{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:X3MIUBPGGNIIIBWO4RJA4LIG3O","short_pith_number":"pith:X3MIUBPG","canonical_record":{"source":{"id":"1712.05864","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-15T22:22:05Z","cross_cats_sorted":[],"title_canon_sha256":"c7a7f6d4ab513fef0bd1fc9a6f003cfda12948d656c2079f044f12a537429f7c","abstract_canon_sha256":"20f07f06ac17219635003402d94f092184a085095c0400de9c3def67b8c11528"},"schema_version":"1.0"},"canonical_sha256":"bed88a05e633508406cee4520e2d06db909c6308a54bb2a18a999a87a40811fd","source":{"kind":"arxiv","id":"1712.05864","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05864","created_at":"2026-05-18T00:26:14Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05864v2","created_at":"2026-05-18T00:26:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05864","created_at":"2026-05-18T00:26:14Z"},{"alias_kind":"pith_short_12","alias_value":"X3MIUBPGGNII","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X3MIUBPGGNIIIBWO","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X3MIUBPG","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:X3MIUBPGGNIIIBWO4RJA4LIG3O","target":"record","payload":{"canonical_record":{"source":{"id":"1712.05864","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-15T22:22:05Z","cross_cats_sorted":[],"title_canon_sha256":"c7a7f6d4ab513fef0bd1fc9a6f003cfda12948d656c2079f044f12a537429f7c","abstract_canon_sha256":"20f07f06ac17219635003402d94f092184a085095c0400de9c3def67b8c11528"},"schema_version":"1.0"},"canonical_sha256":"bed88a05e633508406cee4520e2d06db909c6308a54bb2a18a999a87a40811fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:14.221001Z","signature_b64":"yAgNQGlg4b2pnmIxobOY3XQEp5KGwxdKd3WK1dAa88LQczIHZxHAyM32gkvljuwDeK+CMgThHeRksCHix6llCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bed88a05e633508406cee4520e2d06db909c6308a54bb2a18a999a87a40811fd","last_reissued_at":"2026-05-18T00:26:14.220445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:14.220445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.05864","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":"2026-05-18T00:26:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/79hKxzqw9zPno2UIO1pXPyFK71Sfcxys3D8AO7lgAE4nRnDPuCQCv9WctIkzEgRE+qVFlevi62qq3DDmLMaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:25:08.463818Z"},"content_sha256":"183917a8637088f64d62f02aa6fe05afac4b7bb2c0c1eb1ad1245f3b5f4b8651","schema_version":"1.0","event_id":"sha256:183917a8637088f64d62f02aa6fe05afac4b7bb2c0c1eb1ad1245f3b5f4b8651"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:X3MIUBPGGNIIIBWO4RJA4LIG3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the singular values of matrices with high displacement rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alex Townsend, Heather Wilber","submitted_at":"2017-12-15T22:22:05Z","abstract_excerpt":"We introduce a new ADI-based low rank solver for $AX-XB=F$, where $F$ has rapidly decaying singular values. Our approach results in both theoretical and practical gains, including (1) the derivation of new bounds on singular values for classes of matrices with high displacement rank, (2) a practical algorithm for solving certain Lyapunov and Sylvester matrix equations with high rank right-hand sides, and (3) a collection of low rank Poisson solvers that achieve spectral accuracy and optimal computational complexity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05864","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":"2026-05-18T00:26:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+baZ1gs3kaTIp1qOPJX+QdDsH10qpBPzpl0dfnwyKqHb3OMFFh74FjkaYAfVFM1CRMd8ONEhIUVfIr96NIlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:25:08.464524Z"},"content_sha256":"c00c135f9340ffb63c0b58c748458808ae569863176ae2d4fcd7b3a601437fcc","schema_version":"1.0","event_id":"sha256:c00c135f9340ffb63c0b58c748458808ae569863176ae2d4fcd7b3a601437fcc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X3MIUBPGGNIIIBWO4RJA4LIG3O/bundle.json","state_url":"https://pith.science/