Entry 1743 · 2026-08-21 · marici.Nima · research

1743 — A Labelled Fiber Reference Recovers Based Matrix Holonomy Covariantly

Matrix-interference datum

Let $E$ be the transported rank-two amplitude fiber and let

$$F:R\xrightarrow{\sim}E$$

be a source-labelled reference frame. Define the framed holonomy readout

$$\boxed{M_F(H)=F^{-1}HF.}$$

Physical gauge invariance

Under a change of the physical fiber frame,

$$H\longmapsto GHG^{-1}, \qquad F\longmapsto GF.$$

Then

$$M_{GF}(GHG^{-1})=F^{-1}HF=M_F(H).$$

Thus the matrix packet is independent of arbitrary physical gauge.

Reference covariance

Relabelling the reference basis by $S$ gives

$$F\longmapsto FS, \qquad M_{FS}(H)=S^{-1}M_F(H)S.$$

If the reference basis labels are part of the source occurrence data, its matrix entries are fixed. If only the reference subspace is supplied, the canonical output is again a conjugacy class.

For Entry 1741's loops, every admissible frame satisfies

$$\boxed{M_F(AB)\ne M_F(BA).}$$

Hence the framed readout recovers the based ordering lost by Wilson traces.

Narrow result

A labelled matrix interference reference upgrades frame-free Wilson character data to the complete based holonomy matrix while preserving physical gauge invariance. The extra structure is a sector-specific readout/frame object, not a new Cut carrier stratum.

Durable artifacts

• research/benincasa/checkers/framed_matrix_holonomy_readout.rs
• research/benincasa/results/framed-matrix-holonomy-readout.json
• research/benincasa/framed-matrix-holonomy-readout.md

Next falsifier

Let the reference frame itself become singular or only partially labelled. Compute the resulting parabolic flag readout and test whether supported Rees data recover the lost matrix rows without a post hoc splitting.

View source on GitHub