feat(binding-graph): Phase 4 question-target binding (ADR-0135) (#179)

Refines BoundUnknown from "the symbol whose value the solver determines"
to "the symbol at a specific temporal/state index with a specific
question-form". Two new required fields on BoundUnknown — state_index
(initial/terminal/Operation(operation_index)) and question_form
(count/rate/total/difference/ratio/identity) — populated by the new
pure-function resolver in generate/binding_graph/question_target.py.

The adapter (ADR-0133) now delegates Unknown -> BoundUnknown construction
to bound_unknown_from_math_problem_graph. No runtime wiring, no solver
invocation. Phase 5 (bounded-grammar / B3 integration) remains deferred.

Refusal-first via the new QuestionTargetError (sibling of AdapterError /
AdmissibilityError). Closed reason vocab: not_a_math_problem_graph,
unknown_entity_not_in_entities, apply_rate_unit_mismatch,
unmappable_question_form. Closed precedence rule on question_form
documented in ADR-0135 (compare_multiplicative > compare_additive >
apply_rate{numerator|denominator unit-match} > count); ambiguity refuses.

SemanticSymbolicBindingGraph.__post_init__ gains a cross-collection
guard: Operation(operation_index) must satisfy operation_index <
len(equations). canonical_string emission widened to include
state=... form=... tokens (hash differs from Phase 3 main by design —
not a regression; byte-equal across runs preserved).

Parents: ADR-0132 / ADR-0133 / ADR-0134.

Tests: +70 new (45 unit in test_binding_graph_question_target.py +
25 integration in test_binding_graph_adapter_question_target.py); 5
Phase 1+3 BoundUnknown fixtures migrated. Total binding-graph lane
295/1 pass (1 pre-existing test_symbol_binding_uses_slots failure on
Python 3.14, unrelated to Phase 4 — exists on origin/main). Pyright
clean on new and modified files. No edits to algebra/, chat/, core/,
or runtime hot path. Field invariant untouched.

docs/decisions/ADR-0135-binding-graph-question-target.md

@@ -0,0 +1,130 @@
+# ADR-0135 — Binding Graph Phase 4: question-target binding refinement
+
+**Status:** Accepted.
+**Parents:** [ADR-0132](ADR-0132-binding-graph-data-model.md),
+[ADR-0133](ADR-0133-binding-graph-adapter.md),
+[ADR-0134](ADR-0134-binding-graph-admissibility.md).
+**Phase 5 (bounded-grammar / B3 integration):** deferred.
+
+## Context
+
+Phases 1–3 produced a `SemanticSymbolicBindingGraph` containing a
+`BoundUnknown` that named the symbol the question targets — but only
+the symbol *identity*, not its *temporal index* nor the *shape of the
+expected answer*.
+
+For "How many apples does Tina have?" with a three-operation
+trajectory, the adapter's `BoundUnknown` did not distinguish between
+Tina's apples at `t=0`, after the second operation, or at the terminal
+state. Three different symbols, one ambiguous question.
+
+Likewise, "How much faster did Tina run?" and "How many apples does
+Tina have?" both compile down to a `BoundUnknown` pointing at a symbol,
+but the *verdict shape* a downstream consumer should produce
+(`difference` vs. `count`) is qualitatively different.
+
+Phase 4 closes that ambiguity *deterministically* at the binding-graph
+layer, without invoking a solver or grammar.
+
+## Decision
+
+### Two new required fields on `BoundUnknown`
+
+- `state_index: StateIndex` — a closed tagged union:
+  `Literal["initial", "terminal"]` or `Operation(operation_index: int)`,
+  where `Operation` is a frozen dataclass (not a string) so the index
+  is type-checked at construction.
+- `question_form: Literal["count", "rate", "total", "difference",
+  "ratio", "identity"]`.
+
+Both fields are **required** — no defaults. Phase 1–3 fixtures that
+construct `BoundUnknown` directly have been updated in the same PR.
+
+### Pure-function resolvers — `generate/binding_graph/question_target.py`
+
+- `resolve_state_index(g)` — `"terminal"` when `g.operations` is
+  non-empty, `"initial"` otherwise. The `Operation` variant is reserved
+  for future intermediate-state queries; this resolver does not yet
+  produce it.
+- `infer_question_form(g)` — closed dispatch over operations that
+  *touch* the unknown's entity (actor / target / `Comparison`
+  `reference_actor` matches). Precedence rule (deterministic):
+
+  1. No operations touch → `"identity"`.
+  2. Any `compare_multiplicative` touches → `"ratio"`.
+  3. Any `compare_additive` touches → `"difference"`.
+  4. Any `apply_rate` touches → `"total"` when `unknown.unit ==
+     numerator_unit`; `"rate"` when `unknown.unit == denominator_unit`;
+     otherwise refuse (`apply_rate_unit_mismatch`).
+  5. All touching kinds in `{add, subtract, transfer, multiply,
+     divide}` → `"count"`.
+  6. Anything else → refuse (`unmappable_question_form`).
+
+  The precedence is **closed and ordered**, not a heuristic. A graph
+  mixing `compare_additive` with `add` returns `"difference"` because
+  the comparison establishes the question's shape regardless of any
+  downstream arithmetic.
+
+- `bound_unknown_from_math_problem_graph(g)` — composes the above and
+  yields a fully-populated `BoundUnknown`. The adapter (ADR-0133) calls
+  this in place of its old ad-hoc mapping.
+
+### Refusal-first via `QuestionTargetError`
+
+Sibling of `AdapterError` and `AdmissibilityError`. Reasons are a
+closed set:
+
+- `not_a_math_problem_graph`
+- `unknown_entity_not_in_entities`
+- `apply_rate_unit_mismatch`
+- `unmappable_question_form`
+
+The resolver never silently coerces to a default — ambiguity refuses.
+
+### Cross-collection guard
+
+`SemanticSymbolicBindingGraph.__post_init__` adds: if any
+`BoundUnknown.state_index` is an `Operation`, its `operation_index`
+must be `< len(equations)`. Standalone `BoundUnknown` construction
+checks only the sign (`>= 0`).
+
+## Invariants preserved
+
+- `bind_math_problem_graph(g)` remains pure and deterministic.
+  Byte-equal across runs on a given `g`. The canonical-string emission
+  changes shape (now includes `state=…` and `form=…` tokens), so
+  hashes differ from Phase 3 main *by design* — not a regression.
+- No runtime wiring. No solver coupling. No mutation of
+  `MathProblemGraph`. No `algebra/`, `chat/`, `core/` edits.
+- Field-invariant `versor_condition(F) < 1e-6` untouched.
+
+## Phase 5 — deferred
+
+Bounded-grammar / B3 integration remains out of scope. Phase 4 only
+determines *which symbol* the question targets and *what form* the
+answer takes; producing surface verdicts from those signals belongs to
+a later phase.
+
+## Trust boundary
+
+`question_target.py` reads only frozen, validated `MathProblemGraph`
+input. No filesystem access, no dynamic import, no user-controlled
+formatting. All refusals are typed.
+
+## Tests
+
+- `tests/test_binding_graph_question_target.py` — unit-lane (~45 tests):
+  every operation-kind family, precedence rule, refusal paths, typed
+  `Operation` state-index guards.
+- `tests/test_binding_graph_adapter_question_target.py` — integration
+  (~25 tests): adapter round-trip, hash stability, refusal propagation,
+  cross-collection bounds guard.
+- Phase 1+2+3 fixtures updated where they constructed `BoundUnknown`
+  directly (~5 sites).
+
+## References
+
+- ADR-0132 — data model.
+- ADR-0133 — adapter.
+- ADR-0134 — unit-aware admissibility.
+- `generate/math_problem_graph.py` — input shape (ADR-0115).

generate/binding_graph/__init__.py

@@ -1,4 +1,4 @@
-"""ADR-0132/0133 — Semantic-Symbolic Binding Graph.
+"""ADR-0132/0133/0134/0135 — Semantic-Symbolic Binding Graph.
 
