diff --git a/generate/constraint_comprehension/__init__.py b/generate/constraint_comprehension/__init__.py
new file mode 100644
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+++ b/generate/constraint_comprehension/__init__.py
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+"""R2 finite-integer linear-constraint comprehension organ (off-serving).
+
+A parallel typed organ — the R2 twin of the R1 quantitative-comprehension reader. It
+compiles two-category constraint word problems (buses/seats, chickens/legs, tickets/prices)
+into a typed :class:`ConstraintProblem` graded by an independent setup oracle and solved by
+an independent integer solver. Disjoint from the GSM8K serving path (imports no
+``generate.derivation`` / ``core.reliability_gate``), so it cannot regress the serving metric.
+
+C1 ships the IR only (this package's ``expr`` + ``model``); the gold/oracle (C2), the
+integer solver (C3), the answer-choice verifier (C4), and the reader (C5+) land on top.
+"""
+
+from __future__ import annotations
+
+from generate.constraint_comprehension.expr import (
+    LinearConstraint,
+    LinearExpr,
+    Relation,
+)
+from generate.constraint_comprehension.model import (
+    AttributeFact,
+    ConstraintProblem,
+    ConstraintQuery,
+    Domain,
+    Unknown,
+)
+
+__all__ = [
+    "AttributeFact",
+    "ConstraintProblem",
+    "ConstraintQuery",
+    "Domain",
+    "LinearConstraint",
+    "LinearExpr",
+    "Relation",
+    "Unknown",
+]
diff --git a/generate/constraint_comprehension/expr.py b/generate/constraint_comprehension/expr.py
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+++ b/generate/constraint_comprehension/expr.py
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+"""Typed linear-constraint IR for the R2 finite-integer constraint organ.
+
+The algebraic layer: a linear combination over unknown symbols (:class:`LinearExpr`) and a
+single linear equation (:class:`LinearConstraint`). This is the R2 twin of
+``generate.quantitative_expr`` — the reader's/gold's SOURCE OF MEANING for a constraint,
+kept above the string-serialization boundary. Strings are serialization only: meaning lives
+in these typed terms, never recovered by parsing an expression string.
+
+Pure data — no behavior. Canonicalization (sorting terms, comparing constraints) lives in
+the setup signature (C2); the solver (C3) reads these terms directly. Deterministic; no
+clock, no randomness.
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import Literal
+
+from generate.binding_graph.model import SourceSpanLink
+
+#: v1 admits only equality constraints. Inequalities (``<=`` / ``>=``) are a deliberate
+#: future extension — not representable here, so they cannot be silently half-supported.
+Relation = Literal["eq"]
+
+
+@dataclass(frozen=True, slots=True)
+class LinearExpr:
+    """A linear combination over unknown symbols: ``sum(coeff * symbol) + constant``.
+
+    ``terms`` pairs each symbol with its INTEGER coefficient as ``(symbol, coefficient)`` —
+    matching the gold serialization ``["large_bus", 1]`` (the design sketch's prose comment
+    said "coefficient, symbol"; the concrete JSON artifact and the idiomatic ``{var: coeff}``
+    form both put the symbol first, so the symbol-first pairing is the one pinned here). The
+    canonical form sorts terms by symbol and merges duplicates; that canonicalization lives
+    in the setup signature, so two equal combinations written in different orders compare
+    equal there. No floats: every coefficient and the constant are integers (the domain is
+    finite-integer by construction).
+    """
+
+    terms: tuple[tuple[str, int], ...]
+    constant: int = 0
+
+
+@dataclass(frozen=True, slots=True)
+class LinearConstraint:
+    """A single linear equation ``lhs <relation> rhs`` (v1: ``relation == "eq"``).
+
+    ``source_span`` is provenance populated by the reader (C5+); it is ``None`` for
+    gold-authored constraints (which have no input span). It never participates in canonical
+    equality — two constraints are setup-equal iff their ``lhs`` / ``relation`` / ``rhs``
+    match (the signature in C2 strips the span before comparing).
