diff --git a/teaching/math_evidence.py b/teaching/math_evidence.py
new file mode 100644
index 00000000..a4290483
--- /dev/null
+++ b/teaching/math_evidence.py
@@ -0,0 +1,168 @@
+"""ADR-0167 W1-A — MathReaderRefusalEvidence schema + canonical-bytes.
+
+Typed record wrapping an :class:`AuditRow` from the comprehension reader's
+refusal taxonomy.  Every downstream Wave 2 brief (W2-A through W2-D)
+type-imports :class:`MathReaderRefusalEvidence` and
+:data:`SUB_TYPE_FOR_OPERATOR` from this module.
+
+This module is a standalone schema — it does not mutate any teaching store,
+pack, or runtime state.
+"""
+
+from __future__ import annotations
+
+import hashlib
+import json
+from dataclasses import dataclass
+from typing import Any, Final, Literal
+
+from generate.comprehension.audit import AuditRow
+
+# ---------------------------------------------------------------------------
+# Sub-type literal
+# ---------------------------------------------------------------------------
+
+SubType = Literal["lexical", "frame", "composition", "reference", "slot"]
+
+SUB_TYPE_FOR_OPERATOR: Final[dict[str, SubType]] = {
+    "lexicon_entry": "lexical",
+    "compound_numeric_literal": "lexical",
+    "compound_time_literal": "lexical",
+    "pre_frame_filler_sentence": "frame",
+    "multi_quantity_composition": "composition",
+    "quantity_extraction": "composition",
+    "pronoun_resolution": "reference",
+    "question_frame_slot": "slot",
+    "unit_binding": "slot",
+    "fraction_percentage_literal": "lexical",  # provisional
+    "multi_subject_sentence": "frame",
+    "question_target_slot": "slot",
+    "descriptive_frame_question": "slot",
+}
+
+# ---------------------------------------------------------------------------
+# Canonical-bytes helpers (mirrors generate/comprehension/state.py pattern)
+# ---------------------------------------------------------------------------
+
+
+class _OmitSentinel:
+    __slots__ = ()
+
+
+_OMIT = _OmitSentinel()
+
+
+def _canonical_value(obj: Any) -> Any:
+    """Recursively convert to a canonical JSON-serialisable value.
+
+    None → sentinel _OMIT (caller drops from dict).
+    Tuples/lists → JSON arrays.  Dataclasses → sorted-key dicts.
+    """
+    if obj is None:
+        return _OMIT
+    if isinstance(obj, bool):
+        return obj
+    if isinstance(obj, int):
+        return obj
+    if isinstance(obj, str):
+        return obj
+    if isinstance(obj, (tuple, list)):
+        return [_canonical_value(item) for item in obj]
+    if hasattr(obj, "__dataclass_fields__"):
+        out: dict[str, Any] = {}
+        for key in sorted(obj.__dataclass_fields__.keys()):
+            val = _canonical_value(getattr(obj, key))
+            if val is not _OMIT:
+                out[key] = val
+        return out
+    raise TypeError(
+        f"_canonical_value: cannot serialise {type(obj).__name__}"
+    )
+
+
+def _to_canonical_bytes_for_evidence(
+    evidence: MathReaderRefusalEvidence,
+) -> bytes:
+    """Produce deterministic canonical bytes, excluding evidence_hash itself."""
+    out: dict[str, Any] = {}
+    for key in sorted(evidence.__dataclass_fields__.keys()):
+        if key == "evidence_hash":
+            continue
+        val = _canonical_value(getattr(evidence, key))
+        if val is not _OMIT:
+            out[key] = val
+    return json.dumps(
+        out,
+        ensure_ascii=False,
+        sort_keys=True,
+        separators=(",", ":"),
+    ).encode("utf-8")
+
+
+# ---------------------------------------------------------------------------
+# Evidence record
+# ---------------------------------------------------------------------------
+
+
+@dataclass(frozen=True, slots=True)
+class MathReaderRefusalEvidence:
+    """Typed record binding a comprehension-reader refusal to the teaching corridor.
+
+    Construct via :func:`from_audit_row` — do not instantiate directly.
+    """
+
+    case_id: str
+    sentence_index: int
+    token_index: int
+    refusal_reason: str
+    missing_operator: str | None
+    claim_signature: str
+    evidence_hash: str
+    audit_row: AuditRow
+    sub_type: SubType
+
+    def to_canonical_bytes(self) -> bytes:
+        """Deterministic canonical bytes (evidence_hash excluded)."""
