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If, in addition, M1 and M2 are C^{3,1}, then psi is a second-order retraction.","weakest_assumption":"The two manifolds are C^{2,1} embedded submanifolds of R^n that intersect cleanly (as stated in the abstract as the key assumption enabling the local limiting map and retraction property)."}},"verdict_id":"ffdc81c8-e8b5-462d-ac3e-292c0a03e2bf"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:78fc587697770307503839b2ba9b32b7ab6af3fc5dc12eacb646ea5133642f95","target":"record","created_at":"2026-05-20T00:03:55Z","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":"02354881a377d03a7d4983eeeea4442761671fe6848c08361f82533ed5b38ed7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-17T11:03:31Z","title_canon_sha256":"10887c2dcce6d2ec16083af533adf8e420f65843fa912282c03c7b3aa9939e76"},"schema_version":"1.0","source":{"id":"2605.17384","kind":"arxiv","version":1}},"canonical_sha256":"3ecd7cc5ebfc255dba9eb2b067c5c838523952022ab73d85eba0807b0027d247","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ecd7cc5ebfc255dba9eb2b067c5c838523952022ab73d85eba0807b0027d247","first_computed_at":"2026-05-20T00:03:55.875436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:55.875436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PUtJs02uVhoVR+n5AaTkFU+9WNzOWfVaudd1Dy9I191VRtnABH38yoF2NLFsa8yKYAwOkoDPd6mDF9K4nMEZAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:55.876385Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17384","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78fc587697770307503839b2ba9b32b7ab6af3fc5dc12eacb646ea5133642f95","sha256:4390ec3c1ddf4d8b6b73f4d2dfecaf0fbfe779227c2e10c227102cd7ef7f97c7"],"state_sha256":"718fcd29a48c772702398c6cedf988e985127409a76b8944d5b9463d73b1d30e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+BAz8gMSi3fqJpg1j2Ak1U9STBMPxmnQ+DcGBLQZ1vV/hYWrnZRVOFvg+bmHEyPCM2no4CXQGkECXSDicaWkBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T08:12:06.778458Z","bundle_sha256":"f5e2dfd6ca3e94a6d7ec041fb54d2670289f1c1fb7040e45d8b72b8cb86e72db"}}