+    """
+
+    lhs: LinearExpr
+    relation: Relation
+    rhs: int
+    source_span: SourceSpanLink | None = None
+
+
+__all__ = ["LinearConstraint", "LinearExpr", "Relation"]
diff --git a/generate/constraint_comprehension/model.py b/generate/constraint_comprehension/model.py
new file mode 100644
index 00000000..d0bcecb2
--- /dev/null
+++ b/generate/constraint_comprehension/model.py
@@ -0,0 +1,91 @@
+"""Problem model for the R2 finite-integer constraint organ.
+
+The structural layer above ``generate.constraint_comprehension.expr``: the unknowns, the
+raw per-category attribute coefficients (provenance), the assembled linear system, and the
+query. This is the R2 twin of the binding-graph model — a typed :class:`ConstraintProblem`
+the setup oracle grades and the solver consumes.
+
+Pure data — no behavior. Deterministic.
+
+Deviation from the design sketch: the query is a minimal dedicated :class:`ConstraintQuery`
+(symbol + unit), NOT the binding-graph ``BoundUnknown`` — R2 has no state-index /
+question-form axis, and forcing R1's unknown type onto it would be a degenerate fit.
+Multiple-choice options and the provided answer key are NOT part of the problem IR; they are
+answer-choice concerns graded separately (C4).
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import Literal
+
+from generate.constraint_comprehension.expr import LinearConstraint
+
+#: A finite-integer domain for an unknown. Count categories are nonnegative integers; the
+#: broader signed-integer domain is reserved for future signed-quantity problems (so the
+#: distinction is explicit, not a silent assumption that every unknown is a count).
+Domain = Literal["nonnegative_integer", "integer"]
+
+
+@dataclass(frozen=True, slots=True)
+class Unknown:
+    """One unknown category — ``large_bus``, ``chicken``, ``adult_ticket``.
+
+    ``symbol`` is the canonical identifier used in ``LinearExpr.terms``; ``entity`` is the
+    surface category noun (provenance); ``unit`` is the category's own count unit (``bus``,
+    ``animal``); ``domain`` constrains the solution set (a count -> ``nonnegative_integer``).
+    """
+
+    symbol: str
+    entity: str
+    unit: str
+    domain: Domain
+
+
+@dataclass(frozen=True, slots=True)
+class AttributeFact:
+    """A per-category attribute coefficient read from the prose: ``large bus holds 50
+    students`` -> ``AttributeFact("large_bus", "student", 50)``.
+
+    This is the RAW reading (provenance); the weighted-total constraint
+    ``50*large_bus + 30*small_bus = 260`` is assembled FROM these. ``value`` is the integer
+    coefficient — positivity and cross-category distinctness are the reader's/oracle's gate
+    (C3/C6), not enforced in this pure-data layer.
+    """
+
+    category: str
+    measured_unit: str
+    value: int
+
+
+@dataclass(frozen=True, slots=True)
+class ConstraintQuery:
+    """The asked unknown: which category's count is the answer, and in what unit."""
+
+    symbol: str
+    unit: str
+
+
+@dataclass(frozen=True, slots=True)
+class ConstraintProblem:
+    """A complete finite-integer constraint setup: the unknowns, the raw attribute
+    coefficients, the assembled linear system, and the query.
+
+    The setup oracle (C2) grades unknowns / units / domains / constraints / query
+    canonically; the solver (C3) consumes ``unknowns`` + ``constraints``. ``facts`` is
+    provenance — the coefficients the constraints were built from.
+    """
+
+    unknowns: tuple[Unknown, ...]
+    facts: tuple[AttributeFact, ...]
+    constraints: tuple[LinearConstraint, ...]
+    query: ConstraintQuery
+
+
+__all__ = [
+    "AttributeFact",
+    "ConstraintProblem",
+    "ConstraintQuery",
+    "Domain",
+    "Unknown",
+]
diff --git a/tests/test_constraint_comprehension_model.py b/tests/test_constraint_comprehension_model.py
new file mode 100644
index 00000000..b2a4e65d
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+++ b/tests/test_constraint_comprehension_model.py
@@ -0,0 +1,96 @@
+"""Unit tests for the R2 constraint IR (C1) — pure dataclasses, no behavior.