+        return _to_canonical_bytes_for_evidence(self)
+
+
+# ---------------------------------------------------------------------------
+# Factory
+# ---------------------------------------------------------------------------
+
+
+def from_audit_row(
+    audit_row: AuditRow,
+    sub_type: SubType,
+    *,
+    claim_signature: str = "",
+) -> MathReaderRefusalEvidence:
+    """Build a :class:`MathReaderRefusalEvidence` from an audit row.
+
+    The ``evidence_hash`` is computed from the canonical bytes of all other
+    fields.  ``claim_signature`` defaults to ``""`` in W1-A; W2-B fills it.
+    """
+    placeholder_hash = ""
+    record = MathReaderRefusalEvidence(
+        case_id=audit_row.case_id,
+        sentence_index=audit_row.sentence_index,
+        token_index=audit_row.token_index,
+        refusal_reason=audit_row.refusal_reason,
+        missing_operator=audit_row.missing_operator,
+        claim_signature=claim_signature,
+        evidence_hash=placeholder_hash,
+        audit_row=audit_row,
+        sub_type=sub_type,
+    )
+    canonical = record.to_canonical_bytes()
+    real_hash = hashlib.sha256(canonical).hexdigest()
+    object.__setattr__(record, "evidence_hash", real_hash)
+    return record
+
+
+__all__ = [
+    "MathReaderRefusalEvidence",
+    "SUB_TYPE_FOR_OPERATOR",
+    "SubType",
+    "from_audit_row",
+]
diff --git a/tests/test_math_evidence_schema.py b/tests/test_math_evidence_schema.py
new file mode 100644
index 00000000..884a050e
--- /dev/null
+++ b/tests/test_math_evidence_schema.py
@@ -0,0 +1,197 @@
+"""Tests for ADR-0167 W1-A — MathReaderRefusalEvidence schema + canonical-bytes."""
+
+from __future__ import annotations
+
+import dataclasses
+import hashlib
+import json
+from pathlib import Path
+
+import pytest
+
+from generate.comprehension.audit import AuditRow, audit_problem
+from teaching.math_evidence import (
+    MathReaderRefusalEvidence,
+    SUB_TYPE_FOR_OPERATOR,
+    from_audit_row,
+)
+
+# ---------------------------------------------------------------------------
+# Fixture: a concrete AuditRow for reuse
+# ---------------------------------------------------------------------------
+
+_SAMPLE_ROW = AuditRow(
+    case_id="test-001",
+    sentence_index=0,
+    token_index=3,
+    token_text="hefty",
+    recognized_terms=("James", "has", "5"),
+    skipped_frame="initial_state",
+    missing_operator="lexicon_entry",
+    refusal_reason="unknown_word",
+    refusal_detail="unknown word: hefty",
+)
+
+
+# ---------------------------------------------------------------------------
+# test_evidence_is_frozen
+# ---------------------------------------------------------------------------
+
+
+def test_evidence_is_frozen() -> None:
+    ev = from_audit_row(_SAMPLE_ROW, "lexical")
+    with pytest.raises(dataclasses.FrozenInstanceError):
+        ev.case_id = "mutated"  # type: ignore[misc]
+    with pytest.raises(dataclasses.FrozenInstanceError):
+        ev.evidence_hash = "mutated"  # type: ignore[misc]
+    with pytest.raises(dataclasses.FrozenInstanceError):
+        ev.sub_type = "frame"  # type: ignore[misc]
+
+
+# ---------------------------------------------------------------------------
+# test_canonical_bytes_deterministic
+# ---------------------------------------------------------------------------
+
+
+def test_canonical_bytes_deterministic() -> None:
+    ev1 = from_audit_row(_SAMPLE_ROW, "lexical")
+    ev2 = from_audit_row(_SAMPLE_ROW, "lexical")
+    assert ev1.to_canonical_bytes() == ev2.to_canonical_bytes()
+
+
+# ---------------------------------------------------------------------------
+# test_evidence_hash_matches_canonical_bytes
+# ---------------------------------------------------------------------------
+
+
+def test_evidence_hash_matches_canonical_bytes() -> None:
+    ev = from_audit_row(_SAMPLE_ROW, "lexical")
+    expected = hashlib.sha256(ev.to_canonical_bytes()).hexdigest()
+    assert ev.evidence_hash == expected
+
+
+# ---------------------------------------------------------------------------
+# test_evidence_hash_excludes_itself
+# ---------------------------------------------------------------------------
+
+
+def test_evidence_hash_excludes_itself() -> None:
+    ev = from_audit_row(_SAMPLE_ROW, "lexical")
+    canonical_before = ev.to_canonical_bytes()
+    object.__setattr__(ev, "evidence_hash", "tampered")
+    canonical_after = ev.to_canonical_bytes()
+    assert canonical_before == canonical_after
+
+
+# ---------------------------------------------------------------------------
