{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XAHPKLRIJYAQSHX4MVUDSIOWMF","short_pith_number":"pith:XAHPKLRI","canonical_record":{"source":{"id":"1502.04928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-17T15:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"57da5175b93b84ad82188bb00350ac38ae70136b1dfa884a3ed9926ff3d48a39","abstract_canon_sha256":"b3e1e5325f4629e6c69b6a16ab2bb5b9194d4f54b761e6bd5b692a96f2dfdd3b"},"schema_version":"1.0"},"canonical_sha256":"b80ef52e284e01091efc65683921d66142b87bfb709f7ca6e9b29043329a9b3e","source":{"kind":"arxiv","id":"1502.04928","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04928","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04928v1","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04928","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"XAHPKLRIJYAQ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XAHPKLRIJYAQSHX4","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XAHPKLRI","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XAHPKLRIJYAQSHX4MVUDSIOWMF","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-17T15:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"57da5175b93b84ad82188bb00350ac38ae70136b1dfa884a3ed9926ff3d48a39","abstract_canon_sha256":"b3e1e5325f4629e6c69b6a16ab2bb5b9194d4f54b761e6bd5b692a96f2dfdd3b"},"schema_version":"1.0"},"canonical_sha256":"b80ef52e284e01091efc65683921d66142b87bfb709f7ca6e9b29043329a9b3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:53.517217Z","signature_b64":"3h5nt5xQ/IV2ChWoHJO2UON6eXXAgEY2WYVh3beG7HTOJdSWc6cTY40l+9YZ9tHp1+9iN6cN4k4slWpZ7m8QDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b80ef52e284e01091efc65683921d66142b87bfb709f7ca6e9b29043329a9b3e","last_reissued_at":"2026-05-18T02:26:53.516821Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:53.516821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04928","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":"2026-05-18T02:26:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fcLz+Floep8gjnzDzRAtcBLeSVII+ufE/v6tC1uTPO0Ohkfb8ec+FH7A31qoEkO0lRyVVXQzg+g/xMTn/4GpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:43:10.862575Z"},"content_sha256":"444cd7e248eb5f650f6eb9f7121302b7ec51e975c551532811478d9be4e50cd1","schema_version":"1.0","event_id":"sha256:444cd7e248eb5f650f6eb9f7121302b7ec51e975c551532811478d9be4e50cd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XAHPKLRIJYAQSHX4MVUDSIOWMF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diagonal Riccati Stability and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexander Aleksandrov, Oliver Mason","submitted_at":"2015-02-17T15:39:08Z","abstract_excerpt":"We consider the question of diagonal Riccati stability for a pair of real matrices A, B. A necessary and sufficient condition for diagonal Riccati stability is derived and applications of this to two distinct cases are presented. We also describe some motivations for this question arising in the theory of generalised Lotka-Volterra systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04928","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":"2026-05-18T02:26:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gmenqrQ2J87pWbAkmWxCt86inbYxJxO8Jjw/ApoPso97BV//hxFFpivx6BEPbjZRbyYF15+AdaaxyPBvp7k0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:43:10.862908Z"},"content_sha256":"171287bb45db2eeda4a6579fc39febe0949d0ae059b50a43c511168fb05d7968","schema_version":"1.0","event_id":"sha256:171287bb45db2eeda4a6579fc39febe0949d0ae059b50a43c511168fb05d7968"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAHPKLRIJYAQSHX4MVUDSIOWMF/bundle.json","state_url":"https://pith.science/pith/XAHPKLRIJYAQSHX4MVUDSIOWMF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAHPKLRIJYAQSHX4MVUDSIOWMF/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":"2026-06-27T11:43:10Z","links":{"resolver":"https://pith.science/pith/XAHPKLRIJYAQSHX4MVUDSIOWMF","bundle":"https://pith.science/pith/XAHPKLRIJYAQSHX4MVUDSIOWMF/bundle.json","state":"https://pith.science/pith/XAHPKLRIJYAQSHX4MVUDSIOWMF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAHPKLRIJYAQSHX4MVUDSIOWMF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XAHPKLRIJYAQSHX4MVUDSIOWMF","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":"b3e1e5325f4629e6c69b6a16ab2bb5b9194d4f54b761e6bd5b692a96f2dfdd3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-17T15:39:08Z","title_canon_sha256":"57da5175b93b84ad82188bb00350ac38ae70136b1dfa884a3ed9926ff3d48a39"},"schema_version":"1.0","source":{"id":"1502.04928","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04928","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04928v1","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04928","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"XAHPKLRIJYAQ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XAHPKLRIJYAQSHX4","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XAHPKLRI","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:171287bb45db2eeda4a6579fc39febe0949d0ae059b50a43c511168fb05d7968","target":"graph","created_at":"2026-05-18T02:26:53Z","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 consider the question of diagonal Riccati stability for a pair of real matrices A, B. A necessary and sufficient condition for diagonal Riccati stability is derived and applications of this to two distinct cases are presented. We also describe some motivations for this question arising in the theory of generalised Lotka-Volterra systems.","authors_text":"Alexander Aleksandrov, Oliver Mason","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-17T15:39:08Z","title":"Diagonal Riccati Stability and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04928","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":"sha256:444cd7e248eb5f650f6eb9f7121302b7ec51e975c551532811478d9be4e50cd1","target":"record","created_at":"2026-05-18T02:26:53Z","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":"b3e1e5325f4629e6c69b6a16ab2bb5b9194d4f54b761e6bd5b692a96f2dfdd3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-17T15:39:08Z","title_canon_sha256":"57da5175b93b84ad82188bb00350ac38ae70136b1dfa884a3ed9926ff3d48a39"},"schema_version":"1.0","source":{"id":"1502.04928","kind":"arxiv","version":1}},"canonical_sha256":"b80ef52e284e01091efc65683921d66142b87bfb709f7ca6e9b29043329a9b3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b80ef52e284e01091efc65683921d66142b87bfb709f7ca6e9b29043329a9b3e","first_computed_at":"2026-05-18T02:26:53.516821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:53.516821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3h5nt5xQ/IV2ChWoHJO2UON6eXXAgEY2WYVh3beG7HTOJdSWc6cTY40l+9YZ9tHp1+9iN6cN4k4slWpZ7m8QDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:53.517217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04928","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:444cd7e248eb5f650f6eb9f7121302b7ec51e975c551532811478d9be4e50cd1","sha256:171287bb45db2eeda4a6579fc39febe0949d0ae059b50a43c511168fb05d7968"],"state_sha256":"c0ca14b91371b049990ae0dcf31ff1cb88369bb9d7884e6579db537447cfdd20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jA4UgtqslrbcqBYeY2337/woBF+or+V+OUBV+aqJlrU0czL0BK6w6/qBLVyIYn17JKWZDngR43L59uspJ504CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T11:43:10.864731Z","bundle_sha256":"e2503772563aeb7aaa432098a1d6b9642c841932156340bcbfd4bc5c0ce37d6f"}}