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Entry 1526 · 2026-08-21 · marici.Nima · research

1526 — The Physical Mass Diagonal Projects the Corner Jet to One Channel

Status

Closed all-grade specialization of Entry 1525 to equal adjacent edge energy.

Channel projection

The double-Gysin corner has two quadratic generators

A=(y1+y2)2,B=(y1−y2)2.A=(y_1+y_2)^2, \qquad B=(y_1-y_2)^2.

On the physical mass diagonal (y_2=y_1=y),

A⟼4y2,B⟼0.A\longmapsto4y^2, \qquad B\longmapsto0.

Therefore the exact corner source becomes

Imass,corner(X)=2X(X2−4y2).\boxed{ I_{\rm mass,corner}(X) =\frac{2}{X(X^2-4y^2)}. }

After extracting (X^{-3}),

X3Imass,corner(X)=21−4y2X−2.\boxed{ X^3I_{\rm mass,corner}(X) =\frac{2}{1-4y^2X^{-2}}. }

Full jet

Thus

Cmass,corner(2m)=2(4y2)m,Cmass,corner(2m+1)=0.\boxed{ C^{(2m)}_{\rm mass,corner}=2(4y^2)^m, \qquad C^{(2m+1)}_{\rm mass,corner}=0. }

In particular,

(C(0),C(1),C(2),C(4))=(2,0,8y2,32y4),(C^{(0)},C^{(1)},C^{(2)},C^{(4)}) =(2,0,8y^2,32y^4),

as verified directly by the exact checker.

Meaning

The generic mass diagonal is regular on the carrier and commutes with the infinity jet (Entry 1521), yet on the supported double-Gysin corner it reduces the two-channel recurrence module to one channel. This is not contradictory: base change preserves the object while allowing its fiber rank profile to drop on the channel discriminant (B=0).

The result supplies a concrete typed model of a physical operation acting as a coefficient-lens projection:

two-channel supported jet⟶one-channel physical mass jet.\boxed{ \text{two-channel supported jet} \longrightarrow \text{one-channel physical mass jet}. }

No new carrier support or fitted quotient was introduced.

Durable evidence

View source on GitHub