{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HZ5VPCRSVHLDABFLK7BI5DQPNQ","short_pith_number":"pith:HZ5VPCRS","canonical_record":{"source":{"id":"1612.04722","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-14T16:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"411be3b73c8a3911e438c8f88f8baa38d0fb48b41072b9949845a5280c9fc661","abstract_canon_sha256":"ee026268a8afe43745c2f7cf0eef32022f5284407efb8e74c1fb4df778e96edd"},"schema_version":"1.0"},"canonical_sha256":"3e7b578a32a9d63004ab57c28e8e0f6c015ff2dc4cead3a970ba943226f49c94","source":{"kind":"arxiv","id":"1612.04722","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04722","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04722v1","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04722","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"HZ5VPCRSVHLD","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HZ5VPCRSVHLDABFL","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HZ5VPCRS","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HZ5VPCRSVHLDABFLK7BI5DQPNQ","target":"record","payload":{"canonical_record":{"source":{"id":"1612.04722","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-14T16:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"411be3b73c8a3911e438c8f88f8baa38d0fb48b41072b9949845a5280c9fc661","abstract_canon_sha256":"ee026268a8afe43745c2f7cf0eef32022f5284407efb8e74c1fb4df778e96edd"},"schema_version":"1.0"},"canonical_sha256":"3e7b578a32a9d63004ab57c28e8e0f6c015ff2dc4cead3a970ba943226f49c94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:58.745102Z","signature_b64":"OdLoWw73bh39yZbGD5TYNkNjsboj85pHPOD68kJWWB08V4SYtqfoBU7XBxNmoR+8VrJS+y2usxW4syWbpz+qBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e7b578a32a9d63004ab57c28e8e0f6c015ff2dc4cead3a970ba943226f49c94","last_reissued_at":"2026-05-18T00:54:58.744610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:58.744610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.04722","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":"2026-05-18T00:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pkjkZfduU/w5eooIM9st55NQdxR9hg4L2YPLQDGnNJhwRfIFLb26Wk3wrXlhcn/o/CB+Jsn9TrOyYplS/siICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:20:06.973408Z"},"content_sha256":"a65178593a2a695d28fbcd2754116ad24e17367dd7004ed396f490d955cc20af","schema_version":"1.0","event_id":"sha256:a65178593a2a695d28fbcd2754116ad24e17367dd7004ed396f490d955cc20af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HZ5VPCRSVHLDABFLK7BI5DQPNQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Lyapunov Matrix of Linear Delay Difference Equations in Continuous Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Emanuel Rocha, Michael Di Loreto, Sabine Mondi\\'e","submitted_at":"2016-12-14T16:50:37Z","abstract_excerpt":"The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the case of single delay or commensurate delays. An approximation is proposed for the non-commensurate case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04722","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":"2026-05-18T00:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WWUstzGtGVNxmqn7cTP9Ff7fhi6YzagcHNkucuiivZ5u34lFmxqErf08mZFf4swGrmsu00I4cY+2t0ZhtGowAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:20:06.974091Z"},"content_sha256":"9370b97e1e32ccc65deb325e0f7b9b02bf1aad35ec20a66d700d5702470b0b0a","schema_version":"1.0","event_id":"sha256:9370b97e1e32ccc65deb325e0f7b9b02bf1aad35ec20a66d700d5702470b0b0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HZ5VPCRSVHLDABFLK7BI5DQPNQ/bundle.json","state_url":"https://pith.science/pith/HZ5VPCRSVHLDABFLK7BI5DQPNQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HZ5VPCRSVHLDABFLK7BI5DQPNQ/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":"2026-06-05T19:20:06Z","links":{"resolver":"https://pith.science/pith/HZ5VPCRSVHLDABFLK7BI5DQPNQ","bundle":"https://pith.science/pith/HZ5VPCRSVHLDABFLK7BI5DQPNQ/bundle.json","state":"https://pith.science/pith/HZ5VPCRSVHLDABFLK7BI5DQPNQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HZ5VPCRSVHLDABFLK7BI5DQPNQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HZ5VPCRSVHLDABFLK7BI5DQPNQ","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":"ee026268a8afe43745c2f7cf0eef32022f5284407efb8e74c1fb4df778e96edd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-14T16:50:37Z","title_canon_sha256":"411be3b73c8a3911e438c8f88f8baa38d0fb48b41072b9949845a5280c9fc661"},"schema_version":"1.0","source":{"id":"1612.04722","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04722","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04722v1","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04722","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"HZ5VPCRSVHLD","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HZ5VPCRSVHLDABFL","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HZ5VPCRS","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:9370b97e1e32ccc65deb325e0f7b9b02bf1aad35ec20a66d700d5702470b0b0a","target":"graph","created_at":"2026-05-18T00:54:58Z","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":"The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the case of single delay or commensurate delays. An approximation is proposed for the non-commensurate case.","authors_text":"Emanuel Rocha, Michael Di Loreto, Sabine Mondi\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-14T16:50:37Z","title":"On the Lyapunov Matrix of Linear Delay Difference Equations in Continuous Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04722","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:a65178593a2a695d28fbcd2754116ad24e17367dd7004ed396f490d955cc20af","target":"record","created_at":"2026-05-18T00:54:58Z","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":"ee026268a8afe43745c2f7cf0eef32022f5284407efb8e74c1fb4df778e96edd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-14T16:50:37Z","title_canon_sha256":"411be3b73c8a3911e438c8f88f8baa38d0fb48b41072b9949845a5280c9fc661"},"schema_version":"1.0","source":{"id":"1612.04722","kind":"arxiv","version":1}},"canonical_sha256":"3e7b578a32a9d63004ab57c28e8e0f6c015ff2dc4cead3a970ba943226f49c94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e7b578a32a9d63004ab57c28e8e0f6c015ff2dc4cead3a970ba943226f49c94","first_computed_at":"2026-05-18T00:54:58.744610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:58.744610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OdLoWw73bh39yZbGD5TYNkNjsboj85pHPOD68kJWWB08V4SYtqfoBU7XBxNmoR+8VrJS+y2usxW4syWbpz+qBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:58.745102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04722","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a65178593a2a695d28fbcd2754116ad24e17367dd7004ed396f490d955cc20af","sha256:9370b97e1e32ccc65deb325e0f7b9b02bf1aad35ec20a66d700d5702470b0b0a"],"state_sha256":"c20926ff519aa254e0280627d60534f5661a8fe64cd1f71876c4fd0f3cffcdf1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L4uzdwQhK2xDAprKlfFaBH30URouip+tdRxxx/r8tmzXzSXOctXSoF5dEV3fnTSssqpj6fOEeMdjHRQPzUYCCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:20:06.977836Z","bundle_sha256":"fe5c15b4e8525c4d95c0205f2cd9351e2a91151e2fdd338edf22cc2a56717641"}}