 Phase 1 (ADR-0132): pure data layer (frozen dataclasses, deterministic
 allocator, refusal-first construction; no I/O, no parser, no algebra,
@@ -10,8 +10,13 @@ Phase 2 (ADR-0133): pure-function adapter
 :class:`generate.math_problem_graph.MathProblemGraph` (ADR-0115) into a
 :class:`SemanticSymbolicBindingGraph`. Still no runtime wiring.
 
-Phases 3-5 (unit-aware equation binding / question-target binding /
+Phase 3 (ADR-0134): unit-aware admissibility on equations.
-bounded-grammar integration) are deferred to follow-up PRs.
+
+Phase 4 (ADR-0135): question-target binding refinement —
+:class:`BoundUnknown` now carries ``state_index`` + ``question_form``
+fields resolved by :func:`bound_unknown_from_math_problem_graph`.
+
+Phase 5 (bounded-grammar / B3 integration) deferred.
 """
 
 from __future__ import annotations
@@ -32,16 +37,27 @@ from .admissibility import (
 from .allocation import allocate_symbols
 from .model import (
     ADMISSIBILITY_STATUSES,
+    QUESTION_FORMS,
     SEMANTIC_ROLES,
+    STATE_INDEX_LABELS,
     BindingGraphError,
     BoundConstraint,
     BoundEquation,
     BoundFact,
     BoundUnknown,
+    Operation,
     SemanticSymbolicBindingGraph,
     SourceSpanLink,
+    StateIndex,
     SymbolBinding,
 )
+from .question_target import (
+    QUESTION_TARGET_REASONS,
+    QuestionTargetError,
+    bound_unknown_from_math_problem_graph,
+    infer_question_form,
+    resolve_state_index,
+)
 from .units import (
     BASE_DIMENSIONS,
     DIMENSIONLESS,
@@ -60,8 +76,11 @@ __all__ = (
     "BASE_DIMENSIONS",
     "DIMENSIONLESS",
     "INTRODUCED_BY",
+    "QUESTION_FORMS",
+    "QUESTION_TARGET_REASONS",
     "REFUSED_UNIT_PROOF",
     "SEMANTIC_ROLES",
+    "STATE_INDEX_LABELS",
     "SYNTHETIC_SOURCE_ID",
     "AdapterError",
     "AdmissibilityError",
@@ -70,16 +89,22 @@ __all__ = (
     "BoundEquation",
     "BoundFact",
     "BoundUnknown",
+    "Operation",
+    "QuestionTargetError",
     "SemanticSymbolicBindingGraph",
     "SourceSpanLink",
+    "StateIndex",
     "SymbolBinding",
     "UnitAlgebraError",
     "UnitProof",
     "UnitVector",
     "allocate_symbols",
     "bind_math_problem_graph",
+    "bound_unknown_from_math_problem_graph",
     "check_admissibility",
+    "infer_question_form",
     "parse_unit",
+    "resolve_state_index",
     "unit_inverse",
     "unit_product",
     "unit_quotient",

generate/binding_graph/adapter.py

@@ -53,11 +53,11 @@ from .model import (
     BindingGraphError,
     BoundEquation,
     BoundFact,
-    BoundUnknown,
     SemanticSymbolicBindingGraph,
     SourceSpanLink,
     SymbolBinding,
 )
+from .question_target import bound_unknown_from_math_problem_graph
 
 # ---------------------------------------------------------------------------
 # Constants — locked mapping discipline (read these before editing logic).
@@ -126,14 +126,6 @@ def _op_result_symbol_id(idx: int) -> str:
     return f"op_{idx:03d}_result"
 
 
-def _unknown_symbol_id(entity: str | None, unit: str) -> str:
-    scope = _slug(entity) if entity is not None else "total"
-    if scope == "":
-        scope = "total"
-    unit_slug = _slug(unit) or "x"
-    return f"unknown_{scope}_{unit_slug}"
-
-
 def _span(text: str) -> SourceSpanLink:
     """Synthesize a deterministic ``SourceSpanLink`` for ``text``.
 
@@ -424,14 +416,18 @@ def bind_math_problem_graph(
         )
 
     # ---- Unknown → synthesized unknown symbol + BoundUnknown --------------
+    # ADR-0135: ``bound_unknown_from_math_problem_graph`` now owns the
+    # refined ``BoundUnknown`` (symbol_id / question_span / state_index /
+    # question_form / expected_unit). The adapter only retains responsibility
+    # for the matching ``SymbolBinding`` (``semantic_role='unknown'``).
     unk = g.unknown
-    unk_sid = _unknown_symbol_id(unk.entity, unk.unit)
     unk_text = (
         f"{unk.entity}|{unk.unit}" if unk.entity is not None else f"total|{unk.unit}"
     )
+    bound_unknown = bound_unknown_from_math_problem_graph(g)
     _add(
         SymbolBinding(
-            symbol_id=unk_sid,
+            symbol_id=bound_unknown.symbol_id,
             name=unk_text,
             semantic_role="unknown",
             source_span=_span(unk_text),
@@ -440,13 +436,7 @@ def bind_math_problem_graph(
             unit=unk.unit,
         )
     )
-    unknowns = (
+    unknowns = (bound_unknown,)
-        BoundUnknown(
-            symbol_id=unk_sid,
-            question_span=_span(unk_text),
-            expected_unit=unk.unit,
-        ),
-    )
 
     try:
         return SemanticSymbolicBindingGraph(

generate/binding_graph/model.py

@@ -17,7 +17,7 @@ substrate.
 from __future__ import annotations
 
 from dataclasses import dataclass, field
-from typing import Final
+from typing import Final, Literal, Union
 
 # ---------------------------------------------------------------------------
 # Public errors
@@ -56,6 +56,52 @@ ADMISSIBILITY_STATUSES: Final[frozenset[str]] = frozenset(
     {"admitted", "pending", "refused"}
 )
 
+# ADR-0135 — closed ``BoundUnknown.question_form`` vocabulary. Never coerce
+# silently to a default; refuse with ``QuestionTargetError`` on unmappable
+# graph shapes. Extending this set is a future ADR (not a one-liner).
+QUESTION_FORMS: Final[frozenset[str]] = frozenset(
+    {"count", "rate", "total", "difference", "ratio", "identity"}
+)
+
+# ADR-0135 — closed ``BoundUnknown.state_index`` literal labels. The
+# tagged-union ``StateIndex`` (below) is either one of these strings or
+# an :class:`Operation` instance carrying a typed operation index.
+STATE_INDEX_LABELS: Final[frozenset[str]] = frozenset({"initial", "terminal"})
+
+
+@dataclass(frozen=True, slots=True)
+class Operation:
+    """ADR-0135 — state-index variant pointing at a specific operation.
+
+    The ``operation_index`` is type-checked as ``int`` (not ``str``) so
+    typos like ``Operation("3")`` refuse at construction. Cross-collection
+    bounds (``operation_index < graph operation count``) are enforced by
+    :class:`SemanticSymbolicBindingGraph.__post_init__`, not here — at
+    standalone construction we only know the value must be non-negative.
+    """
+
+    operation_index: int
+
+    def __post_init__(self) -> None:
+        if not isinstance(self.operation_index, int) or isinstance(
+            self.operation_index, bool
+        ):
+            raise BindingGraphError(
+                f"Operation.operation_index must be int; "
+                f"got {type(self.operation_index).__name__}"
+            )
+        if self.operation_index < 0:
+            raise BindingGraphError(
+                f"Operation.operation_index must be >= 0; "
+                f"got {self.operation_index}"
+            )
+
+
+# Tagged union for the state at which a :class:`BoundUnknown`'s symbol
+# is observed. ``"initial"`` / ``"terminal"`` collapse to the obvious
+# endpoints; ``Operation`` references a specific intermediate step.
+StateIndex = Union[Literal["initial", "terminal"], Operation]
+
 
 def _require_non_empty_str(value: object, field_name: str) -> None:
     if not isinstance(value, str) or value == "":
@@ -267,10 +313,20 @@ class BoundEquation:
 
