{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:F26AV2BZDFPGY7SRD4QVFDGLGN","short_pith_number":"pith:F26AV2BZ","canonical_record":{"source":{"id":"1409.0072","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-08-30T00:42:39Z","cross_cats_sorted":[],"title_canon_sha256":"8b1ab420b36104535398dc2aa7f0283759961bddab65b8b190b7b669ae5f05ef","abstract_canon_sha256":"4ad2c4a4f36b4b8da56daba17b70ddf1fa2f1862a46b671456608974351b56ba"},"schema_version":"1.0"},"canonical_sha256":"2ebc0ae839195e6c7e511f21528ccb33637ed62e153675ac8edeb7709f07b1de","source":{"kind":"arxiv","id":"1409.0072","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0072","created_at":"2026-05-18T02:31:59Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0072v2","created_at":"2026-05-18T02:31:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0072","created_at":"2026-05-18T02:31:59Z"},{"alias_kind":"pith_short_12","alias_value":"F26AV2BZDFPG","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F26AV2BZDFPGY7SR","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F26AV2BZ","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:F26AV2BZDFPGY7SRD4QVFDGLGN","target":"record","payload":{"canonical_record":{"source":{"id":"1409.0072","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-08-30T00:42:39Z","cross_cats_sorted":[],"title_canon_sha256":"8b1ab420b36104535398dc2aa7f0283759961bddab65b8b190b7b669ae5f05ef","abstract_canon_sha256":"4ad2c4a4f36b4b8da56daba17b70ddf1fa2f1862a46b671456608974351b56ba"},"schema_version":"1.0"},"canonical_sha256":"2ebc0ae839195e6c7e511f21528ccb33637ed62e153675ac8edeb7709f07b1de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:59.469598Z","signature_b64":"H24LH/fH9G7noYnPGqvlAXbetydYZ/WQlj2TrUQUjM97LHfVVGyXHV0zDZHU4MrZzyQl88TfCWDtT27ZgDJuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ebc0ae839195e6c7e511f21528ccb33637ed62e153675ac8edeb7709f07b1de","last_reissued_at":"2026-05-18T02:31:59.468829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:59.468829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.0072","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":"2026-05-18T02:31:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p1M0gJ8Sm4vkOkTrNQcaHz0mQG/+lf9VaInfTCbezzv4i+JPlX6TxEQ7XpyX/fpPgB4+MCLvXxb17CGFxUi0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:51:41.102644Z"},"content_sha256":"2eec511f765a8263e29c23b7d773fd3b5cc44144843e340a97133cddcd8ba49b","schema_version":"1.0","event_id":"sha256:2eec511f765a8263e29c23b7d773fd3b5cc44144843e340a97133cddcd8ba49b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:F26AV2BZDFPGY7SRD4QVFDGLGN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On minimal realisations of dynamical structure functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Jorge Goncalvees, Keith Glover, Ye Yuan","submitted_at":"2014-08-30T00:42:39Z","abstract_excerpt":"Motivated by the fact that transfer functions do not contain structural information about networks, dynamical structure functions were introduced to capture causal relationships between measured nodes in networks. From the dynamical structure functions, a) we show that the actual number of hidden states can be larger than the number of hidden states estimated from the corresponding transfer function; b) we can obtain partial information about the true state-space equation, which cannot in general be obtained from the transfer function. Based on these properties, this paper proposes algorithms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0072","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":"2026-05-18T02:31:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SYvNfdTemlWOTUirIcLiLmShEbblRPx+TX+VilFsLl6Lvcb2uLXpbsU8CB3j+51xUatEt/5BRi4IMIrMwm1gBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:51:41.103362Z"},"content_sha256":"038146bf64449582598424dc6e3a2f48dea363ce5aa27d90613ea5183e179e81","schema_version":"1.0","event_id":"sha256:038146bf64449582598424dc6e3a2f48dea363ce5aa27d90613ea5183e179e81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F26AV2BZDFPGY7SRD4QVFDGLGN/bundle.json","state_url":"https://pith.science