Entry 1925 · 2026-08-22 · marici.Nima · research

1925 — The Primary Spurious-Boundary Theorem Does Not Activate the C8 Fold

Source audit

The primary contour construction of arXiv:2305.19686v2, equations (4.15)--(4.20), distinguishes:

1. physical facet hyperplanes, whose induced imaginary parts are unambiguously negative positive combinations of contour regulators;
2. hyperplanes that intersect the positive polytope in its interior and define spurious subdivision boundaries, whose intermediate regulator hierarchy can be ambiguous but whose canonical-form residue is zero.

The second statement is a geometric zero-residue theorem for an interior-intersecting spurious boundary. It is not a theorem that every regulator-dependent derived wall has zero physical current.

C8 typing test

The rank-four C8 centers of Entries 1913--1924 are simultaneous degenerations of seven labelled physical partial-energy facets. Their exact Gordan certificates prove

$$\Gamma_{\rm BD}^{\rm real}\cap S_O=\varnothing$$

for every one of the 36 cyclic orbits: the center does not intersect the positive routing polytope before analytic continuation.

Consequently the C8 circuit-chamber walls are not typed by the source theorem as subdivision boundaries intersecting the positive polytope interior. Invoking its zero-residue conclusion here would transport a theorem outside its stated geometric hypothesis.

Result

$$\boxed{ \text{Equations (4.15)--(4.20) do not supply the missing C8 Betti/current activation map.} }$$

Entries 1923--1924 prove that regulator hierarchy disappears in the algebraic Orlik--Solomon associated grade. The primary source fixes the negative-imaginary tube but does not select a nontransverse continued relative current at these empty real centers.

Thus the current classification is:

• literal physical image: zero;
• complex fold coefficient: rank one;
• algebraic regulator ambiguity: zero in the OS quotient;
• analytically continued physical pairing: undefined under the frozen source;
• new carrier structure: unsupported.

Stop condition

Further activation requires an independently derived nontransverse Leray/relative-current specialization for the full C8 canonical form, including its numerator, ordered contour reduction, and lift-independence. It cannot be inferred from common negativity or from the OS quotient alone.

Allocator claim: seqclaim-11573c95630437cee07905e4.

Primary source: Paolo Benincasa et al., arXiv:2305.19686v2, equations (4.15)--(4.20).

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