 @dataclass(frozen=True, slots=True)
 class BoundUnknown:
-    """The target of the question, bound to a known symbol."""
+    """The target of the question, bound to a known symbol.
+
+    ADR-0135 widens the contract from "the symbol whose value the solver
+    determines" to "the symbol at a specific temporal/state index with a
+    specific question-form". The two new fields are *required* — no
+    defaults — so every construction site declares its intent.
+    """
 
     symbol_id: str
     question_span: SourceSpanLink
+    state_index: "StateIndex"
+    question_form: Literal[
+        "count", "rate", "total", "difference", "ratio", "identity"
+    ]
     expected_unit: str | None = None
 
     def __post_init__(self) -> None:
@@ -284,6 +340,18 @@ class BoundUnknown:
             raise BindingGraphError(
                 "BoundUnknown.question_span must be a SourceSpanLink"
             )
+        if isinstance(self.state_index, Operation):
+            pass  # bounds re-checked by the graph; standalone is sign-only
+        elif self.state_index not in STATE_INDEX_LABELS:
+            raise BindingGraphError(
+                f"BoundUnknown.state_index must be 'initial', 'terminal', or "
+                f"an Operation instance; got {self.state_index!r}"
+            )
+        if self.question_form not in QUESTION_FORMS:
+            raise BindingGraphError(
+                f"BoundUnknown.question_form must be one of "
+                f"{sorted(QUESTION_FORMS)}; got {self.question_form!r}"
+            )
         _require_optional_str(self.expected_unit, "BoundUnknown.expected_unit")
 
 
@@ -396,12 +464,20 @@ class SemanticSymbolicBindingGraph:
                         f"{dep!r} (lhs={eq.lhs_symbol_id!r})"
                     )
 
+        equation_count = len(self.equations)
         for unk in self.unknowns:
             if unk.symbol_id not in known_ids:
                 raise BindingGraphError(
                     f"BoundUnknown references unknown symbol_id "
                     f"{unk.symbol_id!r}"
                 )
+            if isinstance(unk.state_index, Operation):
+                if unk.state_index.operation_index >= equation_count:
+                    raise BindingGraphError(
+                        f"BoundUnknown.state_index.operation_index "
+                        f"{unk.state_index.operation_index} >= equation_count "
+                        f"{equation_count}"
+                    )
 
         for con in self.constraints:
             if con.symbol_id not in known_ids:
@@ -440,8 +516,13 @@ class SemanticSymbolicBindingGraph:
                 f"span={eq.source_span.to_canonical_string()}"
             )
         for unk in self.unknowns:
+            if isinstance(unk.state_index, Operation):
+                state_token = f"op({unk.state_index.operation_index})"
+            else:
+                state_token = unk.state_index
             lines.append(
                 f"U {unk.symbol_id} expected_unit={unk.expected_unit} "
+                f"state={state_token} form={unk.question_form} "
                 f"qspan={unk.question_span.to_canonical_string()}"
             )
         for con in self.constraints:

generate/binding_graph/question_target.py

@@ -0,0 +1,274 @@
+"""ADR-0135 — Question-target binding refinement.
+
+Pure-function resolvers that take a :class:`MathProblemGraph` and produce
+the two new fields ``BoundUnknown`` requires under ADR-0135:
+
+  - :func:`resolve_state_index` — picks the temporal index at which the
+    unknown's symbol is observed. Current rule: ``"terminal"`` when at
+    least one :class:`Operation` exists in the graph, ``"initial"`` when
+    not. The :class:`Operation` (state-index) variant is part of the
+    closed vocabulary but not produced by this resolver yet — it exists
+    so future intermediate-state queries have a typed home.
+
+  - :func:`infer_question_form` — closed dispatch over the operations
+    whose actor / target / reference touches the unknown's entity. The
+    precedence rule (documented in ADR-0135) is deterministic; ambiguous
+    or unmappable shapes refuse with :class:`QuestionTargetError`.
+
+  - :func:`bound_unknown_from_math_problem_graph` — the public entry
+    point the adapter uses. Refusal-first, deterministic, pure.
+
+No I/O. No solver. No mutation. The resolver only determines *which*
+symbol the question targets and *what* form the answer takes.
+"""
+
+from __future__ import annotations
+
+import re
+from typing import Final, Literal
+
+from generate.math_problem_graph import (
+    Comparison,
+    MathProblemGraph,
+    Operation as MathOperation,
+    Rate,
+)
+
+from .model import (
+    BoundUnknown,
+    Operation,
+    SourceSpanLink,
+    StateIndex,
+)
+
+
+# ---------------------------------------------------------------------------
+# Public error
+# ---------------------------------------------------------------------------
+
+
+class QuestionTargetError(ValueError):
+    """Raised when the question-target resolver cannot bind deterministically.
+
+    Sibling of :class:`generate.binding_graph.AdapterError` and
+    :class:`generate.binding_graph.AdmissibilityError`. Always carries a
+    typed ``reason`` token from :data:`QUESTION_TARGET_REASONS`. The
+    resolver never silently picks a default form.
+    """
+
+    def __init__(self, reason: str, *, detail: str = "") -> None:
+        if reason not in QUESTION_TARGET_REASONS:
+            raise ValueError(
+                f"QuestionTargetError.reason must be one of "
+                f"{sorted(QUESTION_TARGET_REASONS)}; got {reason!r}"
+            )
+        self.reason: Final[str] = reason
+        self.detail: Final[str] = detail
+        message = f"{reason}: {detail}" if detail else reason
+        super().__init__(message)
+
+
+QUESTION_TARGET_REASONS: Final[frozenset[str]] = frozenset(
+    {
+        "not_a_math_problem_graph",
+        "unknown_entity_not_in_entities",
+        "unmappable_question_form",
+        "apply_rate_unit_mismatch",
+    }
+)
+
+
+# ---------------------------------------------------------------------------
+# Helpers — naming locked to ``generate.binding_graph.adapter`` conventions.
+# ---------------------------------------------------------------------------
+
+_SLUG_NON_ALNUM = re.compile(r"[^a-z0-9]+")
+
+
+def _slug(text: str) -> str:
+    return _SLUG_NON_ALNUM.sub("_", text.strip().lower()).strip("_")
+
+
+def _unknown_symbol_id(entity: str | None, unit: str) -> str:
+    scope = _slug(entity) if entity is not None else "total"
+    if scope == "":
+        scope = "total"
+    unit_slug = _slug(unit) or "x"
+    return f"unknown_{scope}_{unit_slug}"
+
+
+def _unknown_span(entity: str | None, unit: str) -> SourceSpanLink:
+    text = f"{entity}|{unit}" if entity is not None else f"total|{unit}"
+    return SourceSpanLink(
+        source_id="math_problem_graph", start=0, end=len(text), text=text
+    )
+
+
+def _operation_touches_unknown(
+    op: MathOperation, unk_entity: str | None
+) -> bool:
+    """An operation touches the unknown if its actor / target /
+    comparison reference matches the unknown's entity. When the unknown
+    has no entity (``entity is None``, the "total across all entities"
+    case), every operation is considered to touch it.
+    """
+    if unk_entity is None:
+        return True
+    if op.actor == unk_entity:
+        return True
+    if op.target is not None and op.target == unk_entity:
+        return True
+    if isinstance(op.operand, Comparison):
+        if op.operand.reference_actor == unk_entity:
+            return True
+    return False
+
+
+# ---------------------------------------------------------------------------
+# Public resolvers
+# ---------------------------------------------------------------------------
+
+
+def resolve_state_index(g: object) -> StateIndex:
+    """Pick the temporal index at which the unknown is observed.
+
+    Closed rule: ``"terminal"`` when the graph has at least one
+    operation, ``"initial"`` when not. The :class:`Operation` variant of
+    :data:`StateIndex` is part of the public vocabulary so future
+    intermediate-state queries have a typed home, but this resolver
+    never returns it today.
+    """
+    if not isinstance(g, MathProblemGraph):
+        raise QuestionTargetError(
+            "not_a_math_problem_graph",
+            detail=f"got {type(g).__name__}",
+        )
+    if g.operations:
+        return "terminal"
+    return "initial"
+
+
+_COUNT_KINDS: Final[frozenset[str]] = frozenset(
+    {"add", "subtract", "transfer", "multiply", "divide"}
+)
+
+
+def infer_question_form(
+    g: object,
+) -> Literal["count", "rate", "total", "difference", "ratio", "identity"]:
+    """Closed-vocab dispatch on operation kinds touching the unknown.
+
+    Precedence (deterministic; documented in ADR-0135). Evaluate in
+    order, return on first match:
+
+      1. No operations touch the unknown's entity → ``"identity"``.
+      2. Any ``compare_multiplicative`` touches → ``"ratio"``.
+      3. Any ``compare_additive`` touches → ``"difference"``.
+      4. Any ``apply_rate`` touches → ``"total"`` when the unknown's
+         unit matches the rate's ``numerator_unit``; ``"rate"`` when it
+         matches the ``denominator_unit``. Otherwise refuse
+         (``apply_rate_unit_mismatch``).
+      5. Every touching operation is in ``{add, subtract, transfer,
+         multiply, divide}`` → ``"count"``.
+      6. Anything else → refuse (``unmappable_question_form``).
+
+    The precedence order resolves ambiguity: a graph mixing
+    ``compare_additive`` with ``add`` returns ``"difference"`` because
+    the comparison establishes the question's shape regardless of any
+    downstream arithmetic. This is a closed rule, not a heuristic.
+    """
+    if not isinstance(g, MathProblemGraph):
+        raise QuestionTargetError(
+            "not_a_math_problem_graph",
+            detail=f"got {type(g).__name__}",
+        )
+
+    unk_entity = g.unknown.entity
+    if unk_entity is not None and unk_entity not in g.entities:
+        # MathProblemGraph already enforces this invariant, but defensive
+        # restatement keeps the resolver self-contained.
+        raise QuestionTargetError(
+            "unknown_entity_not_in_entities",
+            detail=f"entity={unk_entity!r}",
+        )
+
+    touching: tuple[MathOperation, ...] = tuple(
+        op for op in g.operations if _operation_touches_unknown(op, unk_entity)
+    )
+
+    if not touching:
+        return "identity"
+
+    kinds = {op.kind for op in touching}
+
+    if "compare_multiplicative" in kinds:
+        return "ratio"
+    if "compare_additive" in kinds:
+        return "difference"
+
+    if "apply_rate" in kinds:
+        unk_unit = g.unknown.unit
+        for op in touching:
+            if op.kind == "apply_rate" and isinstance(op.operand, Rate):
+                if unk_unit == op.operand.numerator_unit:
+                    return "total"
+                if unk_unit == op.operand.denominator_unit:
+                    return "rate"
+        raise QuestionTargetError(
+            "apply_rate_unit_mismatch",
+            detail=(
+                f"unknown.unit={unk_unit!r} matches neither numerator nor "
+                f"denominator of any touching apply_rate"
+            ),
+        )
+
+    if kinds.issubset(_COUNT_KINDS):
+        return "count"
+
+    raise QuestionTargetError(
+        "unmappable_question_form",
+        detail=f"touching kinds={sorted(kinds)!r}",
+    )
+
+
+def bound_unknown_from_math_problem_graph(g: object) -> BoundUnknown:
+    """Build the refined :class:`BoundUnknown` for ``g``.
+
+    The adapter (ADR-0133) calls this in place of its old ad-hoc
+    ``Unknown → BoundUnknown`` mapping. Determinism: identical ``g``
+    yields a byte-equal :class:`BoundUnknown`. Refusal-first: any
+    :class:`QuestionTargetError` from the sub-resolvers propagates.
+
+    The synthesized ``symbol_id`` / ``question_span`` mirror the
+    adapter's pre-ADR-0135 convention exactly, so the symbol map in the
+    surrounding binding graph remains the same shape.
+    """
+    if not isinstance(g, MathProblemGraph):
+        raise QuestionTargetError(
+            "not_a_math_problem_graph",
+            detail=f"got {type(g).__name__}",
+        )
+    unk = g.unknown
+    state_index = resolve_state_index(g)
+    question_form = infer_question_form(g)
+    sid = _unknown_symbol_id(unk.entity, unk.unit)
+    span = _unknown_span(unk.entity, unk.unit)
+    return BoundUnknown(
+        symbol_id=sid,
+        question_span=span,
+        state_index=state_index,
+        question_form=question_form,
+        expected_unit=unk.unit,
+    )
+
+
+# Re-export ``Operation`` so callers do not need to thread the model
+# import separately just to construct the state-index variant.
+__all__ = (
+    "QUESTION_TARGET_REASONS",
+    "Operation",
+    "QuestionTargetError",
+    "bound_unknown_from_math_problem_graph",
+    "infer_question_form",
+    "resolve_state_index",
+)

