engine: the verses indexed by root — the pairwise middot read, not scan

Over the whole scroll (861cd4e6) gezerah shavah, binyan av and shnei
ketuvim scanned verse pairs — quadratic over 5,853 verses, 2.9 s in the
middot suite and waiting to be a live cost the day a middah is
consulted. The generator now also writes root_in(Root, Book, Ch, Vs),
one fact per root occurrence (49,542), exported by torah_text; the
pairwise rules read the first verse and find the second (and third) by
the root's index: shared_keyword, binyan_av_two, verses_contradict,
resolving_verse; verses_mentioning_root is the index itself. Same
answers (middot 47/47, phase3 28/28 unchanged), middot suite 2.865 s →
0.112 s. l1_sha256 unchanged (the facts are derived from the same L1);
--check passes.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

scripts/build_engine_verses.py

@@ -59,6 +59,7 @@ def verse_files():
 def build():
     h = hashlib.sha256()
     facts = []
+    index = []  # root_in/4: the verses by root — what the pairwise middot read instead of scanning (2026-10-25)
     nverses = nroots = 0
     for book, ch, vs, path in verse_files():
         data = open(path, "rb").read()
@@ -72,6 +73,8 @@ def build():
                 roots.append(a)
         gloss = " ".join(w.get("consonants", "") for w in d.get("words", []) if w.get("consonants"))
         facts.append(f"verse({book}, {ch}, {vs}, [{', '.join(roots)}], {quote(gloss)}).")
+        for r in roots:
+            index.append(f"root_in({r}, {book}, {ch}, {vs}).")
         nverses += 1
         nroots += len(roots)
     header = f"""%% l1_verses.pl — GENERATED by scripts/build_engine_verses.py from l1/torah.
@@ -82,8 +85,13 @@ def build():
 %%
 %% l1_sha256: {h.hexdigest()}
 %% verses: {nverses}   root_occurrences: {nroots}
+%%
+%% root_in(Root, Book, Ch, Vs) — the same facts inverted, one per root
+%% occurrence, so a rule that asks "which verses carry this root" reads
+%% an indexed table instead of scanning 5,853 verses (the pairwise middot:
+%% gezerah shavah, binyan av, shnei ketuvim).
 """
-    return header + "\n".join(facts) + "\n", h.hexdigest(), nverses
+    return header + "\n".join(facts) + "\n\n" + "\n".join(index) + "\n", h.hexdigest(), nverses
 
 
 def main():