Answer architecture round 2: carry the engine table on its rows table, name the imports items 99 and 102 need, and correct the engine decision's premise

docs/decisions.md

@@ -832,11 +832,10 @@ Valid while names are read only inside the category binding them.
 ## The template engine stays the root package until item 107, and what stands alone lives in `internal/`
 
 2026-10-05, Lilleman auf Larv. Serves goals 3.2 and 3.4. Two architect reviews found the
-engine's types, `template`, `table`, `arm`, `op`, `nameBinding` and the draw state, bound in
-one cycle because several passes each write part of the same structs; the template
+engine's types, `template`, `table`, `arm`, `op` and `nameBinding`, bound in one cycle because several passes each write part of the same structs; the template
 language's recursion needs only a little of it. Moving the engine before items 101 to 106
 give each value one writer would spread that knot across packages, behind forwarding calls
-from every public method. The grammar, the draw state and the reading of data files read no
-engine type; `DataType`, the proofs' bounds, the builtins and a table's rows stop reading one
-once items 99, 100 and 102 cut their edges, so they move now, each behind an import list a
-test checks. Valid until `todo.md` item 107 moves the engine.
+from every public method. The draw state and `DataType` read no engine type, and `DataType`
+moves with the proofs' bounds keyed by it; the grammar, the reading of data files, the
+proofs' bounds, the builtins and a table's rows stop reading one once items 98 to 103 cut
+their edges, so they move now, each behind an import list a test checks. Valid until `todo.md` item 107 moves the engine.

todo.md

@@ -256,7 +256,7 @@ Needs item 5 to score 7.0 or above, per `AGENTS.md`'s comprehension rule. Goal 1
 
 ### 102. Move a table's rows, with their family, proofs, pins, row draws and lookups, into `internal/rows`, and walk a path through one per-step function that refuses a level carrying a `repeat` in the load check and in `Fake` alike.
 
-Needs items 97 and 101. `internal/rows` owns the parent and child links; the root's table holds `{rows, format, cellTemplates}` and finds its relatives through those links, so the family has one writer and `internal/rows` never sees a template. The lookups keep the weights `sumWeights` parsed, where `builtLookup` parses them again. Today `pathCheck.walk` and `probePath` are two loops over one rule for passing a choice, a table or a field, and they have drifted: `probePath` skips `pathCheck.enter`, so `Fake("x.a")` under `"repeat":3` renders one draw where the README's Correlated fields section refuses it; the refusal owes a `CHANGELOG.md` entry. The shared step takes its state as parameters, as `drawSteps` does: one loop switching on a mode raised a repeat of a reference path from 66 to 106 allocations (decision "A path draws through its compiled steps"). Technical principle: DRY.
+Needs items 98 and 101. `internal/rows` owns the parent and child links, and each rows table carries the engine table holding it as a payload set when it is built, so a step to a relative reaches its format and cells with no side map: the family has one writer, and `internal/rows` never sees a template. The rows code reads `checkName` and the selector spelling from `internal/grammar`. The lookups keep the weights `sumWeights` parsed, where `builtLookup` parses them again. Today `pathCheck.walk` and `probePath` are two loops over one rule for passing a choice, a table or a field, and they have drifted: `probePath` skips `pathCheck.enter`, so `Fake("x.a")` under `"repeat":3` renders one draw where the README's Correlated fields section refuses it; the refusal owes a `CHANGELOG.md` entry. The shared step takes its state as parameters, as `drawSteps` does: one loop switching on a mode raised a repeat of a reference path from 66 to 106 allocations (decision "A path draws through its compiled steps"). Technical principle: DRY.
 
 ### 97. Move the seeded randomness and its `{seq()}` counters into `internal/drawstate`, built from a seed, and test which packages each package may import.
 
@@ -294,7 +294,7 @@ The decision "With only the shipped set, a category loads on the first call reac
 
 ### 99. Move `DataType` into `internal/datatype`, aliased by the root, and what a proof knows of a value, `proven`, into `internal/proven`.
 
-Needs item 98. `proven` is keyed by `DataType`, and a package the root imports cannot import the root, so the type moves first. The root declares `type DataType = datatype.DataType` and its four constants by name, so the public spelling stays one; pkg.go.dev then lists the methods under the internal package, which the maintainer accepted on 2026-10-05. `internal/proven` takes `proven` and the arithmetic over it, `combine`, `bounded`, `printing` and the literal and number readers; proving a node stays with the engine in `valueproof.go`.
+Needs item 98. `proven` is keyed by `DataType`, and a package the root imports cannot import the root, so the type moves first. The root declares `type DataType = datatype.DataType` and its four constants by name, so the public spelling stays one; pkg.go.dev then lists the methods under the internal package, which the maintainer accepted on 2026-10-05. `internal/datatype` takes `dataTypeNames` and `dataTypeNouns` with the type. `internal/proven` takes `proven` and the arithmetic over it, `combine`, `bounded`, `printing`, `shortestDecimals` and the literal and number readers, and imports `internal/grammar` for the `calc` syntax `combine` reads; proving a node stays with the engine in `valueproof.go`.
 
 ### 105. Link each template in steps that each return what they build — its references, its bindings' heads and addressed keys, its compiled arms, its column read — so no step writes into what an earlier one built.