/pith/F26AV2BZDFPGY7SRD4QVFDGLGN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F26AV2BZDFPGY7SRD4QVFDGLGN/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":"2026-06-11T16:51:41Z","links":{"resolver":"https://pith.science/pith/F26AV2BZDFPGY7SRD4QVFDGLGN","bundle":"https://pith.science/pith/F26AV2BZDFPGY7SRD4QVFDGLGN/bundle.json","state":"https://pith.science/pith/F26AV2BZDFPGY7SRD4QVFDGLGN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F26AV2BZDFPGY7SRD4QVFDGLGN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F26AV2BZDFPGY7SRD4QVFDGLGN","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":"4ad2c4a4f36b4b8da56daba17b70ddf1fa2f1862a46b671456608974351b56ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-08-30T00:42:39Z","title_canon_sha256":"8b1ab420b36104535398dc2aa7f0283759961bddab65b8b190b7b669ae5f05ef"},"schema_version":"1.0","source":{"id":"1409.0072","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0072","created_at":"2026-05-18T02:31:59Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0072v2","created_at":"2026-05-18T02:31:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0072","created_at":"2026-05-18T02:31:59Z"},{"alias_kind":"pith_short_12","alias_value":"F26AV2BZDFPG","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F26AV2BZDFPGY7SR","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F26AV2BZ","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:038146bf64449582598424dc6e3a2f48dea363ce5aa27d90613ea5183e179e81","target":"graph","created_at":"2026-05-18T02:31:59Z","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":"Motivated by the fact that transfer functions do not contain structural information about networks, dynamical structure functions were introduced to capture causal relationships between measured nodes in networks. From the dynamical structure functions, a) we show that the actual number of hidden states can be larger than the number of hidden states estimated from the corresponding transfer function; b) we can obtain partial information about the true state-space equation, which cannot in general be obtained from the transfer function. Based on these properties, this paper proposes algorithms ","authors_text":"Jorge Goncalvees, Keith Glover, Ye Yuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-08-30T00:42:39Z","title":"On minimal realisations of dynamical structure functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0072","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":"sha256:2eec511f765a8263e29c23b7d773fd3b5cc44144843e340a97133cddcd8ba49b","target":"record","created_at":"2026-05-18T02:31:59Z","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":"4ad2c4a4f36b4b8da56daba17b70ddf1fa2f1862a46b671456608974351b56ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-08-30T00:42:39Z","title_canon_sha256":"8b1ab420b36104535398dc2aa7f0283759961bddab65b8b190b7b669ae5f05ef"},"schema_version":"1.0","source":{"id":"1409.0072","kind":"arxiv","version":2}},"canonical_sha256":"2ebc0ae839195e6c7e511f21528ccb33637ed62e153675ac8edeb7709f07b1de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ebc0ae839195e6c7e511f21528ccb33637ed62e153675ac8edeb7709f07b1de","first_computed_at":"2026-05-18T02:31:59.468829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:59.468829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H24LH/fH9G7noYnPGqvlAXbetydYZ/WQlj2TrUQUjM97LHfVVGyXHV0zDZHU4MrZzyQl88TfCWDtT27ZgDJuDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:59.469598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0072","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2eec511f765a8263e29c23b7d773fd3b5cc44144843e340a97133cddcd8ba49b","sha256:038146bf64449582598424dc6e3a2f48dea363ce5aa27d90613ea5183e179e81"],"state_sha256":"049defe85d4d009c2b021bd574816eafc2b9bfdc63cc369c71e4e5667b9e256e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mOqLulLfxfvisvgnRQ9i37jzESzRcHr0EyXlWyKbOcL/N5otY96lvuuqeAPv7DQbusCvq2CwN/eWeU4rN3u8Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:51:41.107619Z","bundle_sha256":"54360b61c5b1d8b0ffa7532c480402d999f675e92ba329ee72120da16765c7e1"}}