TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/MOVING-NORMAL-KERNEL.json
Original file SHA-256: b8b5b3266f2d2f11181740a6681f9d0113594d55b93d3e818b1c56b5193dd27e
Inclusive original lines: 1-80
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000001 | {
000002 |   "date": "2026-10-31",
000003 |   "result": "R051",
000004 |   "scope": "Original R035 moving normal kernel with supplied metric connection and smooth family. Universal tangent/positive-multiplier identities,not selection of physical geometry or exact band decoupling.",
000005 |   "all_passed": true,
000006 |   "checks": [
000007 |     {
000008 |       "name": "unitary-frame tangent constraints",
000009 |       "passed": true
000010 |     },
000011 |     {
000012 |       "name": "whole moving-frame derivative splits orthogonally",
000013 |       "passed": true
000014 |     },
000015 |     {
000016 |       "name": "connection antihermitian",
000017 |       "passed": true
000018 |     },
000019 |     {
000020 |       "name": "whole kinetic restriction retains positive normal Gram",
000021 |       "passed": true
000022 |     },
000023 |     {
000024 |       "name": "moving-kernel curvature sign and full matrix order",
000025 |       "passed": true
000026 |     },
000027 |     {
000028 |       "name": "off-diagonal Gram blocks need not be Hermitian",
000029 |       "passed": true
000030 |     },
000031 |     {
000032 |       "name": "passive frame covariance of connection",
000033 |       "passed": true
000034 |     },
000035 |     {
000036 |       "name": "passive frame covariance of normal Gram",
000037 |       "passed": true
000038 |     },
000039 |     {
000040 |       "name": "varying unitary-frame derivative has affine connection term",
000041 |       "passed": true
000042 |     },
000043 |     {
000044 |       "name": "varying frame does not change orthogonal derivative",
000045 |       "passed": true
000046 |     },
000047 |     {
000048 |       "name": "differentiated actual normal kernel equation",
000049 |       "passed": true
000050 |     },
000051 |     {
000052 |       "name": "reduced normal inverse gives whole positive kinetic Gram",
000053 |       "passed": true
000054 |     },
000055 |     {
000056 |       "name": "reduced normal inverse gives mixed ordered Gram",
000057 |       "passed": true
000058 |     },
000059 |     {
000060 |       "name": "noncommuting square-root derivative keeps its Sylvester order",
000061 |       "passed": true
000062 |     },
000063 |     {
000064 |       "name": "resulting scaled connection is antihermitian",
000065 |       "passed": true
000066 |     },
000067 |     {
000068 |       "name": "scalar-multiplier compressed projector is exact",
000069 |       "passed": true
000070 |     },
000071 |     {
000072 |       "name": "whole normal covariance including mixed matrix order",
000073 |       "passed": true
000074 |     },
000075 |     {
000076 |       "name": "uniform normal multiplier derivative has zero covariance",
000077 |       "passed": true
000078 |     }
000079 |   ]
000080 | }