pith/X3MIUBPGGNIIIBWO4RJA4LIG3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X3MIUBPGGNIIIBWO4RJA4LIG3O/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":"2026-05-25T21:25:08Z","links":{"resolver":"https://pith.science/pith/X3MIUBPGGNIIIBWO4RJA4LIG3O","bundle":"https://pith.science/pith/X3MIUBPGGNIIIBWO4RJA4LIG3O/bundle.json","state":"https://pith.science/pith/X3MIUBPGGNIIIBWO4RJA4LIG3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X3MIUBPGGNIIIBWO4RJA4LIG3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:X3MIUBPGGNIIIBWO4RJA4LIG3O","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":"20f07f06ac17219635003402d94f092184a085095c0400de9c3def67b8c11528","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-15T22:22:05Z","title_canon_sha256":"c7a7f6d4ab513fef0bd1fc9a6f003cfda12948d656c2079f044f12a537429f7c"},"schema_version":"1.0","source":{"id":"1712.05864","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05864","created_at":"2026-05-18T00:26:14Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05864v2","created_at":"2026-05-18T00:26:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05864","created_at":"2026-05-18T00:26:14Z"},{"alias_kind":"pith_short_12","alias_value":"X3MIUBPGGNII","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X3MIUBPGGNIIIBWO","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X3MIUBPG","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:c00c135f9340ffb63c0b58c748458808ae569863176ae2d4fcd7b3a601437fcc","target":"graph","created_at":"2026-05-18T00:26:14Z","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 introduce a new ADI-based low rank solver for $AX-XB=F$, where $F$ has rapidly decaying singular values. Our approach results in both theoretical and practical gains, including (1) the derivation of new bounds on singular values for classes of matrices with high displacement rank, (2) a practical algorithm for solving certain Lyapunov and Sylvester matrix equations with high rank right-hand sides, and (3) a collection of low rank Poisson solvers that achieve spectral accuracy and optimal computational complexity.","authors_text":"Alex Townsend, Heather Wilber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-15T22:22:05Z","title":"On the singular values of matrices with high displacement rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05864","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":"sha256:183917a8637088f64d62f02aa6fe05afac4b7bb2c0c1eb1ad1245f3b5f4b8651","target":"record","created_at":"2026-05-18T00:26:14Z","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":"20f07f06ac17219635003402d94f092184a085095c0400de9c3def67b8c11528","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-15T22:22:05Z","title_canon_sha256":"c7a7f6d4ab513fef0bd1fc9a6f003cfda12948d656c2079f044f12a537429f7c"},"schema_version":"1.0","source":{"id":"1712.05864","kind":"arxiv","version":2}},"canonical_sha256":"bed88a05e633508406cee4520e2d06db909c6308a54bb2a18a999a87a40811fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bed88a05e633508406cee4520e2d06db909c6308a54bb2a18a999a87a40811fd","first_computed_at":"2026-05-18T00:26:14.220445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:14.220445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yAgNQGlg4b2pnmIxobOY3XQEp5KGwxdKd3WK1dAa88LQczIHZxHAyM32gkvljuwDeK+CMgThHeRksCHix6llCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:14.221001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05864","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:183917a8637088f64d62f02aa6fe05afac4b7bb2c0c1eb1ad1245f3b5f4b8651","sha256:c00c135f9340ffb63c0b58c748458808ae569863176ae2d4fcd7b3a601437fcc"],"state_sha256":"2f396288143e5fab3621a9f7974313fd7dc4d325462461537a1da41414ba6621"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y1Ed02/oR1uvzvRLaDxWHJ+FQakscNsAcH/jXlUhGFEeAIKIm6fdNmr7QLmhmQz6pX8m98BeH/NT4Qh5IzcACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:25:08.468091Z","bundle_sha256":"d9d10d6238d8373626edf96a17e4165df45ef237ad80a4efc14c56613ce7186f"}}