{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:RQX4TPXIFQFAOUTKUNRSGFSJDI","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":"ce48e227e619ab0d8c82865e3757616ac8b5c4f06d0965a734dac0f56d6afc38","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-13T20:49:51Z","title_canon_sha256":"025723610e2c0f5a9f3f39deb70ca7b3524066e7279888426c3c69817384bfa2"},"schema_version":"1.0","source":{"id":"0911.2695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2695","created_at":"2026-06-03T23:06:30Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2695v1","created_at":"2026-06-03T23:06:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2695","created_at":"2026-06-03T23:06:30Z"},{"alias_kind":"pith_short_12","alias_value":"RQX4TPXIFQFA","created_at":"2026-06-03T23:06:30Z"},{"alias_kind":"pith_short_16","alias_value":"RQX4TPXIFQFAOUTK","created_at":"2026-06-03T23:06:30Z"},{"alias_kind":"pith_short_8","alias_value":"RQX4TPXI","created_at":"2026-06-03T23:06:30Z"}],"graph_snapshots":[{"event_id":"sha256:a632916f0a523be6c0b928df44ff16623499367672e83c9637d5196c6e9c2da5","target":"graph","created_at":"2026-06-03T23:06:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0911.2695/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Spectral enhancement -- which aims to undo spectral broadening -- leads to integral equations which are ill-posed and require special regularisation techniques for their solution. Even when an optimal regularisation technique is used, however, the errors in the solution -- which originate in data approximation errors -- can be substantial and it is important to have good bounds for these errors in order to select appropriate enhancement methods. A discussion of the causes and nature of broadening provides regularity or source conditions which are required to obtain bounds for the regularised s","authors_text":"Markus Hegland","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-13T20:49:51Z","title":"Error bounds for spectral enhancement which are based on variable Hilbert scale inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2695","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:c17e42bd00d43b61137959064dc16eebedb7e266b6bcc4cb8600ee584f9dcae6","target":"record","created_at":"2026-06-03T23:06:30Z","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":"ce48e227e619ab0d8c82865e3757616ac8b5c4f06d0965a734dac0f56d6afc38","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-13T20:49:51Z","title_canon_sha256":"025723610e2c0f5a9f3f39deb70ca7b3524066e7279888426c3c69817384bfa2"},"schema_version":"1.0","source":{"id":"0911.2695","kind":"arxiv","version":1}},"canonical_sha256":"8c2fc9bee82c0a07526aa3632316491a2e2a700347c3cb99e1dc9f97cff9ac8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c2fc9bee82c0a07526aa3632316491a2e2a700347c3cb99e1dc9f97cff9ac8f","first_computed_at":"2026-06-03T23:06:30.650277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:30.650277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MelgyHMQ8xM0ttkbq+IJM9asgtZJcFsjrJ3hmkoBjCtnP59iaC/lUOL+ICHUTpivtZRCVNi9nx6JcrhBYvJ4AQ==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:30.650908Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.2695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c17e42bd00d43b61137959064dc16eebedb7e266b6bcc4cb8600ee584f9dcae6","sha256:a632916f0a523be6c0b928df44ff16623499367672e83c9637d5196c6e9c2da5"],"state_sha256":"880ad730bcc224cd05b8e31dfc9e01ad5b90ce3980fb482375bbdd7b8e4cc321"}