tests/test_binding_graph_adapter_question_target.py

@@ -0,0 +1,446 @@
+"""ADR-0135 — Adapter integration tests for question-target binding.
+
+Covers:
+  - the adapter consumes ``bound_unknown_from_math_problem_graph`` and
+    emits a single :class:`BoundUnknown` per graph with populated
+    ``state_index`` + ``question_form`` fields;
+  - byte-equal hash-stability across runs survives the Phase-4 wiring
+    (Phase 2 invariant — value may differ from Phase 3 main, by design);
+  - every Phase-2 / Phase-3 round-trip case still produces a
+    well-formed binding graph;
+  - intentionally-ambiguous inputs surface ``QuestionTargetError``
+    (resolver refusal) — not silent coercion;
+  - cross-collection invariant guards against bogus ``Operation``
+    state-index pointing past ``len(equations)``.
+"""
+
+from __future__ import annotations
+
+import hashlib
+
+import pytest
+
+from generate.binding_graph import (
+    BindingGraphError,
+    BoundEquation,
+    BoundFact,
+    BoundUnknown,
+    Operation as StateIndexOperation,
+    QuestionTargetError,
+    SemanticSymbolicBindingGraph,
+    SourceSpanLink,
+    SymbolBinding,
+    bind_math_problem_graph,
+)
+from generate.math_problem_graph import (
+    Comparison,
+    InitialPossession,
+    MathProblemGraph,
+    Operation,
+    Quantity,
+    Rate,
+    Unknown,
+)
+
+
+# ---------------------------------------------------------------------------
+# Builders
+# ---------------------------------------------------------------------------
+
+
+def _g(
+    *,
+    entities: tuple[str, ...] = ("Tina",),
+    initial_state: tuple[InitialPossession, ...] = (
+        InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+    ),
+    operations: tuple[Operation, ...] = (),
+    unknown: Unknown = Unknown(entity="Tina", unit="apples"),
+) -> MathProblemGraph:
+    return MathProblemGraph(
+        entities=entities,
+        initial_state=initial_state,
+        operations=operations,
+        unknown=unknown,
+    )
+
+
+def _add(actor: str, n: int, unit: str = "apples") -> Operation:
+    return Operation(actor=actor, kind="add", operand=Quantity(n, unit))
+
+
+def _rate_op(actor: str, value: float, num: str, denom: str) -> Operation:
+    return Operation(
+        actor=actor,
+        kind="apply_rate",
+        operand=Rate(value=value, numerator_unit=num, denominator_unit=denom),
+    )
+
+
+def _cmp_add(actor: str, ref: str, delta: int, unit: str = "apples") -> Operation:
+    return Operation(
+        actor=actor,
+        kind="compare_additive",
+        operand=Comparison(
+            reference_actor=ref,
+            delta=Quantity(delta, unit),
+            factor=None,
+            direction="more",
+        ),
+    )
+
+
+def _cmp_mul(actor: str, ref: str, factor: float) -> Operation:
+    return Operation(
+        actor=actor,
+        kind="compare_multiplicative",
+        operand=Comparison(
+            reference_actor=ref, delta=None, factor=factor, direction="times"
+        ),
+    )
+
+
+# ---------------------------------------------------------------------------
+# Smoke: every Phase-2 round-trip case still emits a well-formed graph
+# ---------------------------------------------------------------------------
+
+
+def test_adapter_emits_single_bound_unknown() -> None:
+    bg = bind_math_problem_graph(_g(operations=(_add("Tina", 2),)))
+    assert len(bg.unknowns) == 1
+
+
+def test_adapter_bound_unknown_terminal_count() -> None:
+    bg = bind_math_problem_graph(_g(operations=(_add("Tina", 2),)))
+    bu = bg.unknowns[0]
+    assert bu.state_index == "terminal"
+    assert bu.question_form == "count"
+    assert bu.expected_unit == "apples"
+
+
+def test_adapter_bound_unknown_initial_identity() -> None:
+    bg = bind_math_problem_graph(_g(operations=()))
+    bu = bg.unknowns[0]
+    assert bu.state_index == "initial"
+    assert bu.question_form == "identity"
+
+
+def test_adapter_bound_unknown_total_via_apply_rate() -> None:
+    g = _g(
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(8, "hours")),
+        ),
+        operations=(_rate_op("Tina", 12.5, "dollars", "hours"),),
+        unknown=Unknown(entity="Tina", unit="dollars"),
+    )
+    bg = bind_math_problem_graph(g)
+    assert bg.unknowns[0].question_form == "total"
+
+
+def test_adapter_bound_unknown_rate_via_apply_rate() -> None:
+    g = _g(
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(8, "hours")),
+        ),
+        operations=(_rate_op("Tina", 12.5, "dollars", "hours"),),
+        unknown=Unknown(entity="Tina", unit="hours"),
+    )
+    bg = bind_math_problem_graph(g)
+    assert bg.unknowns[0].question_form == "rate"
+
+
+def test_adapter_bound_unknown_difference() -> None:
+    g = _g(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_cmp_add("Tina", "Sam", 2),),
+    )
+    bg = bind_math_problem_graph(g)
+    assert bg.unknowns[0].question_form == "difference"
+
+
+def test_adapter_bound_unknown_ratio() -> None:
+    g = _g(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_cmp_mul("Tina", "Sam", 2.0),),
+    )
+    bg = bind_math_problem_graph(g)
+    assert bg.unknowns[0].question_form == "ratio"
+
+
+# ---------------------------------------------------------------------------
+# Hash-stability: byte-equal across runs (Phase 2 invariant)
+# ---------------------------------------------------------------------------
+
+
+def _digest(bg: SemanticSymbolicBindingGraph) -> str:
+    return hashlib.sha256(bg.to_canonical_string().encode("utf-8")).hexdigest()
+
+
+def test_byte_equal_across_runs_count() -> None:
+    g = _g(operations=(_add("Tina", 2), _add("Tina", 3)))
+    a = bind_math_problem_graph(g)
+    b = bind_math_problem_graph(g)
+    assert a.to_canonical_string() == b.to_canonical_string()
+    assert _digest(a) == _digest(b)
+
+
+def test_byte_equal_across_runs_identity() -> None:
+    g = _g(operations=())
+    a = bind_math_problem_graph(g)
+    b = bind_math_problem_graph(g)
+    assert a.to_canonical_string() == b.to_canonical_string()
+
+
+def test_byte_equal_across_runs_difference() -> None:
+    g = _g(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_cmp_add("Tina", "Sam", 2),),
+    )
+    assert bind_math_problem_graph(g).to_canonical_string() == bind_math_problem_graph(
+        g
+    ).to_canonical_string()
+
+
+def test_canonical_string_mentions_state_and_form() -> None:
+    bg = bind_math_problem_graph(_g(operations=(_add("Tina", 2),)))
+    s = bg.to_canonical_string()
+    assert "state=terminal" in s
+    assert "form=count" in s
+
+
+def test_canonical_string_identity_form() -> None:
+    bg = bind_math_problem_graph(_g(operations=()))
+    s = bg.to_canonical_string()
+    assert "state=initial" in s
+    assert "form=identity" in s
+
+
+# ---------------------------------------------------------------------------
+# Refusal-first propagation: resolver refusals surface to caller
+# ---------------------------------------------------------------------------
+
+
+def test_adapter_propagates_apply_rate_unit_mismatch() -> None:
+    g = _g(
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(8, "hours")),
+        ),
+        operations=(_rate_op("Tina", 12.5, num="dollars", denom="hours"),),
+        unknown=Unknown(entity="Tina", unit="apples"),
+    )
+    with pytest.raises(QuestionTargetError) as exc:
+        bind_math_problem_graph(g)
+    assert exc.value.reason == "apply_rate_unit_mismatch"
+
+
+# ---------------------------------------------------------------------------
+# Cross-collection guard: Operation(operation_index) out of bounds
+# ---------------------------------------------------------------------------
+
+
+def _span(text: str = "x") -> SourceSpanLink:
+    return SourceSpanLink(source_id="t", start=0, end=len(text), text=text)
+
+
+def test_graph_refuses_operation_state_index_out_of_bounds() -> None:
+    # Construct a manual graph: 1 equation (so equation_count == 1), but
+    # the BoundUnknown points to Operation(operation_index=5) → refuse.
+    lhs = "op_000_result"
+    sym_q = SymbolBinding(
+        symbol_id="q_x_apples_t0",
+        name="x@t0",
+        semantic_role="quantity",
+        source_span=_span(),
+        introduced_by="test",
+        entity="x",
+        unit="apples",
+    )
+    sym_r = SymbolBinding(
+        symbol_id=lhs,
+        name="r",
+        semantic_role="quantity",
+        source_span=_span(),
+        introduced_by="test",
+        entity="x",
+    )
+    sym_u = SymbolBinding(
+        symbol_id="unknown_x_apples",
+        name="u",
+        semantic_role="unknown",
+        source_span=_span(),
+        introduced_by="test",
+        entity="x",
+        unit="apples",
+    )
+    fact = BoundFact(
+        symbol_id="q_x_apples_t0", value="5", source_span=_span(), unit="apples"
+    )
+    eq = BoundEquation(
+        lhs_symbol_id=lhs,
+        rhs_canonical="add(x, 2 apples)",
+        dependencies=frozenset({"q_x_apples_t0"}),
+        operation_kind="add",
+        unit_proof="apples",
+        admissibility_status="admitted",
+        source_span=_span(),
+    )
+    bu = BoundUnknown(
+        symbol_id="unknown_x_apples",
+        question_span=_span(),
+        state_index=StateIndexOperation(operation_index=5),
+        question_form="count",
+    )
+    with pytest.raises(BindingGraphError):
+        SemanticSymbolicBindingGraph(
+            symbols=(sym_q, sym_r, sym_u),
+            facts=(fact,),
+            equations=(eq,),
+            unknowns=(bu,),
+        )
+
+
+def test_graph_accepts_operation_state_index_within_bounds() -> None:
+    # Same shape, but operation_index=0 is within bounds (equation_count==1).
+    lhs = "op_000_result"
+    sym_q = SymbolBinding(
+        symbol_id="q_x_apples_t0",
+        name="x@t0",
+        semantic_role="quantity",
+        source_span=_span(),
+        introduced_by="test",
+        entity="x",
+        unit="apples",
+    )
+    sym_r = SymbolBinding(
+        symbol_id=lhs,
+        name="r",
+        semantic_role="quantity",
+        source_span=_span(),
+        introduced_by="test",
+        entity="x",
+    )
+    sym_u = SymbolBinding(
+        symbol_id="unknown_x_apples",
+        name="u",
+        semantic_role="unknown",
+        source_span=_span(),
+        introduced_by="test",
+        entity="x",
+        unit="apples",
+    )
+    fact = BoundFact(
+        symbol_id="q_x_apples_t0", value="5", source_span=_span(), unit="apples"
+    )
+    eq = BoundEquation(
+        lhs_symbol_id=lhs,
+        rhs_canonical="add(x, 2 apples)",
+        dependencies=frozenset({"q_x_apples_t0"}),
+        operation_kind="add",
+        unit_proof="apples",
+        admissibility_status="admitted",
+        source_span=_span(),
+    )
+    bu = BoundUnknown(
+        symbol_id="unknown_x_apples",
+        question_span=_span(),
+        state_index=StateIndexOperation(operation_index=0),
+        question_form="count",
+    )
+    bg = SemanticSymbolicBindingGraph(
+        symbols=(sym_q, sym_r, sym_u),
+        facts=(fact,),
+        equations=(eq,),
+        unknowns=(bu,),
+    )
+    assert bg.unknowns[0].state_index == StateIndexOperation(operation_index=0)
+
+
+# ---------------------------------------------------------------------------
+# MathProblemGraph is read-only (frozen) — assert in test as brief requires
+# ---------------------------------------------------------------------------
+
+
+def test_adapter_does_not_mutate_input_graph() -> None:
+    g = _g(operations=(_add("Tina", 2),))
+    before = g.canonical_bytes()
+    _ = bind_math_problem_graph(g)
+    after = g.canonical_bytes()
+    assert before == after
+
+
+def test_math_problem_graph_is_frozen() -> None:
+    g = _g()
+    with pytest.raises((AttributeError, Exception)):
+        g.unknown = Unknown(entity="Tina", unit="apples")  # type: ignore[misc]
+
+
+# ---------------------------------------------------------------------------
+# Symbol binding for the unknown still emitted (Phase 2 invariant)
+# ---------------------------------------------------------------------------
+
+
+def test_unknown_symbol_binding_still_emitted() -> None:
+    bg = bind_math_problem_graph(_g(operations=(_add("Tina", 2),)))
+    unk_syms = [s for s in bg.symbols if s.semantic_role == "unknown"]
+    assert len(unk_syms) == 1
+    assert unk_syms[0].symbol_id == "unknown_tina_apples"
+    assert unk_syms[0].entity == "Tina"
+    assert unk_syms[0].unit == "apples"
+
+
+def test_unknown_symbol_id_matches_bound_unknown() -> None:
+    bg = bind_math_problem_graph(_g(operations=(_add("Tina", 2),)))
+    unk_sym = next(s for s in bg.symbols if s.semantic_role == "unknown")
+    assert unk_sym.symbol_id == bg.unknowns[0].symbol_id
+
+
+# ---------------------------------------------------------------------------
+# Parametric: question_form is one of the closed vocabulary on smoke graphs
+# ---------------------------------------------------------------------------
+
+
+@pytest.mark.parametrize(
+    "ops, expected_form",
+    [
+        ((), "identity"),
+        ((_add("Tina", 1),), "count"),
+        (
+            (
+                Operation(actor="Tina", kind="subtract", operand=Quantity(1, "apples")),
+            ),
+            "count",
+        ),
+        (
+            (
+                Operation(actor="Tina", kind="multiply", operand=Quantity(3, "apples")),
+            ),
+            "count",
+        ),
+        (
+            (
+                Operation(actor="Tina", kind="divide", operand=Quantity(2, "apples")),
+            ),
+            "count",
+        ),
+    ],
+)
+def test_adapter_form_table(ops, expected_form) -> None:
+    bg = bind_math_problem_graph(_g(operations=ops))
+    assert bg.unknowns[0].question_form == expected_form
+
+
+def test_adapter_bound_unknown_is_instance() -> None:
+    bg = bind_math_problem_graph(_g(operations=(_add("Tina", 1),)))
+    assert isinstance(bg.unknowns[0], BoundUnknown)

