{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GL2EFWI6FDU5XSZQ2ZGEG6XSGB","short_pith_number":"pith:GL2EFWI6","canonical_record":{"source":{"id":"1603.06336","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-21T06:45:51Z","cross_cats_sorted":[],"title_canon_sha256":"b7eef2be2ce170af7ae1ec2e385ada7937a571e8ac7bf90c4da8a674a509f5ef","abstract_canon_sha256":"6457356a84102eb42240c4fd3b6afcf432538d0b559f3568b62d111c8fc0adb8"},"schema_version":"1.0"},"canonical_sha256":"32f442d91e28e9dbcb30d64c437af230594807e01370524869809e7a558e0fc0","source":{"kind":"arxiv","id":"1603.06336","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06336","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06336v3","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06336","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"GL2EFWI6FDU5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GL2EFWI6FDU5XSZQ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GL2EFWI6","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GL2EFWI6FDU5XSZQ2ZGEG6XSGB","target":"record","payload":{"canonical_record":{"source":{"id":"1603.06336","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-21T06:45:51Z","cross_cats_sorted":[],"title_canon_sha256":"b7eef2be2ce170af7ae1ec2e385ada7937a571e8ac7bf90c4da8a674a509f5ef","abstract_canon_sha256":"6457356a84102eb42240c4fd3b6afcf432538d0b559f3568b62d111c8fc0adb8"},"schema_version":"1.0"},"canonical_sha256":"32f442d91e28e9dbcb30d64c437af230594807e01370524869809e7a558e0fc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:19.462389Z","signature_b64":"ICJK9irtp7MOLL+y7RTxm/39P4WTesfLs0/dNEoss6p9UjClyB1G/my1He16ccZfuQywWxwbJLYKU5tHYkydBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32f442d91e28e9dbcb30d64c437af230594807e01370524869809e7a558e0fc0","last_reissued_at":"2026-05-18T01:03:19.461838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:19.461838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.06336","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JqcdQIbrtgNqCKEkTL2ZsA3yiy9NJWfVm+QX8ijFlvWQU/zSk1GCFSbCpglHOgw5J4LCrOwnUhlnTtQZtayiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T07:39:48.450627Z"},"content_sha256":"18adb4ea5b9abbf6edc6f66ac7d5c3c624daa873928ee37fa850d20c5acb27a8","schema_version":"1.0","event_id":"sha256:18adb4ea5b9abbf6edc6f66ac7d5c3c624daa873928ee37fa850d20c5acb27a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GL2EFWI6FDU5XSZQ2ZGEG6XSGB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A unified approach to the well-posedness of some non-Lambertian models in Shape-from-Shading theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fabio Camilli, Silvia Tozza","submitted_at":"2016-03-21T06:45:51Z","abstract_excerpt":"In this paper we show that the introduction of an attenuation factor in the %image irradiance brightness equations relative to various perspective Shape from Shading models allows to make the corresponding differential problems well-posed. We propose a unified approach based on the theory of viscosity solution and we show that the brightness equations with the attenuation term admit a unique viscosity solution. We also discuss in detail the possible boundary conditions that we can use for the Hamilton-Jacobi equations associated to these models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06336","kind":"arxiv","version":3},"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":"2026-05-18T01:03:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"atVHMPs55RWvHrSMUrxE4wKfv+Nyc+crUJuTHoolVShHjaSqzH+0lw4kCQK5SMicjrdzzf2Orxn6gPlMZfMuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T07:39:48.450976Z"},"content_sha256":"fc47c9b7bc896ffa41737569c42b77f586470882b8a9f4cf0e3393d83225c23c","schema_version":"1.0","event_id":"sha256:fc47c9b7bc896ffa41737569c42b77f586470882b8a9f4cf0e3393d83225c23c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GL2EFWI6FDU5XSZQ2ZGEG6XSGB/bundle.json","state_url":"https://pith.science/pith/GL2EFWI6FDU5XSZQ2ZGEG6XSGB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GL2EFWI6FDU5XSZQ2ZGEG6XSGB/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":"2026-07-06T07:39:48Z","links":{"resolver":"https://pith.science/pith/GL2EFWI6FDU5XSZQ2ZGEG6XSGB","bundle":"https://pith.science/pith/GL2EFWI6FDU5XSZQ2ZGEG6XSGB/bundle.json","state":"https://pith.science/pith/GL2EFWI6FDU5XSZQ2ZGEG6XSGB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GL2EFWI6FDU5XSZQ2ZGEG6XSGB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GL2EFWI6FDU5XSZQ2ZGEG6XSGB","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":"6457356a84102eb42240c4fd3b6afcf432538d0b559f3568b62d111c8fc0adb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-21T06:45:51Z","title_canon_sha256":"b7eef2be2ce170af7ae1ec2e385ada7937a571e8ac7bf90c4da8a674a509f5ef"},"schema_version":"1.0","source":{"id":"1603.06336","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06336","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06336v3","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06336","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"GL2EFWI6FDU5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GL2EFWI6FDU5XSZQ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GL2EFWI6","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:fc47c9b7bc896ffa41737569c42b77f586470882b8a9f4cf0e3393d83225c23c","target":"graph","created_at":"2026-05-18T01:03:19Z","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":"In this paper we show that the introduction of an attenuation factor in the %image irradiance brightness equations relative to various perspective Shape from Shading models allows to make the corresponding differential problems well-posed. We propose a unified approach based on the theory of viscosity solution and we show that the brightness equations with the attenuation term admit a unique viscosity solution. We also discuss in detail the possible boundary conditions that we can use for the Hamilton-Jacobi equations associated to these models.","authors_text":"Fabio Camilli, Silvia Tozza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-21T06:45:51Z","title":"A unified approach to the well-posedness of some non-Lambertian models in Shape-from-Shading theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06336","kind":"arxiv","version":3},"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":"sha256:18adb4ea5b9abbf6edc6f66ac7d5c3c624daa873928ee37fa850d20c5acb27a8","target":"record","created_at":"2026-05-18T01:03:19Z","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":"6457356a84102eb42240c4fd3b6afcf432538d0b559f3568b62d111c8fc0adb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-21T06:45:51Z","title_canon_sha256":"b7eef2be2ce170af7ae1ec2e385ada7937a571e8ac7bf90c4da8a674a509f5ef"},"schema_version":"1.0","source":{"id":"1603.06336","kind":"arxiv","version":3}},"canonical_sha256":"32f442d91e28e9dbcb30d64c437af230594807e01370524869809e7a558e0fc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32f442d91e28e9dbcb30d64c437af230594807e01370524869809e7a558e0fc0","first_computed_at":"2026-05-18T01:03:19.461838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:19.461838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ICJK9irtp7MOLL+y7RTxm/39P4WTesfLs0/dNEoss6p9UjClyB1G/my1He16ccZfuQywWxwbJLYKU5tHYkydBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:19.462389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06336","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18adb4ea5b9abbf6edc6f66ac7d5c3c624daa873928ee37fa850d20c5acb27a8","sha256:fc47c9b7bc896ffa41737569c42b77f586470882b8a9f4cf0e3393d83225c23c"],"state_sha256":"0cb03ec3d78dafb76047baf08e3715ef601aa06325c8cffc7092b013d49ba566"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KDcpk+NK+bizilAoC1BjhlbLkkF+kUmr7fX5ceZK4eVgHSEcEQBNczB7De3FGdLWvdwxYj3WeHWGrf/+zMv1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T07:39:48.452868Z","bundle_sha256":"dddf9f2b3119cd4ee5917c52afcb26c609a28df593f4cb0477746338d2c3238c"}}