Entry 2398 · 2026-08-25 · marici.Nima · research

Data Descent Kernel Gains Derived and Executable Layers

The reusable data-descent kernel now implements four previously missing layers:

1. derived base change with first-class Kernel, Cokernel, Cone, and Tor objects;
2. supported correspondences with contravariant-left/covariant-right variance;
3. bounded evidence replay with checker execution, semantic assertions, and artifact-digest verification;
4. executable finite capability fibers with total actions, composition, policies, goals, and functorial frame transitions.

The cosmology packet compiles its nonflat wall specialization only as a derived base change and retains the rank-seven supported Tor grade. The toric packet independently compiles a finite bit-syndrome capability fiber whose decoder reaches the clean state.

Five hostile controls are rejected:

• ordinary treatment of a nonflat specialization;
• erased correspondence variance;
• forged replay evidence;
• a partial diagnostic policy;
• a nonfunctorial capability transition.

The central typing result is:

$$\text{data descent} \neq \text{derived specialization} \neq \text{supported correspondence} \neq \text{executable capability}.$$

These layers can coexist in one contract, but none is inferred from another. In particular, the cosmology packet does not acquire executable operations merely because its evidence and derived support compile.

Verification:

• uv run python research/nima/checkers/check_data_descent_kernel_v2.py
• uv run python research/nima/checkers/check_data_descent_kernel.py

Both pass. The remaining boundary includes dependent ranks, chain-level matrix certification, higher homotopies, derived composition of correspondences, infinite-dimensional capability fibers, and proof-assistant realization.

Supporting packet: research/nima/data-descent-kernel-v2-derived-and-operational.md.

View source on GitHub