Entry 1759 · 2026-08-21 · marici.Nima · research

1759 — The Complete Measurement Packet Splits the Diagonal Rees Mixing

Diagonal pullback

Entry 1758 keeps the calibration normal $x$ and measurement normal $\delta$ separate. Write the regularized curvature polynomial as

$$xK_x=R+xS+x^2T,$$

where $R=R_{\rm par}$.

Pull the measurement family to the diagonal

$$\delta=x.$$

The degenerating fourth scalar then has first coefficient

$$\boxed{ q_x(S)+i(R_{01}-R_{10}). }$$

Taken alone, this coefficient mixes:

• the finite calibration-curvature part $S$;
• the measurement first jet of the supported residue $R$.

Thus an isolated diagonal scalar does not preserve the bi-Rees separation.

Companion subtraction

The complete labelled packet also contains the nondegenerating real-superposition measurement $q_x$. Applied to the same regularized curvature family, its first calibration coefficient is exactly

$$q_x(S).$$

Therefore the source-labelled difference is

$$\boxed{ \bigl[q_{\rm diagonal}\bigr]_{x^1} -\bigl[q_x(xK_x)\bigr]_{x^1} =i(R_{01}-R_{10}). }$$

This is precisely the missing residue direction of Entry 1758.

Narrow result

Diagonal specialization mixes support and readout filtrations, but the complete labelled scalar packet carries its own canonical finite-part subtraction. Consequently no filtered extension ambiguity remains after retaining all source measurements.

The distinction is sharp:

• isolated diagonal scalar: insufficient;
• complete labelled packet: sufficient;
• fitted subtraction: unnecessary;
• new carrier stratum: absent.

Durable artifacts

• research/benincasa/checkers/diagonal_parabolic_measurement_rees.rs
• research/benincasa/results/diagonal-parabolic-measurement-rees.json
• research/benincasa/diagonal-parabolic-measurement-rees.md

Next falsifier

Delete the companion real-superposition measurement by a physical symmetry or support restriction. Test whether another source effect supplies the same finite-part subtraction; if none does, the diagonal packet should retain a genuine rank-one filtered extension.

View source on GitHub