tests/test_binding_graph_model.py

@@ -298,19 +298,33 @@ def test_bound_equation_is_frozen() -> None:
 
 def test_bound_unknown_construction() -> None:
     unk = BoundUnknown(
-        symbol_id="sym_y_000", question_span=_span(), expected_unit="dollars"
+        symbol_id="sym_y_000",
+        question_span=_span(),
+        state_index="terminal",
+        question_form="count",
+        expected_unit="dollars",
     )
     assert unk.expected_unit == "dollars"
 
 
 def test_bound_unknown_refuses_bad_id() -> None:
     with pytest.raises(BindingGraphError):
-        BoundUnknown(symbol_id="bad id", question_span=_span())
+        BoundUnknown(
+            symbol_id="bad id",
+            question_span=_span(),
+            state_index="terminal",
+            question_form="count",
+        )
 
 
 def test_bound_unknown_refuses_non_span_question() -> None:
     with pytest.raises(BindingGraphError):
-        BoundUnknown(symbol_id="sym_y_000", question_span="text")  # type: ignore[arg-type]
+        BoundUnknown(
+            symbol_id="sym_y_000",
+            question_span="text",  # type: ignore[arg-type]
+            state_index="terminal",
+            question_form="count",
+        )
 
 
 # ---------------------------------------------------------------------------
@@ -380,7 +394,12 @@ def test_graph_rejects_equation_with_unknown_dependency() -> None:
 
 
 def test_graph_rejects_unknown_referencing_missing_symbol() -> None:
-    unk = BoundUnknown(symbol_id="sym_ghost_000", question_span=_span())
+    unk = BoundUnknown(
+        symbol_id="sym_ghost_000",
+        question_span=_span(),
+        state_index="terminal",
+        question_form="count",
+    )
     with pytest.raises(BindingGraphError):
         SemanticSymbolicBindingGraph(symbols=(_sym(),), unknowns=(unk,))
 
@@ -402,7 +421,14 @@ def test_graph_full_round_trip_canonical_string_stable() -> None:
         BoundFact(symbol_id="sym_x_000", value="5", source_span=_span(), unit="apples"),
     )
     eqs = (_eq(),)
-    unks = (BoundUnknown(symbol_id="sym_y_000", question_span=_span()),)
+    unks = (
+        BoundUnknown(
+            symbol_id="sym_y_000",
+            question_span=_span(),
+            state_index="terminal",
+            question_form="count",
+        ),
+    )
     cons = (
         BoundConstraint(symbol_id="sym_x_000", predicate="x >= 0", source_span=_span()),
     )

