TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/native-arc-charge-source-interface-20261026/ALGORITHMIC-ATLAS-NOTE.txt
Original file SHA-256: 65f197b4590210e331151720968eb2c8329616d05723ba5107fdc289f1eeee16
Inclusive original lines: 1-87
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 | UR.NATIVE.ARCCHARGE.ALGORITHMIC-COMPARISON.01
000002 | 26 October2026. Recover the first source/algorithm comparison into the Atlas.
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000015 | 
000016 | 2. Exact operator connection, not matching dimensions
000017 | In the original V=C4 frame on four tensor registers, the Pauli average
000018 |  Q=(1/16)sum_(a,b in F2²) W_ab^tensor4
000019 | obeys Pi_native=Q Pi_sym4=Pi_sym4 Q exactly. Full Pauli fixed rank16,
000020 | symmetric fourth tensor rank35, common native rank5. These are different
000021 | spaces, not16 physical particle species or four spacetime coordinates.
000022 | All64 original single-register matrix-unit checks give
000023 |  Pi_native E_ab^(s) Pi_native=delta_ab Pi_native/4.
000024 | Thus the existing native code has its exact one-register erasure property.
000025 | The mathematical recovery property does not select physical noise or controls.
000026 | The original Atlas finding native-symmetric-quartic-erasure-common-object
000027 | already contains the group/source mechanism; this replay adds direct checks
000028 | and the explicit algorithmic correspondence rather than claiming priority.
000029 | 
000030 | 3. Exact moment information and its loss under reduction
000031 | For the60 actual Gaussian E8/J source lines, the projective frame potentials
000032 | at orders1,2,3 are1/4,1/10,1/20, matching their Haar references. At order4
000033 | the actual value is1/32 instead of1/35; ratio35/32 and squared HS defect3/1120.
000034 | Projective moments of source vectors and unitary designs of operations are
000035 | not equated. The original identity40M4=Pi_native+Pi_sym4 explains the same
000036 | five-space. These are shared structural consequences, not independent votes.
000037 | For the known pair rhoC=Pi_native/5,rhoS=Pi_sym4/35, all PROPER marginals
000038 | coincide. The original collective-native-marginal-origin-20261026/PROOF.txt
000039 | lines47-74 supplies that exact marginal statement. Their global relative
000040 | entropy islog7 and trace distance6/7; after a proper partial trace D=0.
000041 | This reduction loses information for THIS pair. It is not a claim that all
000042 | pure codewords have identical outputs or that all compression fails.
000043 | 
000044 | 4. Symmetry, algorithms and physical selection stay distinct
000045 | The known Clifford fourth-commutant theorem decomposes Sym4(C4) into5+30.
000046 | A Hermitian generator commuting with the full stated Clifford action is
000047 | therefore scalar on each irreducible block. On the five-space it cannot by
000048 | itself select an internal nontrivial clock or3+2 mark. This is only that
000049 | fully invariant autonomous generator class, not a no-go for all source laws.
000050 | On the full tensor space the symmetric complement and nonsymmetric complement
000051 | allow independently positive coefficients, so symmetry and the code ground
000052 | space alone do not determine their energy ratio. The original moment parent
000053 | has a fixed ratio by its definition, not by a derived physical identification.
000054 | Primary source checked: Zhu/Kueng/Grassl/Gross, arxiv1609.08172v1,
000055 | Sections3.1,3.2, Table1. Known mathematics is not claimed as a new TFPT theorem.
000056 | The direct external gate U=diag(1,1,exp(i*pi/4),exp(i*pi/4)) has literal
000057 | U^tensor4 compression diag(0,0,i,i,i), hence leaks two native directions.
000058 | It is an external algorithm comparison, not a physically allowed TFPT gate.
000059 | Clifford/stabilizer structure alone is not a universal-computation proof.
000060 | 
000061 | 5. Other literature links and explicit non-results
000062 | The original survey also retains the known Hamming/ConstructionA/E8 link,
000063 | E8 energy optimality in its prescribed dimension/metric/potential class,
000064 | one-dimensional reversible quantum cellular automata, positive-transfer
000065 | convergence, sufficient statistics/process tensors and reversible computing.
000066 | These are explanatory primary-literature pointers with their original scopes.
000067 | No TFPT local dynamics, spacetime dimension, measurement rule or state law is
000068 | obtained by importing those theorems. Alpha's existing closure root is not
000069 | promoted to an external computer parameter. The4 tensor slots, polynomial
000070 | degree4, seed term48*c3^4 and four spacetime coordinates remain distinct.
000071 | No evidence that our universe is a simulation was found by this comparison.
000072 | 
000073 | 6. Later correction to the ORIGINAL snapshot's proposed next step
000074 | The old snapshot ends by proposing F_a -> deltaD_rel. That is a historical
000075 | research target, not the final current requirement for defining a neutral
000076 | composite. BILOCAL-RECONSTRUCTION.txt subsequently reconstructs the neutral
000077 | fields from the existing connected current source. A new elementary coupling
000078 | is unnecessary merely to DEFINE them. The field-to-D variation remains a
000079 | requirement if a particular primitive physical coupling/Hessian is asserted.
000080 | The current source-origin route is in HALF-PERIOD-GNS-SEWING.txt: derive
000081 | actual P1 odd-field modular/Sewing transport and its marked real carrier.
000082 | The distinction is explicitly retained so the archived first report cannot
000083 | silently override the later constructive result.
000084 | 
000085 | Verdict: EXACT_FINITE_NATIVE_ALGORITHMIC_SOURCE_REPLAY;
000086 | KNOWN_MATHEMATICAL_CORRESPONDENCES; PHYSICAL_SOURCE_AND_SIMULATION_OPEN.
000087 | No ledger, empirical or physical gate promotion.