TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-source-clock-field-closure-20261102/CLOCK-CLOSURE-INDEPENDENT-REVIEW.txt
Original file SHA-256: 80719ced7e33f9c86d353a2d4608f47e50633eb0bc8bee380ef4bec38674824d
Inclusive original lines: 1-97
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | ACTUAL NATIVE CLOCK AND SOURCE D8: INDEPENDENT CONDITIONAL CLOSURE REVIEW
000002 | 2 November 2026. No canonical or Atlas mutation.
000003 | 
000004 | Verified result
000005 | For the supplied literal native permutation sigma and the actual source
000006 | isometry M, the integral span
000007 |   L=span_Z(D8 union R(D8)), R=M^T sigma M,
000008 | is even and unimodular. Explicitly L=D8+Z p=D8 union (D8+s), where
000009 |   s=(1,1,1,1,1,1,1,1)/2,
000010 |   p=R(e0+e2)=(1,1,-1,1,-1,1,1,1)/2.
000011 | The index [L:D8]=2 and R(L)=L. No E8 basis, root set or target lattice
000012 | was loaded in the independent HNF calculation. Thus the usual D8+s
000013 | completion is an OUTPUT of this conditional charge-closure test.
000014 | 
000015 | Inputs and exact provenance
000016 | M: experiments/theory-contracts/v16-operator-pullback-20261014/
000017 |    fold-results.json, key explicit_Weyl_matrix.
000018 | sigma: verification/v634_st31_structure.py, literal SIGMA_IDX assignment
000019 |    [4,5,0,1,2,3,6,7]. The actual convention is (sigma x)_j=x_idx[j].
000020 | The script extracts only that assignment with AST. It does not import
000021 | v634, execute its E8 root constructor, or assume that sigma preserves E8.
000022 | All arithmetic is exact rational/integer arithmetic.
000023 | 
000024 | Analytic proof without E8 classification
000025 | Write D8={q in Z8:sum q even}. Its standard simple-root basis is
000026 |   e0-e1,...,e6-e7,e6+e7,
000027 | with covolume2 and Gram determinant4.
000028 | 
000029 | The computed R is orthogonal of order3. Its columns fall into two sets
000030 | A={0,1,4,5}, B={2,3,6,7}. A columns have support in rows0,1,2,3;
000031 | B columns in rows4,5,6,7. Each supported four-vector has entries +/-1/2
000032 | and an ODD number of minus signs. The four entries of every column sum
000033 | to +1 or -1. These are identities of the explicit R, not root-count data.
000034 | 
000035 | Every D8 root is +/-e_i +/-e_j. For i,j in the same column set the
000036 | image is integral, has even coordinate sum and norm2, hence belongs to
000037 | D8. There are 2*binom(4,2)*4=48 such roots. For i,j in different column
000038 | sets the image has eight entries +/-1/2. Each four-entry block still
000039 | has odd sign parity, since multiplying a block by -1 flips four signs.
000040 | The total sign parity is therefore even. All these 4*4*4=64 images
000041 | lie in the SAME coset D8+s. In particular p is one such image, and
000042 | p-s=(0,0,-1,0,-1,0,0,0) belongs to D8.
000043 | 
000044 | D8 roots generate D8. Consequently R(D8) is contained in D8+Zs.
000045 | Conversely p belongs to R(D8), so D8+Zp=D8+Zs is contained in L.
000046 | This proves equality L=D8+Zs, without using W(D8) orbit saturation.
000047 | 
000048 | For q in D8, q*s=sum(q)/2 is integral, s*s=2 and 2s belongs to D8.
000049 | The lattice D8+Zs is therefore integral and even. The new coset has
000050 | order2, so its Gram determinant is det(D8)/2^2=4/4=1. Its norm2
000051 | half vectors are exactly the 128 choices of signs with even parity.
000052 | These facts identify the conventional D8+s even-unimodular lattice,
000053 | without needing the classification of rank8 unimodular lattices.
000054 | 
000055 | The independent HNF also verifies R(L) subset L. Orthogonality and
000056 | detR=1 then give equality. Thus no third application of the order3
000057 | clock enlarges the output lattice.
000058 | 
000059 | Independent 8x8 HNF
000060 | The executable uses the source basis B above and computes the column HNF
000061 |   H=HNF([2B,2RB]), L_basis=H/2.
000062 | Its diagonal entries are (4,2,2,2,2,2,2,1), detH=256, so
000063 |   covolume(L)=256/2^8=1.
000064 | It directly checks that (H/2)^T(H/2) is integral with even diagonal and
000065 | determinant1. It independently checks HNF([2B,2p])=H, and only AFTER
000066 | obtaining H compares HNF([2B,2s]) with it. It checks all112 old roots,
000067 | all128 resulting half weights, and R stability on the full HNF basis.
000068 | 
000069 | Files in the shared work/seam_origin directory:
000070 |   clock_closure_hnf.py
000071 |   clock_closure_hnf_result.json
000072 | Executed with python3 -B, result
000073 |   PASS_CONDITIONAL_SOURCE_CLOCK_LATTICE_CLOSURE.
000074 | The initial Sympy domain-type error was repaired by constructing the
000075 | doubled integer matrix explicitly over ZZ before HNF. The final checks pass.
000076 | 
000077 | Crucial active/passive distinction
000078 | The physical inference requires an ACTIVE allowed source operation whose
000079 | charged images and the old source fields belong to ONE common local field
000080 | fibre, with their cocycles, admissible restrictions, state, reflection and
000081 | actual source time transported compatibly. Under that premise, admission
000082 | of Rq for every old q forces the common charge lattice to contain L.
000083 | 
000084 | A PASSIVE coordinate/background change A -> R(A) supplies an equivalent
000085 | description on another chart or source fibre. It does not require the
000086 | physical algebra to contain BOTH A and R(A), so by itself it does not
000087 | force this generated union. Merely permuting native coordinates is not
000088 | the missing active source-field operation. No diagonal sigma_d operation
000089 | has been identified with this coordinate permutation in the present test.
000090 | 
000091 | The first additional origin premise is therefore actual active clock
000092 | admission in that common physical field fibre, NOT even unimodularity or
000093 | an E8 target. Historically v634 constructs its sigma in an already
000094 | E8-marked native model. The HNF does not use that E8 target, but the source
000095 | dictionary from original P1 to this active sigma is still to be derived.
000096 | This result is conditional lattice selection and does not establish P1
000097 | locality, a physical time symmetry, an observable menu or fundamental origin.