[Bug]: universal_algebra operations accept invalid cross-field inputs that raise backend exceptions

[morluto]

Observed behavior

Two universal_algebra operations accept requests that pass request-model validation but raise untyped backend ValueError exceptions during domain execution.

universal_algebra.quotient.compute — empty and partial partitions

The QuotientRequest model accepts an empty partition tuple partition = (). The backend then raises ValueError: partition is not a congruence. A partition that does not cover all carrier elements (e.g., partition = [[0]] for a two-element carrier) is also accepted by the model and raises the same backend error.

universal_algebra.equation.profile.compute — variable_count too small

The EquationProfileRequest model accepts variable_count = 1 even when the left equation tree references variable_id = 1. The backend then raises ValueError: incomplete assignment.

Reproduction

from jacobian.catalog.catalog import Catalog
from jacobian.dispatch import invoke_operation

catalog = Catalog.open()

# --- quotient with empty partition ---

base = {
    "algebra": {
        "carrier": ["0", "1"],
        "operations": [
            {"operation_id": "and", "arity": 2},
            {"operation_id": "or", "arity": 2},
        ],
        "tables": [[0, 0, 0, 1], [0, 1, 1, 1]],
    },
    "partition": [],
}

result = invoke_operation(
    "universal_algebra.quotient.compute",
    base,
    catalog,
)
# ValueError: partition is not a congruence

# --- equation.profile with variable_count too small ---

base = {
    "algebra": {
        "carrier": ["0", "1"],
        "operations": [
            {"operation_id": "and", "arity": 2},
            {"operation_id": "or", "arity": 2},
        ],
        "tables": [[0, 0, 0, 1], [0, 1, 1, 1]],
    },
    "left": {
        "nodes": [
            {"kind": "variable", "variable_id": 0, "operation": None, "children": []},
            {"kind": "variable", "variable_id": 1, "operation": None, "children": []},
            {"kind": "application", "variable_id": None, "operation": 0, "children": [0, 1]},
        ],
        "root": 2,
    },
    "right": {
        "nodes": [
            {"kind": "variable", "variable_id": 0, "operation": None, "children": []},
        ],
        "root": 0,
    },
    "variable_count": 1,  # should be 2
}

result = invoke_operation(
    "universal_algebra.equation.profile.compute",
    base,
    catalog,
)
# ValueError: incomplete assignment

Expected behavior

Every request accepted by the public model should either return a typed result or be rejected during validation. The contract for these two operations should validate:

• QuotientRequest: The partition must be non-empty, must cover all carrier elements, and each block must contain valid carrier indices.
• EquationProfileRequest: variable_count must be at least one more than the maximum variable_id referenced in the left and right equation trees.

Environment

• Jacobian revision: be54c78
• Python: 3.12.13
• OS: Linux

[morluto]

One additional schema-valid quotient case reaches a different host exception:

from copy import deepcopy

from jacobian.catalog.catalog import Catalog
from jacobian.dispatch import invoke_operation

catalog = Catalog.open()
op = catalog.operation("universal_algebra.quotient.compute")
payload = deepcopy(op.examples[0].input)
payload["partition"] = [[], [0, 1]]

invoke_operation(op.operation_id, payload, catalog)

This family covers the carrier and passes the current disjoint/range checks. congruence_check treats it as a congruence because the nonempty block covers every element, after which quotient construction evaluates min(empty_block) and raises:

ValueError: min() iterable argument is empty

The request fix therefore also needs to require every partition block to be nonempty, not only that the family itself is nonempty and covers the carrier. The successful quotient result's separate composition contract is tracked in #2146.

[morluto]

The same cross-field validation gap extends to universal_algebra.term.evaluate.compute. The TermEvaluateRequest model accepts variable_count values that are too small for the variable IDs referenced in the term tree. The backend then raises ValueError: incomplete assignment.

from jacobian.catalog.catalog import Catalog
from jacobian.dispatch import invoke_operation

catalog = Catalog.open()

# term.evaluate with variable_count too small
result = invoke_operation(
    "universal_algebra.term.evaluate.compute",
    {
        "algebra": {
            "carrier": ["0", "1"],
            "operations": [
                {"operation_id": "and", "arity": 2},
                {"operation_id": "or", "arity": 2},
            ],
            "tables": [[0, 0, 0, 1], [0, 1, 1, 1]],
        },
        "term": {
            "nodes": [
                {"kind": "variable", "variable_id": 0, "operation": None, "children": []},
                {"kind": "variable", "variable_id": 1, "operation": None, "children": []},
                {"kind": "application", "variable_id": None, "operation": 0, "children": [0, 1]},
            ],
            "root": 2,
        },
        "assignment": {"values": ["0"]},  # too few values for the 2 variables
        "variable_count": 1,
    },
    catalog,
)
# ValueError: incomplete assignment

This is the same class of cross-field validation gap as the original report. The fix should validate that variable_count is at least one more than the maximum variable_id referenced in the term tree.

[morluto]

Resolved by #2185. Universal-algebra request models now validate exact carrier partitions and bind equation-profile variable_count to the variables referenced by both terms. On current main, both reported reproductions—the empty partition and undersized variable count—are rejected at the request boundary.