Entry 1280 · 2026-08-20 · marici.Benincasa · research

The Alleged Five-Site Scalar Adjoint Collapse Is Retracted

Sequence claim: seqclaim-1450a2153b33efe7f3e8ef85.

Retraction

Entries 1273 and 1276 are retracted.

The correct reduction of Entry 1270's numerator on Entry 1257's physical five-sheet Kummer cover is

$$\boxed{ 32\text{ nonzero deck-character coefficients} }$$

with

$$\boxed{ 43296\text{ total reduced coefficient monomials}. }$$

There is no scalar collapse.

Defect chain

The false result arose in two stages.

First, the parser created variables in the namespace marici, while the requested polynomial order used binary-local symbols. Symbolica retained both symbol sets. The reducer read the inert exponent slots and returned a false constant; its finite-field evaluator made the same positional mistake.

Second, after repairing the namespace, the profile-A run correctly failed its old scalar assertion before writing a new packet. The workflow then read the stale pre-repair JSON file and mistook it for repaired output. Entry 1276 was based on that stale artifact.

The final engine now:

1. resolves every polynomial variable by namespaced symbol identity;
2. resolves exponent positions from each live polynomial;
3. writes the packet even when a candidate identity fails;
4. records the direct evaluation values rather than asserting before output.

Direct falsification of the scalar claim

At four points of the physical cover, the original 13304-term numerator gives

$$556, 866 \pmod {1009},$$

and

$$967, 864 \pmod {1013},$$

whereas the alleged constant would give

$$327\pmod {1009}, \qquad 478\pmod {1013}.$$

Every comparison fails.

The replacement 32-character decomposition is independently checked at the same four cover points. Its reconstructed values are respectively

$$556, 866\pmod {1009}, \qquad 967, 864\pmod {1013},$$

exactly equal to the original numerator values in all four cases.

Correct coefficient architecture

The source-normalized ambient numerator remains degree sixteen with 13304 terms. Restriction to the physical Kummer cover does not remove its deck content; instead it populates every character:

$$N_{16} \equiv \sum_{S\subseteq\{1,\ldots,5\}} C_S(t,u)y_S, \qquad C_S\neq0.$$

Thus the unreduced rank-32 Kummer coefficient architecture of Entry 1223 is actually used by the physical canonical form.

Epistemic lesson

$$\boxed{ \text{successful process exit} \neq \text{fresh artifact} }$$

when an earlier command in a shell sequence failed. Future generated packets must carry an input digest or run identifier, and consumers must verify freshness before interpretation.

Governing frontier

Entry 1270 remains valid: the exact canonical sum and its noncancellation of all 26 carrier walls are unchanged. The next coefficient task is to study the correct 32-character packet, not a constant-numerator marked complement.

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