Baseline

Terms are defined in review.md; works are listed in the bibliography.

The named baseline

Coh-Metrix (Graesser et al. 2004; McNamara et al. 2014): a multilevel set of text indices aligned with comprehension theory.
Its five major factors (Graesser et al. 2011): word concreteness, syntactic simplicity, referential cohesion, causal cohesion, narrativity.
Index family names in the table below were read in a secondary overview of Coh-Metrix 3.0.
Plus per-word surprisal from a language model, reported per sentence as mean, maximum and variance (operationalizations as in Meister et al. 2021).
Floor: Flesch reading ease (Flesch 1948), which a useful rule must beat, and which can be beaten (Crossley et al. 2017).

Scale	Coh-Metrix family	Open alternative	Model-based
1. Information rate	none direct	none	surprisal mean, maximum, variance
2. Sentence locality	syntactic complexity	mean dependency distance (Hansen et al. 2023)	none needed
3. Nesting	syntactic complexity	depth from a parse	none needed
4. Text	referential cohesion, semantic overlap	TAACO local cohesion and givenness (Crossley et al. 2016)	none needed
5. Text tree	situation model, connectives	TAACO global cohesion; sentence coherence (Hansen et al. 2023)	surprisal contour by section (Tsipidi et al. 2024)

Tool	What it computes	Access
Coh-Metrix (Graesser et al. 2004)	cohesion, syntax, word and readability indices	web tool; no official source repository found
TAACO 2.1 (Crossley et al. 2016)	local, global and text cohesion, givenness	Python and spaCy; source on GitHub; no license file found
TextDescriptives (Hansen et al. 2023)	dependency distance, readability formulas, sentence coherence	Python and spaCy; Apache-2.0
minicons (Misra 2022)	word and sentence probabilities from transformer models	Python; MIT
Linear Arrangement Library (from the authors of Alemany-Puig et al. 2022)	sums of edge lengths and minimum arrangements	C++ with Python bindings; AGPL-3.0

Model choice matters: larger, lower-perplexity models fit reading time worse (Oh & Schuler 2023); report the model.

Check	Scale	Cost	Exact?
Sentence length, words per sentence	1, 2	O(n)	yes, given a tokenizer
Flesch reading ease	floor	O(n)	up to the syllable-counting rule
Markdown nesting: heading level, list indentation	3, 5	O(n)	yes, from syntax alone
Definition-to-use distance for marked terms (bold first use)	ordering	O(n), one pass with a hash map	yes
Use before definition	ordering	O(n)	yes
Ordering cost D(π) of a note's concept graph, and the bound D ≥ number of edges	ordering	O(V + E)	yes
Given a dependency parse: D, maximum depth, center-embedding degree, Yngve depth	2, 3	O(n) per sentence	yes, given the parse
Tree minimum D_min, hence an optimality score	2	polynomial (Chung 1984); linear if projective (Alemany-Puig et al. 2022)	yes, given the parse
Argument overlap of adjacent sentences	4	O(n)	yes, given lemmas
Entity grid transitions	5	O(sentences × entities)	yes, given entity mentions

A parser or lemmatizer is itself a statistical model, but a small local one; parsing runs in polynomial time.
Not a check: the optimal ordering of concepts, NP-hard in general by the sources in state-of-the-art.md §6.
Not zero-cost: surprisal, which needs one language-model pass per text.

Take a text and its rewrite under one rule.
Compute the baseline indices and the exact checks for both.
Report the differences per scale, never a single score.
Claim a reader effect only from reader data: reading time plus questions split into text base and situation model (McNamara et al. 1996b).
Run each comparison for at least two reader levels, since cohesion effects reverse with knowledge (O'Reilly & McNamara 2007).

People compare against a grade score and a sentence cap, not Coh-Metrix.

Report the grade tools beside the indices above, never in place of them.
A tool grade is a floor-type baseline, like Flesch; it was not shown to track comprehension.