{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:RQX4TPXIFQFAOUTKUNRSGFSJDI","short_pith_number":"pith:RQX4TPXI","canonical_record":{"source":{"id":"0911.2695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-13T20:49:51Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"025723610e2c0f5a9f3f39deb70ca7b3524066e7279888426c3c69817384bfa2","abstract_canon_sha256":"ce48e227e619ab0d8c82865e3757616ac8b5c4f06d0965a734dac0f56d6afc38"},"schema_version":"1.0"},"canonical_sha256":"8c2fc9bee82c0a07526aa3632316491a2e2a700347c3cb99e1dc9f97cff9ac8f","source":{"kind":"arxiv","id":"0911.2695","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:RQX4TPXIFQFAOUTKUNRSGFSJDI","target":"record","payload":{"canonical_record":{"source":{"id":"0911.2695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-13T20:49:51Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"025723610e2c0f5a9f3f39deb70ca7b3524066e7279888426c3c69817384bfa2","abstract_canon_sha256":"ce48e227e619ab0d8c82865e3757616ac8b5c4f06d0965a734dac0f56d6afc38"},"schema_version":"1.0"},"canonical_sha256":"8c2fc9bee82c0a07526aa3632316491a2e2a700347c3cb99e1dc9f97cff9ac8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:30.650908Z","signature_b64":"MelgyHMQ8xM0ttkbq+IJM9asgtZJcFsjrJ3hmkoBjCtnP59iaC/lUOL+ICHUTpivtZRCVNi9nx6JcrhBYvJ4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c2fc9bee82c0a07526aa3632316491a2e2a700347c3cb99e1dc9f97cff9ac8f","last_reissued_at":"2026-06-03T23:06:30.650277Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:30.650277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.2695","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":"2026-06-03T23:06:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oOQhkWlErBa01rsGTht7MdHuGeOUcWP9/eFQZd6Jy4PgYlmg6gbIoSLJcnEQ3d06QYJRMRYaZBdbruP9vCJvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:15:19.745840Z"},"content_sha256":"c17e42bd00d43b61137959064dc16eebedb7e266b6bcc4cb8600ee584f9dcae6","schema_version":"1.0","event_id":"sha256:c17e42bd00d43b61137959064dc16eebedb7e266b6bcc4cb8600ee584f9dcae6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:RQX4TPXIFQFAOUTKUNRSGFSJDI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error bounds for spectral enhancement which are based on variable Hilbert scale inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Markus Hegland","submitted_at":"2009-11-13T20:49:51Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2695","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0911.2695/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-03T23:06:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4mu7KSKXMCWwOiiDyt4PeZE9jH+rgPT6B4rDgFfkGzRgE08BgBvwhdfRHrM1Ex+fih4tWGpGZtJir0h7AkbLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:15:19.746699Z"},"content_sha256":"a632916f0a523be6c0b928df44ff16623499367672e83c9637d5196c6e9c2da5","schema_version":"1.0","event_id":"sha256:a632916f0a523be6c0b928df44ff16623499367672e83c9637d5196c6e9c2da5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RQX4TPXIFQFAOUTKUNRSGFSJDI/bundle.json","state_url":"https://pith.science/pith/RQX4TPXIFQFAOUTKUNRSGFSJDI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RQX4TPXIFQFAOUTKUNRSGFSJDI/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":"2026-06-09T03:15:19Z","links":{"resolver":"https://pith.science/pith/RQX4TPXIFQFAOUTKUNRSGFSJDI","bundle":"https://pith.science/pith/RQX4TPXIFQFAOUTKUNRSGFSJDI/bundle.json","state":"https://pith.science/pith/RQX4TPXIFQFAOUTKUNRSGFSJDI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RQX4TPXIFQFAOUTKUNRSGFSJDI/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u1I/FSKmtzZfgCCLI7sKgLOKTr5HPSvsnkSWZArWBi5pthECpi1Yr2LedUdClyr15LExI/arq9ilsinxN5dsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:15:19.751410Z","bundle_sha256":"3d2cd80e03b6f9fc3aa8b48dd1d2683fce92691b8335e4fbd802e37d7623e256"}}