{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JSKH5II3AXI5DEHPUET22CDSZI","short_pith_number":"pith:JSKH5II3","canonical_record":{"source":{"id":"1202.1618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-08T08:05:56Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"d01e9fd138ae3d4e3a705e094db4d5ea12c40e6b33d8b78e1bbd719b6d752566","abstract_canon_sha256":"1d1b3d236a580dae5a071d59279342e149322f12f0a4cdfe59daedae01580237"},"schema_version":"1.0"},"canonical_sha256":"4c947ea11b05d1d190efa127ad0872ca3699c7afe726d340c3df786de884b7d6","source":{"kind":"arxiv","id":"1202.1618","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1618","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1618v2","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1618","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"pith_short_12","alias_value":"JSKH5II3AXI5","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JSKH5II3AXI5DEHP","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JSKH5II3","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JSKH5II3AXI5DEHPUET22CDSZI","target":"record","payload":{"canonical_record":{"source":{"id":"1202.1618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-08T08:05:56Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"d01e9fd138ae3d4e3a705e094db4d5ea12c40e6b33d8b78e1bbd719b6d752566","abstract_canon_sha256":"1d1b3d236a580dae5a071d59279342e149322f12f0a4cdfe59daedae01580237"},"schema_version":"1.0"},"canonical_sha256":"4c947ea11b05d1d190efa127ad0872ca3699c7afe726d340c3df786de884b7d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:49.625788Z","signature_b64":"/t3Vy2D7xGQ7j4M2lI5+JaV6G1h5fPwIRKsQ7Gd9fRE2TAOrABAylFJTmoCFAN1GcosqnTGiSjV/Vg8CtdQPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c947ea11b05d1d190efa127ad0872ca3699c7afe726d340c3df786de884b7d6","last_reissued_at":"2026-05-18T00:29:49.625149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:49.625149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.1618","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":"2026-05-18T00:29:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CBtIENGGU1oc4fiQh6GUi8dnjr4IUb8NkyfKG0YNjOXFYtkasZBw7197mntVljQfI/l1z34lPOhtPDGCyDb0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:00:01.190180Z"},"content_sha256":"20feb78aed986801b9cf4e9ca5b0df9e98af8281631976a53c706ac46454c68a","schema_version":"1.0","event_id":"sha256:20feb78aed986801b9cf4e9ca5b0df9e98af8281631976a53c706ac46454c68a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JSKH5II3AXI5DEHPUET22CDSZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isospectral flows on a class of finite-dimensional Jacobi matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC"],"primary_cat":"math.DS","authors_text":"Debasish Chatterjee, Federico Ramponi, John Lygeros, Tobias Sutter","submitted_at":"2012-02-08T08:05:56Z","abstract_excerpt":"We present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes $n\\times n$ zero-diagonal Jacobi matrices employed as its initial condition. This o.d.e.\\ features a right-hand side with a nested commutator of matrices, and structurally resembles the double-bracket o.d.e.\\ studied by R.W.\\ Brockett in 1991. We prove that its solutions converge asymptotically, that the limit is block-diagonal, and above all, that the limit matrix is defined uniquely as follows: For $n$ even, a block-diagonal matrix containing $2\\times 2$ blocks, such that the supe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1618","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":"2026-05-18T00:29:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"09ZgtloB4FYF0VDbFGXSKoMUpzjgHHHOePe+ALdh+nOB7Xbjfl/pu4sbebfUUA4HSQ09loc9MBsJ03AXiC+6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:00:01.190551Z"},"content_sha256":"fb6fa17522fccc784067cf55033db96fa85d4683635db12e70c081295c6934da","schema_version":"1.0","event_id":"sha256:fb6fa17522fccc784067cf55033db96fa85d4683635db12e70c081295c6934da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JSKH5II3AXI5DEHPUET22CDSZI/bundle.json","state_url":"https://pith.science/pith/JSKH5II3AXI5DEHPUET22CDSZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JSKH5II3AXI5DEHPUET22CDSZI/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":"2026-05-28T02:00:01Z","links":{"resolver":"https://pith.science/pith/JSKH5II3AXI5DEHPUET22CDSZI","bundle":"https://pith.science/pith/JSKH5II3AXI5DEHPUET22CDSZI/bundle.json","state":"https://pith.science/pith/JSKH5II3AXI5DEHPUET22CDSZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JSKH5II3AXI5DEHPUET22CDSZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JSKH5II3AXI5DEHPUET22CDSZI","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":"1d1b3d236a580dae5a071d59279342e149322f12f0a4cdfe59daedae01580237","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-08T08:05:56Z","title_canon_sha256":"d01e9fd138ae3d4e3a705e094db4d5ea12c40e6b33d8b78e1bbd719b6d752566"},"schema_version":"1.0","source":{"id":"1202.1618","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1618","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1618v2","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1618","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"pith_short_12","alias_value":"JSKH5II3AXI5","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JSKH5II3AXI5DEHP","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JSKH5II3","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:fb6fa17522fccc784067cf55033db96fa85d4683635db12e70c081295c6934da","target":"graph","created_at":"2026-05-18T00:29:49Z","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 present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes $n\\times n$ zero-diagonal Jacobi matrices employed as its initial condition. This o.d.e.\\ features a right-hand side with a nested commutator of matrices, and structurally resembles the double-bracket o.d.e.\\ studied by R.W.\\ Brockett in 1991. We prove that its solutions converge asymptotically, that the limit is block-diagonal, and above all, that the limit matrix is defined uniquely as follows: For $n$ even, a block-diagonal matrix containing $2\\times 2$ blocks, such that the supe","authors_text":"Debasish Chatterjee, Federico Ramponi, John Lygeros, Tobias Sutter","cross_cats":["cs.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-08T08:05:56Z","title":"Isospectral flows on a class of finite-dimensional Jacobi matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1618","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":"sha256:20feb78aed986801b9cf4e9ca5b0df9e98af8281631976a53c706ac46454c68a","target":"record","created_at":"2026-05-18T00:29:49Z","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":"1d1b3d236a580dae5a071d59279342e149322f12f0a4cdfe59daedae01580237","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-08T08:05:56Z","title_canon_sha256":"d01e9fd138ae3d4e3a705e094db4d5ea12c40e6b33d8b78e1bbd719b6d752566"},"schema_version":"1.0","source":{"id":"1202.1618","kind":"arxiv","version":2}},"canonical_sha256":"4c947ea11b05d1d190efa127ad0872ca3699c7afe726d340c3df786de884b7d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c947ea11b05d1d190efa127ad0872ca3699c7afe726d340c3df786de884b7d6","first_computed_at":"2026-05-18T00:29:49.625149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:49.625149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/t3Vy2D7xGQ7j4M2lI5+JaV6G1h5fPwIRKsQ7Gd9fRE2TAOrABAylFJTmoCFAN1GcosqnTGiSjV/Vg8CtdQPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:49.625788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1618","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20feb78aed986801b9cf4e9ca5b0df9e98af8281631976a53c706ac46454c68a","sha256:fb6fa17522fccc784067cf55033db96fa85d4683635db12e70c081295c6934da"],"state_sha256":"8fa0db13e47668298423015bbd0861300979149e33e640906a76b8a87b8b0bea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fxPcdRsxAFO6lg7syA2crIwq4fWMlDtrrG2Z5EuQHlcdCeqOd5tFYCLib8izpjkixK+BJCM8D/CaQMrpYzmnAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:00:01.192566Z","bundle_sha256":"e82332c2826a0d68cd547400ac857f401caea3d0b9681667a5325e6ae1be4b0c"}}