{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:5C63BCL2S3ZXYU3IMPZFEM6EPW","short_pith_number":"pith:5C63BCL2","canonical_record":{"source":{"id":"math/0412112","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2004-12-06T14:25:56Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"9ee7d1e82cb5b50639b48ad67c34d7f4eb3721b3dd01efce2910bf9f406bbb35","abstract_canon_sha256":"eeea08ce2ccfc1ac28d6f97daa2d0b0b6dd37af258ee5a3eaf2f67c55aca32be"},"schema_version":"1.0"},"canonical_sha256":"e8bdb0897a96f37c536863f25233c47dba390f370fce2bc5f192ebf83dd4c55f","source":{"kind":"arxiv","id":"math/0412112","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412112","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412112v1","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412112","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"5C63BCL2S3ZX","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_16","alias_value":"5C63BCL2S3ZXYU3I","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_8","alias_value":"5C63BCL2","created_at":"2026-06-03T22:06:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:5C63BCL2S3ZXYU3IMPZFEM6EPW","target":"record","payload":{"canonical_record":{"source":{"id":"math/0412112","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2004-12-06T14:25:56Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"9ee7d1e82cb5b50639b48ad67c34d7f4eb3721b3dd01efce2910bf9f406bbb35","abstract_canon_sha256":"eeea08ce2ccfc1ac28d6f97daa2d0b0b6dd37af258ee5a3eaf2f67c55aca32be"},"schema_version":"1.0"},"canonical_sha256":"e8bdb0897a96f37c536863f25233c47dba390f370fce2bc5f192ebf83dd4c55f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:16.061777Z","signature_b64":"RZK+6DUn/nDSFwBADFI+5RBdAEAv8CZ5KpUW+yQXgUaX/SVKx62eWQs8AN0ijrz/NDYzbCzvTQqG5Fkyl0bDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8bdb0897a96f37c536863f25233c47dba390f370fce2bc5f192ebf83dd4c55f","last_reissued_at":"2026-06-03T22:06:16.061301Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:16.061301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0412112","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":"2026-06-03T22:06:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bu1G5qiEJugOQIIgnqZbDyZgMrNHPMUI6FG95x/L1rNY62RJiZm6h7i0vhe6VrQd6J3yzG26LzZ4eWiSSji0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:30:25.033009Z"},"content_sha256":"0b4a66ac5bb6e6562e599b0d6ffb183abc9d2121f26afc650c8a80726032fad1","schema_version":"1.0","event_id":"sha256:0b4a66ac5bb6e6562e599b0d6ffb183abc9d2121f26afc650c8a80726032fad1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:5C63BCL2S3ZXYU3IMPZFEM6EPW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear projection digital image inpainting and restoration methods","license":"","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Massimo Fornasier","submitted_at":"2004-12-06T14:25:56Z","abstract_excerpt":"This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized image inpainting problem and the restoration of digital signals. In particular, we discuss the problem of reconstructing a digital signal/image from very few, sparse, and complete information and a substantial incomplete information, which will be assumed as the result of a nonlinear distortion. As a typical and inspiring example, we illustrate the concrete problem of the color restoration of a destroyed art fresco from its few known fragments and some gray "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412112","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/math/0412112/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":"2026-06-03T22:06:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s4PhhOTSE6McRZDkKzanUBsBYzeE9WLr0FsOM9jI3qOzczmYmaZUfnSVMXOR81HaYFpwOPjq3RO82HXJ56cWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:30:25.033400Z"},"content_sha256":"84c4d2640136aa6c4f2d0c913bde38ca318339d2da4708be9965b4dfd13d80b9","schema_version":"1.0","event_id":"sha256:84c4d2640136aa6c4f2d0c913bde38ca318339d2da4708be9965b4dfd13d80b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5C63BCL2S3ZXYU3IMPZFEM6EPW/bundle.json","state_url":"https://pith.science/pith/5C63BCL2S3ZXYU3IMPZFEM6EPW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5C63BCL2S3ZXYU3IMPZFEM6EPW/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":"2026-06-04T03:30:25Z","links":{"resolver":"https://pith.science/pith/5C63BCL2S3ZXYU3IMPZFEM6EPW","bundle":"https://pith.science/pith/5C63BCL2S3ZXYU3IMPZFEM6EPW/bundle.json","state":"https://pith.science/pith/5C63BCL2S3ZXYU3IMPZFEM6EPW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5C63BCL2S3ZXYU3IMPZFEM6EPW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:5C63BCL2S3ZXYU3IMPZFEM6EPW","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":"eeea08ce2ccfc1ac28d6f97daa2d0b0b6dd37af258ee5a3eaf2f67c55aca32be","cross_cats_sorted":["cs.NA","math.AP"],"license":"","primary_cat":"math.NA","submitted_at":"2004-12-06T14:25:56Z","title_canon_sha256":"9ee7d1e82cb5b50639b48ad67c34d7f4eb3721b3dd01efce2910bf9f406bbb35"},"schema_version":"1.0","source":{"id":"math/0412112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412112","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412112v1","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412112","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"5C63BCL2S3ZX","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_16","alias_value":"5C63BCL2S3ZXYU3I","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_8","alias_value":"5C63BCL2","created_at":"2026-06-03T22:06:16Z"}],"graph_snapshots":[{"event_id":"sha256:84c4d2640136aa6c4f2d0c913bde38ca318339d2da4708be9965b4dfd13d80b9","target":"graph","created_at":"2026-06-03T22:06:16Z","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/math/0412112/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized image inpainting problem and the restoration of digital signals. In particular, we discuss the problem of reconstructing a digital signal/image from very few, sparse, and complete information and a substantial incomplete information, which will be assumed as the result of a nonlinear distortion. As a typical and inspiring example, we illustrate the concrete problem of the color restoration of a destroyed art fresco from its few known fragments and some gray ","authors_text":"Massimo Fornasier","cross_cats":["cs.NA","math.AP"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2004-12-06T14:25:56Z","title":"Nonlinear projection digital image inpainting and restoration methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412112","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":"sha256:0b4a66ac5bb6e6562e599b0d6ffb183abc9d2121f26afc650c8a80726032fad1","target":"record","created_at":"2026-06-03T22:06:16Z","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":"eeea08ce2ccfc1ac28d6f97daa2d0b0b6dd37af258ee5a3eaf2f67c55aca32be","cross_cats_sorted":["cs.NA","math.AP"],"license":"","primary_cat":"math.NA","submitted_at":"2004-12-06T14:25:56Z","title_canon_sha256":"9ee7d1e82cb5b50639b48ad67c34d7f4eb3721b3dd01efce2910bf9f406bbb35"},"schema_version":"1.0","source":{"id":"math/0412112","kind":"arxiv","version":1}},"canonical_sha256":"e8bdb0897a96f37c536863f25233c47dba390f370fce2bc5f192ebf83dd4c55f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8bdb0897a96f37c536863f25233c47dba390f370fce2bc5f192ebf83dd4c55f","first_computed_at":"2026-06-03T22:06:16.061301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:16.061301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RZK+6DUn/nDSFwBADFI+5RBdAEAv8CZ5KpUW+yQXgUaX/SVKx62eWQs8AN0ijrz/NDYzbCzvTQqG5Fkyl0bDCg==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:16.061777Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0412112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b4a66ac5bb6e6562e599b0d6ffb183abc9d2121f26afc650c8a80726032fad1","sha256:84c4d2640136aa6c4f2d0c913bde38ca318339d2da4708be9965b4dfd13d80b9"],"state_sha256":"c709ad26973bc38fe64e3885a8ed18f876f01db00399bd744e2819a90add07e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sPPLP9SvXYQzcVcjzJpwUByk353LBi3j1YMcd0/ge3gQMKbwlH/T8pQUBi8tR2YgP85UHZRMiN5tSQJ3aNYrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:30:25.035969Z","bundle_sha256":"8b0240505c8501fdd8cf3aaa602db30c692d3b7eb476605cd091f41e19fd3990"}}