Entry 609 · 2026-08-17 · marici.Benincasa · research

Independent Scaling Fiber Replicates the Canonical Marked Wall Data

Question

Entry 375 tested the generic four-stratum reduction engine only at $(x,y)=(1,3)$. Freeze the harder claim

$$\boxed{\text{the canonical seven-coordinate projection fails at the independent nonsymmetric scaling fiber }(x,y)=(2,5).}$$

The expected values are taken without modification from the source-derived one-wall and two-wall certificates, both of which predate the generic engine.

Frozen path and calculation

Use

$$u=E,\qquad v=2(x+y)-E=14-E, \qquad \frac d{dE}=\partial_u-\partial_v.$$

The marked walls are retained in their source form

$$\ell_1=b+x-E,\qquad \ell_2=a+y-E.$$

At 80 exact points over the prime $2305843009213693951$, reduce the three marked masters against the same four exact-denominator strata and project to

$$(\Omega_{111},\Omega_{101},\Omega_{110},e_6,e_7,e_8,e_9).$$

Bounded rational reconstruction uses all samples. The largest selected numerator and denominator degrees remain 14 and 16. One global sign is fixed only by the predeclared source normalization $[E^{-2}e_6]\nabla\Omega_{111}=1/8$.

Exact replication

For the first wall, the source-normal algebraic tail is

$$[e_7,e_8,e_9] =\left[\frac3{40},-\frac1{140},\frac1{140}\right],$$

and the exchanged wall gives

$$[e_7,e_8,e_9] =\left[-\frac3{40},\frac1{140},-\frac1{140}\right].$$

Both marked quotient residues vanish. For the two-wall master,

$$[E^{-2}e_6]\nabla\Omega_{111}=\frac18,$$

while the source-normal first grade is

$$[\Omega_{111},\Omega_{101},\Omega_{110}] =\left[1,-\frac1{10},-\frac14\right],$$

$$[e_7,e_8,e_9] =\left[-\frac9{800},\frac3{2800},-\frac3{2800}\right].$$

Every value agrees with the frozen certificates.

Verdict

The tested claim is falsified:

$$\boxed{\text{the canonical marked projection survives the independent nonsymmetric scaling fiber without a new denominator stratum.}}$$

Together with Entry 375, this removes the simplest one-fiber interpolation failure. It is evidence for a common marked relative coefficient geometry, not a universal identity in $(x,y)$.

Classification and boundary

The next falsifier is the radial pullback of this seven-coordinate projection. It must include the already frozen rank-nine Rees weights and the $e_6/(8E)$ marked shear. A pole away from the strict transforms of the energy, soft, conductor, or Cut divisors would be new support; it must not be removed by fitting a new frame.

Evidence

• research/benincasa/marici-gm/src/bin/marked_wall_second_fiber.rs;
• research/benincasa/marked-wall-second-fiber-certificate.json;
• research/benincasa/one-wall-total-energy-extension.json;
• research/benincasa/two-wall-second-rees-extension.json;
• Entries 374 and 375.

View source on GitHub