refactor: remove equivalence class folding from entropy pipeline

Removes circular-reverse complement machinery and explicit k-mer canonicalization across the entropy pipeline. Frequency tallying and Shannon entropy computation now operate directly on raw k-mer values, eliminating prior score inflation and alignment-dependent artifacts while preserving orientation invariance. Updates build scripts to generate normalized lookup tables for k-mer lengths 1–6, restricts the public API to `EntropyTracker`, and bumps crate versions. Documentation is updated to reflect the simplified raw-value approach and revised module structure.

docmd/theory/entropy.md

@@ -1,6 +1,6 @@
 # Kmer entropy filter
 
-Low-complexity kmers (polyA, polyT, tandem repeats) are detected and excluded during phase 1. The filter computes a **normalized Shannon entropy** over sub-words of multiple sizes, corrected for two sources of bias: the small number of observations within a single kmer, and the unequal sizes of circular equivalence classes.
+Low-complexity kmers (polyA, polyT, tandem repeats) are detected and excluded during phase 1. The filter computes a **normalized Shannon entropy** over sub-words of multiple sizes, corrected for one source of bias: the small number of observations within a single kmer relative to the number of possible sub-words.
 
 ## Sub-word frequencies
 
@@ -8,17 +8,15 @@ For a kmer of length k and a sub-word size ws (1 ≤ ws ≤ ws_max, typically ws
 
 $$w_i = \text{kmer}[i \mathinner{..} i+ws-1], \quad i = 0, \ldots, n_{\text{words}}-1$$
 
-Each sub-word is mapped to its **circular canonical form**: the lexicographic minimum among all cyclic rotations of the word **and all cyclic rotations of its reverse complement**. This extended equivalence relation ensures that entropy(K) = entropy(revcomp(K)) — the filter is strand-symmetric. Let $s_j$ be the size of equivalence class $j$ (number of distinct raw words mapping to canonical form $j$), and $f_j$ the count of canonical form $j$ among the $n_{\text{words}}$ sub-words ($\sum_j f_j = n_{\text{words}}$).
+Each sub-word is tallied under its own raw 2-bit-packed value — **no canonicalization**. Let $f_j$ be the count of raw word $j$ among the $n_{\text{words}}$ sub-words ($\sum_j f_j = n_{\text{words}}$), over the $4^{ws}$ possible raw words.
+
+An earlier version of this filter first folded each sub-word into a circular+reverse-complement equivalence class, then "unfolded" the observed class frequency back onto its members to correct for unequal class sizes. That machinery bought nothing it was claimed for — see *Why no equivalence classes* below — while measurably weakening detection of the very sequences the filter exists to catch, so it was removed.
 
 ## Corrected Shannon entropy
 
-The circular equivalence classes have unequal sizes: under a uniform distribution over all $4^{ws}$ raw words, class $j$ is visited with probability $s_j / 4^{ws}$, not $1/n_a$. Computing entropy directly over canonical classes therefore underestimates the entropy of a random sequence.
+$$H_{\text{corr}} = \log(n_{\text{words}}) - \frac{1}{n_{\text{words}}} \sum_j f_j \log f_j$$
 
-The correction "unfolds" each canonical class back to its member raw words, redistributing each observation of class $j$ equally among its $s_j$ members:
-
-$$H_{\text{corr}} = \log(n_{\text{words}}) - \frac{1}{n_{\text{words}}} \sum_j f_j \log f_j + \frac{1}{n_{\text{words}}} \sum_j f_j \log s_j$$
-
-The last term is the correction for unequal class sizes. For a uniformly random sequence ($f_j \approx n_{\text{words}} \cdot s_j / 4^{ws}$), this gives $H_{\text{corr}} \approx \log(4^{ws}) = 2 \cdot ws \cdot \log 2$, the maximum entropy over raw words.
+This is a plain Shannon entropy over the observed raw-word frequencies.
 
 ## Maximum entropy correction for small samples
 
@@ -42,27 +40,45 @@ $$\text{entropy}(kmer) = \min_{ws=1}^{ws_{\max}} \hat{H}(ws)$$
 
 A value near 0 indicates low complexity (e.g. AAAA…); near 1 indicates high complexity. A kmer is rejected if $\text{entropy}(kmer) < \theta$, where $\theta$ is a collection parameter (default 0.7). The minimum across word sizes ensures that any scale of repetition is detected independently: polyA is caught at ws=1, dinucleotide repeats at ws=2, etc.
 
