Documentation

Start here for the public API, the theorem map, and the main limits of the package. The page is written to be easy to scan first and easy to inspect in detail after that.

API overview

Main API groups

Group	Key functions	Use
Core geometry	`visible_precision`, `canonical_lift`, `hidden_projector`, `local_visible_calculus`, `visible_geometry`	Visible precision, lift/projector structure, and local visible calculus.
Hidden-load layer	`hidden_load`, `visible_from_hidden_load`, `inverse_visible_class`, `transport_hidden_load`, `hidden_contraction`, `load_from_hidden_contraction`, `clock`	Fixed-ceiling hidden geometry, transport, and long-chain composition.
Bridge and quotient	`dv_bridge`, `observed_covariance`, Gaussian KL and Hellinger functions, `gaussian_data_processing_contraction`, `observer_collapse_descends`	Thin bridge and quotient-side Gaussian utilities.
Batch	`batch_map`	Deterministic wrapper for repeated tasks.

Theorem map

Where the public functions come from

This is the short version of the theorem map. It is meant to orient you quickly; the full source mapping remains in the repository docs.

Function	What it covers	Source note
`visible_precision`	Visible precision with variational, tower-law, and Schur-form identities.	`prop:visible-precision`
`local_visible_calculus`	Local expansion objects and determinant-curvature split.	`thm:local-calculus`
`hidden_load`	Hidden-load geometry beneath a fixed ceiling.	`thm:hidden-load`
`inverse_visible_class`	The explicit fixed-ceiling inverse surface.	Theorem-facing alias of the same inverse map.
`transport_hidden_load` and `clock`	Transport law and determinant clock.	`prop:transport`
`dv_bridge`	Thin Donsker-Varadhan bridge.	`thm:dv-bridge`

Important note

The inverse theorem is fixed-ceiling, not global.

inverse_visible_class(T, Lambda, ...) is the public inverse surface for a fixed ceiling T. It is not an inverse of the global map (H, C) -> Phi_C(H).

Important note

Long hidden composition uses contraction factors.

transport_hidden_load is the exact transport law, but long associative composition is exposed through hidden_contraction and load_from_hidden_contraction.

Public exports

visible_precision
canonical_lift
hidden_projector
local_visible_calculus
visible_geometry
hidden_load
visible_from_hidden_load
inverse_visible_class
canonical_hidden_realisation
minimal_hidden_realisation
transport_hidden_load
hidden_contraction
load_from_hidden_contraction
clock
dv_bridge
observed_covariance
gaussian_forward_kl
gaussian_reverse_kl
gaussian_hellinger_squared
gaussian_bhattacharyya_distance
gaussian_data_processing_contraction
observer_collapse_descends
batch_map

Out of scope

Not a general scientific platform

The package does not try to be a notebook layer, a document reader, or a general-purpose assistant.

Not the whole downstream stack

Full quotient-observation, empirical ingestion, benchmarking, and application wrappers remain outside the kernel.

Not a widened theorem domain

The release surface makes existing structure easier to use. It does not relax the package limits.