{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:X7OBVNZIKAQITX3GNZYXTMHRDT","short_pith_number":"pith:X7OBVNZI","canonical_record":{"source":{"id":"2510.16354","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-10-18T05:15:01Z","cross_cats_sorted":[],"title_canon_sha256":"b4d3c1b755544b7f683dc636afaaeb876b0829ad39ad89c1bac860ee6a853d56","abstract_canon_sha256":"d49894e546d9fd3cbad45c4457fada48c3850271726b2197176df9816e606c4b"},"schema_version":"1.0"},"canonical_sha256":"bfdc1ab728502089df666e7179b0f11cc56b2b02539d8a33c5ffa94691344ef0","source":{"kind":"arxiv","id":"2510.16354","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.16354","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"2510.16354v2","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.16354","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"X7OBVNZIKAQI","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"pith_short_16","alias_value":"X7OBVNZIKAQITX3G","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"pith_short_8","alias_value":"X7OBVNZI","created_at":"2026-05-20T00:02:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:X7OBVNZIKAQITX3GNZYXTMHRDT","target":"record","payload":{"canonical_record":{"source":{"id":"2510.16354","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-10-18T05:15:01Z","cross_cats_sorted":[],"title_canon_sha256":"b4d3c1b755544b7f683dc636afaaeb876b0829ad39ad89c1bac860ee6a853d56","abstract_canon_sha256":"d49894e546d9fd3cbad45c4457fada48c3850271726b2197176df9816e606c4b"},"schema_version":"1.0"},"canonical_sha256":"bfdc1ab728502089df666e7179b0f11cc56b2b02539d8a33c5ffa94691344ef0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:57.477534Z","signature_b64":"A2vWL1/ilGBw23q0VVxLrnu25lKLlTPyOznCGcPrzPuXgjAf/WnxRobs2ISWIn8MijtEYtYKBlnsmpgm2qIrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfdc1ab728502089df666e7179b0f11cc56b2b02539d8a33c5ffa94691344ef0","last_reissued_at":"2026-05-20T00:02:57.476690Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:57.476690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2510.16354","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":"2026-05-20T00:02:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xUl8P0AJqBvcye+vOVAhtQqcj+eybKrcjF8TXcE+uJBDnmOmf3G/erPlWOJqF1/YNSO3LgANhN9SeNFr8D0dAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:00:57.070356Z"},"content_sha256":"1f6b1b151dd5a556460613154f7117874dea45f931d5d995fbfb45e010f4607f","schema_version":"1.0","event_id":"sha256:1f6b1b151dd5a556460613154f7117874dea45f931d5d995fbfb45e010f4607f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:X7OBVNZIKAQITX3GNZYXTMHRDT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic and Pseudo-Parabolic PDE System with Orientation-Adaptive Anisotropy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Naotaka Ukai","submitted_at":"2025-10-18T05:15:01Z","abstract_excerpt":"In this paper, we consider a coupled system of nonlinear elliptic and pseudo-parabolic PDEs arising in anisotropic monochrome image denoising with orientation-adaptation. The system is derived from the minimization process of a nonconvex energy functional. In particular, we focus on the problem of determining the initial data for the orientation variable. In previous studies, a natural procedure for determining such initial data has not been sufficiently clarified. To address this issue, we introduce a formulation in which the time derivative of the orientation variable is removed. This formul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.16354","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.16354/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":"2026-05-20T00:02:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IRH8rAd9enkT5QoI00djuJcNLqO5jzNLlDzxYEk7lmKbLxpUapCPfoHLRXB76gKDxHVWI9pRDn2frZ0UWX1+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:00:57.070737Z"},"content_sha256":"7a09b66b0a6dad3065bd189ce5e67028c02fe76991a730b5407a5810d8f9a3c0","schema_version":"1.0","event_id":"sha256:7a09b66b0a6dad3065bd189ce5e67028c02fe76991a730b5407a5810d8f9a3c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7OBVNZIKAQITX3GNZYXTMHRDT/bundle.json","state_url":"https://pith