+# test_sub_type_table_covers_all_missing_operators
+# ---------------------------------------------------------------------------
+
+
+def test_sub_type_table_covers_all_missing_operators() -> None:
+    artifact_path = Path(
+        "evals/gsm8k_math/train_sample/v1/audit_brief_11.json"
+    )
+    data = json.loads(artifact_path.read_text())
+    operators_in_artifact: set[str] = set()
+    for case in data["per_case"]:
+        op = case.get("missing_operator")
+        if op is not None:
+            operators_in_artifact.add(op)
+    assert operators_in_artifact, "artifact has no missing_operator values"
+    missing = operators_in_artifact - set(SUB_TYPE_FOR_OPERATOR)
+    assert not missing, f"operators not in SUB_TYPE_FOR_OPERATOR: {sorted(missing)}"
+
+
+# ---------------------------------------------------------------------------
+# test_sub_type_table_covers_live_audit (against cases.jsonl)
+# ---------------------------------------------------------------------------
+
+
+def test_sub_type_table_covers_live_audit() -> None:
+    cases_path = Path("evals/gsm8k_math/train_sample/v1/cases.jsonl")
+    operators_found: set[str] = set()
+    for line in cases_path.read_text().splitlines():
+        c = json.loads(line)
+        _result, rows = audit_problem(c["question"], case_id=c["case_id"])
+        for row in rows:
+            if row.missing_operator is not None:
+                operators_found.add(row.missing_operator)
+                assert row.missing_operator in SUB_TYPE_FOR_OPERATOR, (
+                    f"live audit operator {row.missing_operator!r} "
+                    f"not in SUB_TYPE_FOR_OPERATOR"
+                )
+    assert operators_found, "no refusals found in live audit — data may have changed"
+
+
+# ---------------------------------------------------------------------------
+# test_distinct_sub_types_have_distinct_hashes
+# ---------------------------------------------------------------------------
+
+
+def test_distinct_sub_types_have_distinct_hashes() -> None:
+    ev_lexical = from_audit_row(_SAMPLE_ROW, "lexical")
+    ev_frame = from_audit_row(_SAMPLE_ROW, "frame")
+    assert ev_lexical.evidence_hash != ev_frame.evidence_hash
+    assert ev_lexical.to_canonical_bytes() != ev_frame.to_canonical_bytes()
+
+
+# ---------------------------------------------------------------------------
+# test_from_audit_row_factory
+# ---------------------------------------------------------------------------
+
+
+def test_from_audit_row_factory() -> None:
+    ev = from_audit_row(_SAMPLE_ROW, "lexical")
+    assert ev.case_id == _SAMPLE_ROW.case_id
+    assert ev.sentence_index == _SAMPLE_ROW.sentence_index
+    assert ev.token_index == _SAMPLE_ROW.token_index
+    assert ev.refusal_reason == _SAMPLE_ROW.refusal_reason
+    assert ev.missing_operator == _SAMPLE_ROW.missing_operator
+    assert ev.audit_row is _SAMPLE_ROW
+    assert ev.sub_type == "lexical"
+    assert isinstance(ev.evidence_hash, str)
+    assert len(ev.evidence_hash) == 64  # sha256 hex
+
+
+# ---------------------------------------------------------------------------
+# test_claim_signature_default_empty_in_w1a
+# ---------------------------------------------------------------------------
+
+
+def test_claim_signature_default_empty_in_w1a() -> None:
+    ev = from_audit_row(_SAMPLE_ROW, "lexical")
+    assert ev.claim_signature == ""
+
+
+# ---------------------------------------------------------------------------
+# test_determinism_across_n_builds
+# ---------------------------------------------------------------------------
+
+
+def test_determinism_across_n_builds() -> None:
+    hashes = {from_audit_row(_SAMPLE_ROW, "lexical").evidence_hash for _ in range(20)}
+    assert len(hashes) == 1, f"non-deterministic hashes: {hashes}"
+
+
+# ---------------------------------------------------------------------------
+# test_from_audit_row_with_none_missing_operator
+# ---------------------------------------------------------------------------
+
+
+def test_from_audit_row_with_none_missing_operator() -> None:
+    row = AuditRow(
+        case_id="test-nil",
+        sentence_index=1,
+        token_index=0,
+        token_text="?",
+        recognized_terms=(),
+        skipped_frame=None,
+        missing_operator=None,
+        refusal_reason="no_question_target",
+        refusal_detail="no target found",
+    )
+    ev = from_audit_row(row, "slot")
+    assert ev.missing_operator is None
+    canonical = json.loads(ev.to_canonical_bytes())
+    assert "missing_operator" not in canonical