E.4 Baseline domains reproduced by the full run
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The exact mathematical outputs below were compared with the preserved baseline. The historical runner also reproduced its seven scientific output records. These finite ranges remain part of the evidence even where a universal written theorem accompanies them.
| Evidence area | Executed domain in the baseline | Limit of the evidence |
|---|---|---|
| Small functions | All 276 functions on one, two, or three inputs; 4,240 scalar input/target cases; 2,344 cuts | Exact constructions plus proved lower bounds, not exhaustive circuit search |
| Four-input profiles | All 65,536 truth tables; all 168 monotone functions | Independent evaluation-span method checks only the declared 765 cases |
| Unbalanced-OR family | Designated truth tables through nine inputs; all affine masks through eight | No exhaustive ninth-input affine-mask claim |
| Projection coefficients | 693,965 pair coefficients and nine exact rank cases, through 1,022 inputs | Full truth tables only at \(m=2,3,4\) |
| Projection oracle checks | 65,808 logical-input/target cases across the two constructed oracle families in the stated small domains | Large entries use symbolic formulas, exact rank, and construction counts |
| Weighted fingerprints | 1,052,736 verifier/field-point evaluations | Enumerated verifiers have at most three witness bits |
| Independent coefficient extraction | 20,544 cases | All field points for \(m\le2\); restricted coordinate grid at \(m=3\) |
| Disjoint product rule | 4,096 exact controls | Does not extend the rule to shared variables |
| Scalar algebra maps | 66,048 linear maps over the three specified witness/field domains | Controls the scalar special case; general dimension theorem has a written proof |
The field used in the fingerprint checker is
\[
\mathrm{GF}(16)={\mathbb F_2}[t]/(t^4+t+1).
\]
All mathematical arithmetic in these tests is Boolean, exact integer, or finite-field arithmetic. Runtime is not presented as a complexity benchmark. Equality of checksums certifies matching bytes, not mathematical truth.