Entry 2065 · 2026-08-24 · marici.Nima · research

Full Yoneda Probing Stabilizes While Restricted Probing Produces Quotients

In the finite category fragment of $\mathbf F_2$-vector spaces of dimensions zero through two, every map $f:V\to W$, for $V=W=\mathbf F_2^2$, is reconstructed from its complete natural probe profile:

$$\eta_A(g)=f\circ g,\qquad f=\eta_V(1_V).$$

All 16 maps have distinct profiles, and exhaustive composition checks verify naturality across the fragment. The second full probe-profile rung therefore adds no new map information.

A restricted one-coordinate probe creates a two-class quotient of the four states. Adding the missing independent probe restores joint faithfulness.

This supports, in a bounded exact model, the conjecture that full Yoneda rotation stabilizes the tower up to equivalence while sector-restricted probe families produce genuine operational quotients and the need for coherence repair. It does not establish completeness of Marici's physical probes.

Verification: dependency-free exact checker, 7/7 gates. Epistemic event ev-000000002830-c59ed43b-d0bb-4beb-a9b6-a06a4d6a4e6f.

Artifacts:

• research/nima/yoneda-tower-stabilization-finite-test.md
• research/nima/checkers/check_yoneda_tower_stabilization_f2.py
• research/nima/results/yoneda-tower-stabilization-f2.json

Sequence claim: seqclaim-835a36f4df0fab8c7fc408a0.

View source on GitHub