+
+Pins the typed shape the gold/oracle (C2) and solver (C3) build on: unknowns with a
+finite-integer domain, attribute coefficients, a canonical linear system, and a minimal
+query. Frozen-ness is load-bearing (the immutability doctrine — the IR is value data); the
+bus + chickens systems are pinned as IR so later slices can assert the reader reconstructs
+exactly these.
+"""
+
+from __future__ import annotations
+
+import dataclasses
+from typing import Any
+
+import pytest
+
+from generate.constraint_comprehension import (
+    AttributeFact,
+    ConstraintProblem,
+    ConstraintQuery,
+    LinearConstraint,
+    LinearExpr,
+    Unknown,
+)
+
+
+def _bus_problem() -> ConstraintProblem:
+    # 6 buses total; large holds 50, small holds 30; 260 students; ask large.
+    return ConstraintProblem(
+        unknowns=(
+            Unknown("large_bus", "large bus", "bus", "nonnegative_integer"),
+            Unknown("small_bus", "small bus", "bus", "nonnegative_integer"),
+        ),
+        facts=(
+            AttributeFact("large_bus", "student", 50),
+            AttributeFact("small_bus", "student", 30),
+        ),
+        constraints=(
+            LinearConstraint(LinearExpr((("large_bus", 1), ("small_bus", 1))), "eq", 6),
+            LinearConstraint(LinearExpr((("large_bus", 50), ("small_bus", 30))), "eq", 260),
+        ),
+        query=ConstraintQuery("large_bus", "bus"),
+    )
+
+
+def test_bus_problem_ir_shape() -> None:
+    p = _bus_problem()
+    assert tuple(u.symbol for u in p.unknowns) == ("large_bus", "small_bus")
+    assert all(u.domain == "nonnegative_integer" for u in p.unknowns)
+    assert p.constraints[0].relation == "eq" and p.constraints[0].rhs == 6
+    assert p.constraints[1].lhs.terms == (("large_bus", 50), ("small_bus", 30))
+    assert p.query == ConstraintQuery("large_bus", "bus")
+
+
+def test_chickens_problem_ir_shape() -> None:
+    # 18 animals; chickens 2 legs, cows 4 legs; 50 legs; ask chickens.
+    p = ConstraintProblem(
+        unknowns=(
+            Unknown("chicken", "chicken", "animal", "nonnegative_integer"),
+            Unknown("cow", "cow", "animal", "nonnegative_integer"),
+        ),
+        facts=(AttributeFact("chicken", "leg", 2), AttributeFact("cow", "leg", 4)),
+        constraints=(
+            LinearConstraint(LinearExpr((("chicken", 1), ("cow", 1))), "eq", 18),
+            LinearConstraint(LinearExpr((("chicken", 2), ("cow", 4))), "eq", 50),
+        ),
+        query=ConstraintQuery("chicken", "animal"),
+    )
+    assert {f.measured_unit for f in p.facts} == {"leg"}
+    assert p.constraints[1].lhs.terms == (("chicken", 2), ("cow", 4))
+
+
+def test_linear_expr_constant_defaults_zero() -> None:
+    assert LinearExpr((("x", 1),)).constant == 0
+
+
+def test_constraint_source_span_defaults_none() -> None:
+    # Gold-authored constraints carry no input span; the reader (C5+) populates it.
+    assert LinearConstraint(LinearExpr((("x", 1),)), "eq", 3).source_span is None
+
+
+@pytest.mark.parametrize(
+    "obj",
+    [
+        Unknown("x", "x", "item", "integer"),
+        AttributeFact("x", "leg", 2),
+        ConstraintQuery("x", "item"),
+        LinearExpr((("x", 1),)),
+        LinearConstraint(LinearExpr((("x", 1),)), "eq", 1),
+    ],
+)
+def test_ir_dataclasses_are_frozen(obj: Any) -> None:
+    # Immutability doctrine: the IR is value data — mutation must raise, never silently alias.
+    field = dataclasses.fields(obj)[0].name
+    with pytest.raises(dataclasses.FrozenInstanceError):
+        setattr(obj, field, getattr(obj, field))