{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RM4RTHCAUCTBRZAVSUYPRKGRNB","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":"f609b1ad902107bd1bdbee435fc995d4f5af4b47aeec874bcd506a44d25d1c8f","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-16T02:34:19Z","title_canon_sha256":"99f74b296825a85714fd5c9541634499b16965eb22b1df577db0bade639fd73f"},"schema_version":"1.0","source":{"id":"2601.10950","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.10950","created_at":"2026-05-22T01:03:16Z"},{"alias_kind":"arxiv_version","alias_value":"2601.10950v2","created_at":"2026-05-22T01:03:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.10950","created_at":"2026-05-22T01:03:16Z"},{"alias_kind":"pith_short_12","alias_value":"RM4RTHCAUCTB","created_at":"2026-05-22T01:03:16Z"},{"alias_kind":"pith_short_16","alias_value":"RM4RTHCAUCTBRZAV","created_at":"2026-05-22T01:03:16Z"},{"alias_kind":"pith_short_8","alias_value":"RM4RTHCA","created_at":"2026-05-22T01:03:16Z"}],"graph_snapshots":[{"event_id":"sha256:6b795611b3db4cade9c13ae3aeea6bcfdb27b7f003aa875b156e617787df2807","target":"graph","created_at":"2026-05-22T01:03:16Z","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/2601.10950/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces specular differentiation, which generalizes G\\^ateaux and Fr\\'echet differentiation in normed vector spaces. We investigate its fundamental theoretical properties and establish weak forms of the Mean Value Theorem and Fermat's Theorem in the specular sense. Finally, we identify a distinguished element of the Fr\\'echet subdifferential of a convex function through specular differentiation.","authors_text":"Kiyuob Jung","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-16T02:34:19Z","title":"Specular differentiation in normed vector spaces: Quasi-Mean Value and Quasi-Fermat Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.10950","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:edf91daf227a11f1f3e1e7aadbdfb6ed716c8f6b952aae7ac89c1040c6920562","target":"record","created_at":"2026-05-22T01:03:16Z","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":"f609b1ad902107bd1bdbee435fc995d4f5af4b47aeec874bcd506a44d25d1c8f","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-16T02:34:19Z","title_canon_sha256":"99f74b296825a85714fd5c9541634499b16965eb22b1df577db0bade639fd73f"},"schema_version":"1.0","source":{"id":"2601.10950","kind":"arxiv","version":2}},"canonical_sha256":"8b39199c40a0a618e4159530f8a8d1684af64b63ec86c6db50d996d04ff441f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b39199c40a0a618e4159530f8a8d1684af64b63ec86c6db50d996d04ff441f9","first_computed_at":"2026-05-22T01:03:16.983563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:03:16.983563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zhPTv5RQ6ekxKkkhmb9lw6CkYJP6Z1jEoED45g7I1OBlVuluN/tM84FJBWm08c3CWI3vpTZM4ozGPO3J4CDKDg==","signature_status":"signed_v1","signed_at":"2026-05-22T01:03:16.984457Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.10950","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edf91daf227a11f1f3e1e7aadbdfb6ed716c8f6b952aae7ac89c1040c6920562","sha256:6b795611b3db4cade9c13ae3aeea6bcfdb27b7f003aa875b156e617787df2807"],"state_sha256":"8779b6373971935256022cc78573037087e60de455b1e286230089a6907fe174"}