https://pith.science/pith/TOUPYKMZEVTHVBHPWZSLICI7X2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TOUPYKMZEVTHVBHPWZSLICI7X2/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":"2026-05-30T06:08:56Z","links":{"resolver":"https://pith.science/pith/TOUPYKMZEVTHVBHPWZSLICI7X2","bundle":"https://pith.science/pith/TOUPYKMZEVTHVBHPWZSLICI7X2/bundle.json","state":"https://pith.science/pith/TOUPYKMZEVTHVBHPWZSLICI7X2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TOUPYKMZEVTHVBHPWZSLICI7X2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TOUPYKMZEVTHVBHPWZSLICI7X2","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":"17b227a17cd5a69a55cd82d0235ac87abe2c0eae557073c06f7f65a9fcfd200d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-21T14:52:36Z","title_canon_sha256":"9b6c47284861493350e96e180eb97a1928c93745aae67f84360887757be37bac"},"schema_version":"1.0","source":{"id":"1412.6792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6792","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6792v1","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6792","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"TOUPYKMZEVTH","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TOUPYKMZEVTHVBHP","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TOUPYKMZ","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:88e2cd797f4d0d8a2d345c011643a1ab1f7f5884bf98a1451769b5938423e7fd","target":"graph","created_at":"2026-05-18T00:57:51Z","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 prove that strong structural controllability of a pair of structural matrices $(\\mathcal{A},\\mathcal{B})$ can be verified in time linear in $n + r + \\nu$, where $\\mathcal{A}$ is square, $n$ and $r$ denote the number of columns of $\\mathcal{A}$ and $\\mathcal{B}$, respectively, and $\\nu$ is the number of non-zero entries in $(\\mathcal{A},\\mathcal{B})$. We also present an algorithm realizing this bound, which depends on a recent, high-level method to verify strong structural controllability and uses sparse matrix data structures. Linear time complexity is actually achieved by separately storin","authors_text":"Alexander Weber, Ferdinand Svaricek, Gunther Reissig","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-21T14:52:36Z","title":"A linear time algorithm to verify strong structural controllability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6792","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":"sha256:3764380ed79186a5a987b68408f50411477efe8963a56010ccba7f041a803445","target":"record","created_at":"2026-05-18T00:57:51Z","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":"17b227a17cd5a69a55cd82d0235ac87abe2c0eae557073c06f7f65a9fcfd200d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-21T14:52:36Z","title_canon_sha256":"9b6c47284861493350e96e180eb97a1928c93745aae67f84360887757be37bac"},"schema_version":"1.0","source":{"id":"1412.6792","kind":"arxiv","version":1}},"canonical_sha256":"9ba8fc299925667a84efb664b4091fbe80b13ffbeaa667512575fc44cdcc9c54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ba8fc299925667a84efb664b4091fbe80b13ffbeaa667512575fc44cdcc9c54","first_computed_at":"2026-05-18T00:57:51.225432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:51.225432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FSEApD6yb3qUfQgo0JaEG/HtM3N/KZlXJ8f2OL9xEoZClp1TKeAAmJXbYs9ILGJGMGym09vwmLpoGeJ7fE3FCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:51.226110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3764380ed79186a5a987b68408f50411477efe8963a56010ccba7f041a803445","sha256:88e2cd797f4d0d8a2d345c011643a1ab1f7f5884bf98a1451769b5938423e7fd"],"state_sha256":"4c1d71a0188d36ebeaa3e6a1cf7360c3fd2933209f7910554b7c18ef050eb60d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OorI5gmNCayJLI0iuUBFK8K/zhXQeiqcFdpCcEXQtX95ceG9gBgm2DztnMnOeSkI6H5z+23nHol/BAS/kDpXCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:08:56.268833Z","bundle_sha256":"e9e718ed7845c05056a6dbce082ed7c8d78561ef0ecfde27d52568b62f468c17"}}