tests/test_binding_graph_question_target.py

@@ -0,0 +1,550 @@
+"""ADR-0135 — Tests for the question-target resolver.
+
+Covers:
+  - ``resolve_state_index`` boundary cases (0 / 1 / many operations);
+  - ``infer_question_form`` for every operation-kind family;
+  - precedence rule on mixed-kind graphs;
+  - refusal-first ``QuestionTargetError`` paths;
+  - ``bound_unknown_from_math_problem_graph`` deterministic shape;
+  - typed ``Operation`` (state-index variant) construction guards.
+
+Pure unit lane — adapter integration lives in
+``test_binding_graph_adapter_question_target.py``.
+"""
+
+from __future__ import annotations
+
+import pytest
+
+from generate.binding_graph import (
+    BindingGraphError,
+    BoundUnknown,
+    Operation as StateIndexOperation,
+    QUESTION_FORMS,
+    QUESTION_TARGET_REASONS,
+    QuestionTargetError,
+    STATE_INDEX_LABELS,
+    bound_unknown_from_math_problem_graph,
+    infer_question_form,
+    resolve_state_index,
+)
+from generate.math_problem_graph import (
+    Comparison,
+    InitialPossession,
+    MathProblemGraph,
+    Operation,
+    Quantity,
+    Rate,
+    Unknown,
+)
+
+
+# ---------------------------------------------------------------------------
+# Fixture builders
+# ---------------------------------------------------------------------------
+
+
+def _graph(
+    *,
+    entities: tuple[str, ...] = ("Tina",),
+    initial_state: tuple[InitialPossession, ...] = (
+        InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+    ),
+    operations: tuple[Operation, ...] = (),
+    unknown: Unknown = Unknown(entity="Tina", unit="apples"),
+) -> MathProblemGraph:
+    return MathProblemGraph(
+        entities=entities,
+        initial_state=initial_state,
+        operations=operations,
+        unknown=unknown,
+    )
+
+
+def _add(actor: str, n: int, unit: str = "apples") -> Operation:
+    return Operation(actor=actor, kind="add", operand=Quantity(n, unit))
+
+
+def _sub(actor: str, n: int, unit: str = "apples") -> Operation:
+    return Operation(actor=actor, kind="subtract", operand=Quantity(n, unit))
+
+
+def _transfer(actor: str, target: str, n: int, unit: str = "apples") -> Operation:
+    return Operation(
+        actor=actor, kind="transfer", operand=Quantity(n, unit), target=target
+    )
+
+
+def _mul(actor: str, n: int, unit: str = "apples") -> Operation:
+    return Operation(actor=actor, kind="multiply", operand=Quantity(n, unit))
+
+
+def _div(actor: str, n: int, unit: str = "apples") -> Operation:
+    return Operation(actor=actor, kind="divide", operand=Quantity(n, unit))
+
+
+def _rate_op(
+    actor: str, value: float, num: str, denom: str
+) -> Operation:
+    return Operation(
+        actor=actor,
+        kind="apply_rate",
+        operand=Rate(value=value, numerator_unit=num, denominator_unit=denom),
+    )
+
+
+def _cmp_add(
+    actor: str, ref: str, delta: int, unit: str = "apples", direction: str = "more"
+) -> Operation:
+    return Operation(
+        actor=actor,
+        kind="compare_additive",
+        operand=Comparison(
+            reference_actor=ref,
+            delta=Quantity(delta, unit),
+            factor=None,
+            direction=direction,  # type: ignore[arg-type]
+        ),
+    )
+
+
+def _cmp_mul(
+    actor: str, ref: str, factor: float, direction: str = "times"
+) -> Operation:
+    return Operation(
+        actor=actor,
+        kind="compare_multiplicative",
+        operand=Comparison(
+            reference_actor=ref,
+            delta=None,
+            factor=factor,
+            direction=direction,  # type: ignore[arg-type]
+        ),
+    )
+
+
+# ---------------------------------------------------------------------------
+# StateIndex / Operation dataclass guards
+# ---------------------------------------------------------------------------
+
+
+def test_operation_state_index_construction() -> None:
+    op = StateIndexOperation(operation_index=3)
+    assert op.operation_index == 3
+
+
+def test_operation_state_index_refuses_negative() -> None:
+    with pytest.raises(BindingGraphError):
+        StateIndexOperation(operation_index=-1)
+
+
+def test_operation_state_index_refuses_bool() -> None:
+    with pytest.raises(BindingGraphError):
+        StateIndexOperation(operation_index=True)  # type: ignore[arg-type]
+
+
+def test_operation_state_index_refuses_string() -> None:
+    with pytest.raises(BindingGraphError):
+        StateIndexOperation(operation_index="3")  # type: ignore[arg-type]
+
+
+def test_state_index_labels_locked() -> None:
+    assert STATE_INDEX_LABELS == frozenset({"initial", "terminal"})
+
+
+def test_question_forms_locked() -> None:
+    assert QUESTION_FORMS == frozenset(
+        {"count", "rate", "total", "difference", "ratio", "identity"}
+    )
+
+
+# ---------------------------------------------------------------------------
+# resolve_state_index
+# ---------------------------------------------------------------------------
+
+
+def test_resolve_state_index_no_operations_is_initial() -> None:
+    g = _graph(operations=())
+    assert resolve_state_index(g) == "initial"
+
+
+def test_resolve_state_index_one_operation_is_terminal() -> None:
+    g = _graph(operations=(_add("Tina", 2),))
+    assert resolve_state_index(g) == "terminal"
+
+
+def test_resolve_state_index_many_operations_is_terminal() -> None:
+    g = _graph(
+        operations=tuple(_add("Tina", n) for n in (1, 2, 3, 4, 5)),
+    )
+    assert resolve_state_index(g) == "terminal"
+
+
+def test_resolve_state_index_refuses_non_graph() -> None:
+    with pytest.raises(QuestionTargetError) as exc:
+        resolve_state_index({"entities": ["Tina"]})
+    assert exc.value.reason == "not_a_math_problem_graph"
+
+
+def test_resolve_state_index_deterministic() -> None:
+    g = _graph(operations=(_add("Tina", 2), _sub("Tina", 1)))
+    assert resolve_state_index(g) == resolve_state_index(g)
+
+
+# ---------------------------------------------------------------------------
+# infer_question_form — single-kind families
+# ---------------------------------------------------------------------------
+
+
+def test_infer_count_pure_add() -> None:
+    g = _graph(operations=(_add("Tina", 2), _add("Tina", 3)))
+    assert infer_question_form(g) == "count"
+
+
+def test_infer_count_pure_subtract() -> None:
+    g = _graph(operations=(_sub("Tina", 2),))
+    assert infer_question_form(g) == "count"
+
+
+def test_infer_count_pure_transfer() -> None:
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_transfer("Tina", "Sam", 2),),
+    )
+    assert infer_question_form(g) == "count"
+
+
+def test_infer_count_multiply() -> None:
+    g = _graph(operations=(_mul("Tina", 3),))
+    assert infer_question_form(g) == "count"
+
+
+def test_infer_count_divide() -> None:
+    g = _graph(operations=(_div("Tina", 5),))
+    assert infer_question_form(g) == "count"
+
+
+def test_infer_count_mixed_arithmetic() -> None:
+    g = _graph(
+        operations=(_add("Tina", 4), _sub("Tina", 1), _mul("Tina", 2)),
+    )
+    assert infer_question_form(g) == "count"
+
+
+def test_infer_difference_compare_additive() -> None:
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_cmp_add("Tina", "Sam", 2),),
+    )
+    assert infer_question_form(g) == "difference"
+
+
+def test_infer_ratio_compare_multiplicative() -> None:
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_cmp_mul("Tina", "Sam", 2.0),),
+    )
+    assert infer_question_form(g) == "ratio"
+
+
+def test_infer_total_apply_rate_unknown_is_numerator() -> None:
+    # "How many dollars does Tina earn?" — apply_rate consumes hours,
+    # produces dollars. Unknown.unit == numerator_unit ⇒ total.
+    g = _graph(
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(8, "hours")),
+        ),
+        operations=(_rate_op("Tina", 12.5, num="dollars", denom="hours"),),
+        unknown=Unknown(entity="Tina", unit="dollars"),
+    )
+    assert infer_question_form(g) == "total"
+
+
+def test_infer_rate_apply_rate_unknown_is_denominator() -> None:
+    # Unknown.unit == denominator_unit ⇒ rate.
+    g = _graph(
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(8, "hours")),