.science/pith/X7OBVNZIKAQITX3GNZYXTMHRDT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7OBVNZIKAQITX3GNZYXTMHRDT/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":"2026-06-09T14:00:57Z","links":{"resolver":"https://pith.science/pith/X7OBVNZIKAQITX3GNZYXTMHRDT","bundle":"https://pith.science/pith/X7OBVNZIKAQITX3GNZYXTMHRDT/bundle.json","state":"https://pith.science/pith/X7OBVNZIKAQITX3GNZYXTMHRDT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7OBVNZIKAQITX3GNZYXTMHRDT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:X7OBVNZIKAQITX3GNZYXTMHRDT","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":"d49894e546d9fd3cbad45c4457fada48c3850271726b2197176df9816e606c4b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-10-18T05:15:01Z","title_canon_sha256":"b4d3c1b755544b7f683dc636afaaeb876b0829ad39ad89c1bac860ee6a853d56"},"schema_version":"1.0","source":{"id":"2510.16354","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.16354","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"2510.16354v2","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.16354","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"X7OBVNZIKAQI","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"pith_short_16","alias_value":"X7OBVNZIKAQITX3G","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"pith_short_8","alias_value":"X7OBVNZI","created_at":"2026-05-20T00:02:57Z"}],"graph_snapshots":[{"event_id":"sha256:7a09b66b0a6dad3065bd189ce5e67028c02fe76991a730b5407a5810d8f9a3c0","target":"graph","created_at":"2026-05-20T00:02:57Z","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/2510.16354/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider a coupled system of nonlinear elliptic and pseudo-parabolic PDEs arising in anisotropic monochrome image denoising with orientation-adaptation. The system is derived from the minimization process of a nonconvex energy functional. In particular, we focus on the problem of determining the initial data for the orientation variable. In previous studies, a natural procedure for determining such initial data has not been sufficiently clarified. To address this issue, we introduce a formulation in which the time derivative of the orientation variable is removed. This formul","authors_text":"Naotaka Ukai","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-10-18T05:15:01Z","title":"Elliptic and Pseudo-Parabolic PDE System with Orientation-Adaptive Anisotropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.16354","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":"sha256:1f6b1b151dd5a556460613154f7117874dea45f931d5d995fbfb45e010f4607f","target":"record","created_at":"2026-05-20T00:02:57Z","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":"d49894e546d9fd3cbad45c4457fada48c3850271726b2197176df9816e606c4b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-10-18T05:15:01Z","title_canon_sha256":"b4d3c1b755544b7f683dc636afaaeb876b0829ad39ad89c1bac860ee6a853d56"},"schema_version":"1.0","source":{"id":"2510.16354","kind":"arxiv","version":2}},"canonical_sha256":"bfdc1ab728502089df666e7179b0f11cc56b2b02539d8a33c5ffa94691344ef0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfdc1ab728502089df666e7179b0f11cc56b2b02539d8a33c5ffa94691344ef0","first_computed_at":"2026-05-20T00:02:57.476690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:57.476690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A2vWL1/ilGBw23q0VVxLrnu25lKLlTPyOznCGcPrzPuXgjAf/WnxRobs2ISWIn8MijtEYtYKBlnsmpgm2qIrDw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:57.477534Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.16354","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f6b1b151dd5a556460613154f7117874dea45f931d5d995fbfb45e010f4607f","sha256:7a09b66b0a6dad3065bd189ce5e67028c02fe76991a730b5407a5810d8f9a3c0"],"state_sha256":"8567a6a25d6f85497de02ed61a786e3391af07b2505555dc0bdf27e9d4435a73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"40AvjHa54W8GDoXAdgFDlu8ve2804FCP2Pljaut82E2SEvgT7QLf6HWPEKZyNRz65hZ/EE9XolEsXEICatc1Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T14:00:57.073182Z","bundle_sha256":"7c32a65bd266296b8f30de02516a480144f22a790b205c1c867bf41a7071a6b8"}}