+## Why no equivalence classes
+
+A prior design folded each sub-word into the canonical form of its circular-rotation + reverse-complement equivalence class before tallying, on the reasoning that (a) it guarantees $\text{entropy}(K) = \text{entropy}(\text{revcomp}(K))$, and (b) collapsing phase-shifted repeats (e.g. `ATG` ≡ `TGA` ≡ `GAT`) into one class better reflects that they are "the same" low-complexity pattern.
+
+Both properties already hold for the raw, unfolded entropy above, without any class machinery:
+
+- **Reverse complement**: for any K of length n, window $j$ of $\text{revcomp}(K)$ equals $\text{revcomp}$ of window $(n{-}ws{-}j)$ of K. This is a bijection between the window sets under which each window maps to its own revcomp — and revcomp is itself a bijection (involution) on the space of raw ws-mers. So the multiset of raw-word frequencies for $\text{revcomp}(K)$ is exactly a relabeling of the multiset for K, and Shannon entropy — a function of the frequency multiset alone — is exactly invariant. No folding required, for any K.
+- **Tandem repeats**: a period-p repeat sampled by a stride-1 sliding window naturally cycles through its own rotations as raw tokens (e.g. `ATGATGATG…` yields the raw words `ATG`, `TGA`, `GAT` in rotation as the window slides). The low diversity this represents (few distinct raw words out of $4^{ws}$ possible) is already visible in the raw frequency distribution — no folding needed to detect it.
+
+What the fold-then-unfold step actually did was credit each observed class with the frequency of equivalence-class members that were **never observed on the read strand**, inflating $H_{\text{corr}}$ for genuine repeats. Worked example: k=31, ws=3, kmer = `ATG` repeated ($n_{\text{words}}=29$, all 29 windows fall into one class of size 6 under the old scheme — 3 rotations × forward/revcomp):
+
+| | $H_{\text{corr}}$ | normalized |
+|---|---|---|
+| old (folded, class size 6) | $\log 6 \approx 1.79$ | $\approx 0.53$ |
+| current (raw, unfolded) | $\log 3 \approx 1.10$ | $\approx 0.33$ |
+
+The gap is not a rounding artifact: per sub-word order, the folded score for this same repeat swings from 0.53 (ws=3, aligned with the period) up to **1.03** (ws=5, misaligned with the period) — i.e. a period-3 repeat could score *above* the theoretical maximum for a random sequence, depending on which ws happens to divide the repeat's period. The raw formula stays flat at ≈0.33–0.40 across ws=2..6 regardless of alignment, which is the robustness the "minimum across ws" design was meant to provide in the first place.
+
 ## Interpretation as an effective number of classes
 
-$H_{\text{corr}}$ is a standard Shannon entropy over raw words (after unfolding the equivalence classes), so the classical perplexity interpretation holds directly: $N_{\text{eff}} = e^{H_{\text{corr}}}$ is the number of equiprobable classes that would yield the same entropy.
+$H_{\text{corr}}$ is a standard Shannon entropy over raw words, so the classical perplexity interpretation holds directly: $N_{\text{eff}} = e^{H_{\text{corr}}}$ is the number of equiprobable raw words that would yield the same entropy.
 
-For the normalised score $\hat{H}$, dividing by $H_{\text{max}}$ changes the logarithm base:
+For the normalised score $\hat{H}$, dividing by $H_{\max}$ changes the logarithm base:
 
-$$\hat{H} = \frac{\log N_{\text{eff}}}{\log N_{\text{max}}} = \log_{N_{\text{max}}} N_{\text{eff}} \quad \Longleftrightarrow \quad N_{\text{eff}} = N_{\text{max}}^{\,\hat{H}}$$
+$$\hat{H} = \frac{\log N_{\text{eff}}}{\log N_{\max}} = \log_{N_{\max}} N_{\text{eff}} \quad \Longleftrightarrow \quad N_{\text{eff}} = N_{\max}^{\,\hat{H}}$$
 
-The property is preserved: $\hat{H}$ is the logarithm (in base $N_{\text{max}}$) of the effective number of equi-represented classes.
+The property is preserved: $\hat{H}$ is the logarithm (in base $N_{\max}$) of the effective number of equi-represented raw words.
 
-In the large-sample limit ($n_{\text{words}} \gg 4^{ws}$), $N_{\text{max}} \approx 4^{ws}$, giving:
+In the large-sample limit ($n_{\text{words}} \gg 4^{ws}$), $N_{\max} \approx 4^{ws}$, giving:
 
 $$N_{\text{eff}} \approx 4^{ws \cdot \hat{H}}$$
 
-This has a clean interpretation: $ws \cdot \hat{H}$ is the **effective word length** (in bases) of a perfectly uniform distribution that would produce the same entropy. At $\hat{H} = 1$ the full space of $4^{ws}$ words is used; at $\hat{H} = 0.5$ with ws=2, only $4^1 = 4$ effective classes out of 16 are occupied.
+This has a clean interpretation: $ws \cdot \hat{H}$ is the **effective word length** (in bases) of a perfectly uniform distribution that would produce the same entropy. At $\hat{H} = 1$ the full space of $4^{ws}$ words is used; at $\hat{H} = 0.5$ with ws=2, only $4^1 = 4$ effective words out of 16 are occupied.
 
-In our actual regime, $n_{\text{words}}$ is small and $4^{ws}$ can exceed $n_{\text{words}}$, so $H_{\text{max}} < \log(4^{ws})$ due to the small-sample correction. The exact effective count is $N_{\text{max}}^{\hat{H}}$, not $4^{ws \cdot \hat{H}}$.
+In our actual regime, $n_{\text{words}}$ is small and $4^{ws}$ can exceed $n_{\text{words}}$, so $H_{\max} < \log(4^{ws})$ due to the small-sample correction. The exact effective count is $N_{\max}^{\hat{H}}$, not $4^{ws \cdot \hat{H}}$.
 
 ## Properties
 
 The entropy score is a function of the kmer sequence alone — it does not depend on the surrounding context or on the position within any genome. Two consequences:
 
-- **Orientation invariance**: $\text{entropy}(K) = \text{entropy}(\text{revcomp}(K))$, guaranteed by the strand-symmetric canonical form.
+- **Orientation invariance**: $\text{entropy}(K) = \text{entropy}(\text{revcomp}(K))$ — see *Why no equivalence classes* above for why this holds without any explicit strand-folding step.
 - **Context independence**: the same kmer is always rejected or always kept, regardless of which genome it occurs in, where in that genome it appears, or which strand is considered. The filter defines a fixed partition of the kmer space into low-complexity and valid kmers.