+        ),
+        operations=(_rate_op("Tina", 12.5, num="dollars", denom="hours"),),
+        unknown=Unknown(entity="Tina", unit="hours"),
+    )
+    assert infer_question_form(g) == "rate"
+
+
+def test_infer_identity_no_operations() -> None:
+    g = _graph(operations=())
+    assert infer_question_form(g) == "identity"
+
+
+def test_infer_identity_when_no_operation_touches_unknown_entity() -> None:
+    # Tina is in entities (has initial possession) but the only operation
+    # belongs to Sam → no touching op → identity.
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_add("Sam", 2),),
+        unknown=Unknown(entity="Tina", unit="apples"),
+    )
+    assert infer_question_form(g) == "identity"
+
+
+# ---------------------------------------------------------------------------
+# infer_question_form — precedence on mixed kinds
+# ---------------------------------------------------------------------------
+
+
+def test_precedence_compare_multiplicative_beats_additive() -> None:
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(
+            _cmp_add("Tina", "Sam", 2),
+            _cmp_mul("Tina", "Sam", 2.0),
+        ),
+    )
+    assert infer_question_form(g) == "ratio"
+
+
+def test_precedence_compare_additive_beats_count() -> None:
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(
+            _add("Tina", 4),
+            _cmp_add("Tina", "Sam", 2),
+        ),
+    )
+    assert infer_question_form(g) == "difference"
+
+
+def test_precedence_compare_beats_apply_rate() -> None:
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(8, "hours")),
+            InitialPossession(entity="Sam", quantity=Quantity(4, "hours")),
+        ),
+        operations=(
+            _rate_op("Tina", 12.5, "dollars", "hours"),
+            _cmp_add("Tina", "Sam", 2, unit="hours"),
+        ),
+        unknown=Unknown(entity="Tina", unit="hours"),
+    )
+    assert infer_question_form(g) == "difference"
+
+
+def test_precedence_apply_rate_beats_count() -> None:
+    g = _graph(
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(8, "hours")),
+        ),
+        operations=(
+            _add("Tina", 1, unit="hours"),
+            _rate_op("Tina", 12.5, "dollars", "hours"),
+        ),
+        unknown=Unknown(entity="Tina", unit="dollars"),
+    )
+    assert infer_question_form(g) == "total"
+
+
+# ---------------------------------------------------------------------------
+# infer_question_form — refusals
+# ---------------------------------------------------------------------------
+
+
+def test_apply_rate_unit_mismatch_refuses() -> None:
+    # Unknown unit matches neither numerator nor denominator of any
+    # touching apply_rate → typed refusal.
+    g = _graph(
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(8, "hours")),
+        ),
+        operations=(_rate_op("Tina", 12.5, num="dollars", denom="hours"),),
+        unknown=Unknown(entity="Tina", unit="apples"),
+    )
+    with pytest.raises(QuestionTargetError) as exc:
+        infer_question_form(g)
+    assert exc.value.reason == "apply_rate_unit_mismatch"
+
+
+def test_infer_refuses_non_graph_input() -> None:
+    with pytest.raises(QuestionTargetError) as exc:
+        infer_question_form(object())
+    assert exc.value.reason == "not_a_math_problem_graph"
+
+
+def test_question_target_reasons_locked() -> None:
+    assert QUESTION_TARGET_REASONS == frozenset(
+        {
+            "not_a_math_problem_graph",
+            "unknown_entity_not_in_entities",
+            "unmappable_question_form",
+            "apply_rate_unit_mismatch",
+        }
+    )
+
+
+def test_question_target_error_refuses_unknown_reason() -> None:
+    with pytest.raises(ValueError):
+        QuestionTargetError("nonexistent_reason")
+
+
+def test_question_target_error_carries_typed_reason() -> None:
+    exc = QuestionTargetError("unmappable_question_form", detail="weird shape")
+    assert exc.reason == "unmappable_question_form"
+    assert "weird shape" in str(exc)
+
+
+# ---------------------------------------------------------------------------
+# bound_unknown_from_math_problem_graph
+# ---------------------------------------------------------------------------
+
+
+def test_bound_unknown_terminal_count() -> None:
+    g = _graph(operations=(_add("Tina", 2),))
+    bu = bound_unknown_from_math_problem_graph(g)
+    assert isinstance(bu, BoundUnknown)
+    assert bu.symbol_id == "unknown_tina_apples"
+    assert bu.state_index == "terminal"
+    assert bu.question_form == "count"
+    assert bu.expected_unit == "apples"
+
+
+def test_bound_unknown_initial_identity_no_ops() -> None:
+    g = _graph(operations=())
+    bu = bound_unknown_from_math_problem_graph(g)
+    assert bu.state_index == "initial"
+    assert bu.question_form == "identity"
+
+
+def test_bound_unknown_total_unknown_entity_none() -> None:
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_add("Tina", 2), _sub("Sam", 1)),
+        unknown=Unknown(entity=None, unit="apples"),
+    )
+    bu = bound_unknown_from_math_problem_graph(g)
+    assert bu.symbol_id == "unknown_total_apples"
+    assert bu.state_index == "terminal"
+    assert bu.question_form == "count"
+
+
+def test_bound_unknown_deterministic_byte_equal() -> None:
+    g = _graph(operations=(_add("Tina", 2),))
+    a = bound_unknown_from_math_problem_graph(g)
+    b = bound_unknown_from_math_problem_graph(g)
+    assert a == b
+
+
+def test_bound_unknown_refuses_non_graph_input() -> None:
+    with pytest.raises(QuestionTargetError):
+        bound_unknown_from_math_problem_graph(123)
+
+
+# ---------------------------------------------------------------------------
+# Defensive: input is read-only
+# ---------------------------------------------------------------------------
+
+
+def test_resolver_does_not_mutate_input() -> None:
+    g = _graph(operations=(_add("Tina", 2),))
+    before = g.canonical_bytes()
+    _ = bound_unknown_from_math_problem_graph(g)
+    after = g.canonical_bytes()
+    assert before == after
+
+
+# ---------------------------------------------------------------------------
+# Parametric coverage of every operation kind in every question_form bucket
+# ---------------------------------------------------------------------------
+
+
+@pytest.mark.parametrize(
+    "kind_op",
+    [
+        _add("Tina", 2),
+        _sub("Tina", 1),
+        _mul("Tina", 2),
+        _div("Tina", 2),
+    ],
+)
+def test_count_kinds_single_op_terminal_count(kind_op: Operation) -> None:
+    g = _graph(operations=(kind_op,))
+    bu = bound_unknown_from_math_problem_graph(g)
+    assert bu.question_form == "count"
+    assert bu.state_index == "terminal"
+
+
+def test_transfer_count_form_for_actor() -> None:
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_transfer("Tina", "Sam", 1),),
+        unknown=Unknown(entity="Tina", unit="apples"),
+    )
+    bu = bound_unknown_from_math_problem_graph(g)
+    assert bu.question_form == "count"
+
+
+def test_transfer_count_form_for_target() -> None:
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_transfer("Tina", "Sam", 1),),
+        unknown=Unknown(entity="Sam", unit="apples"),
+    )
+    bu = bound_unknown_from_math_problem_graph(g)
+    assert bu.question_form == "count"
+
+
+# ---------------------------------------------------------------------------
+# Unknown-entity boundary: comparison reference_actor counts as "touching"
+# ---------------------------------------------------------------------------
+
+
+def test_comparison_reference_actor_is_touching() -> None:
+    # Unknown.entity == reference_actor (Sam). The compare_additive op
+    # touches via the reference_actor edge → difference.
+    g = _graph(
+        entities=("Tina", "Sam"),
+        initial_state=(
+            InitialPossession(entity="Tina", quantity=Quantity(5, "apples")),
+            InitialPossession(entity="Sam", quantity=Quantity(3, "apples")),
+        ),
+        operations=(_cmp_add("Tina", "Sam", 2),),
+        unknown=Unknown(entity="Sam", unit="apples"),
+    )
+    bu = bound_unknown_from_math_problem_graph(g)
+    assert bu.question_form == "difference"