API REFERENCE/omnibias-sos

omnibias.sos.families

0.1.0a2AlphaPython >=3.10AGPL / commercial

Sum-of-squares constructions, polynomial positivity checks, and rigorous validation of proposed Gram matrices.

import omnibias.sos.families

Module contract & mathematical conventions

SOS degree box: positivity in a Gram span, not “only equations.”

Shared formulas do not imply universal floating-point identity. Verify dtype, shape, derivative-order support, and the stated numerical assumptions for the path you use.

Module source ↗Source revision 9a2d73df0573Running reference examples →

CLASS

SosDegreeFamily

omnibias.sos.families.SosDegreeFamilySource ↗

class SosDegreeFamily

Dataclass constructor fields; inherited fields, if any, are declared by the base class. A field(...) expression describes a default factory or field options, not a literal argument default.

Candidate = half-degree; check = existing certify_sos on a planted poly.

Parameters

Name	Type & default	Contract
polynomialdataclass field	PolynomialDefault: field(default_factory=planted_sum_of_squares)	See the operation contract and implementation below.
max_half_degreedataclass field	intDefault: 2	See the operation contract and implementation below.
namedataclass field	strDefault: 'sos_degree_search'	See the operation contract and implementation below.
completedataclass field	boolDefault: True	See the operation contract and implementation below.
statementdataclass field	StatementDefault: field(default_factory=lambda: Statement(name='sos_degree_search', obligation='the planted polynomial is SOS at some half-degree in the box', parent='global nonnegativity', parent_status='already_true'))	See the operation contract and implementation below.

Executed regression · sos template planted hits

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_sos_template_planted_hits() -> None:
    family = SosTemplateFamily()
    result = run_discovery(family.statement, family, "score_guided", budget=4)
    assert result.status == "PROVED"
    assert result.check is not None
    assert result.check.payload["honesty"]["no_condition_exists_claim"] is False
    assert result.check.payload["honesty"]["discovered_by_omnibias"] is True

python -m pytest "packages/omnibias-sos/tests/test_conditions.py::test_sos_template_planted_hits" -q

Fields & methods

polynomialfield

polynomial: Polynomial = field(default_factory=planted_sum_of_squares)

Declared Polynomial field on SosDegreeFamily. Default expression: field(default_factory=planted_sum_of_squares).

View source ↗

max_half_degreefield

max_half_degree: int = 2

Declared int field on SosDegreeFamily. Default expression: 2.

View source ↗

namefield

name: str = 'sos_degree_search'

Declared str field on SosDegreeFamily. Default expression: 'sos_degree_search'.

View source ↗

completefield

complete: bool = True

Declared bool field on SosDegreeFamily. Default expression: True.

View source ↗

statementfield

statement: Statement = field(default_factory=lambda: Statement(name='sos_degree_search', obligation='the planted polynomial is SOS at some half-degree in the box', parent='global nonnegativity', parent_status='already_true'))

Declared Statement field on SosDegreeFamily. Default expression: field(default_factory=lambda: Statement(name='sos_degree_search', obligation='the planted polynomial is SOS at some half-degree in the box', parent='global nonnegativity', parent_status='already_true')).

View source ↗

cardinalitymethod

cardinality(self) -> int

See the class contract above and the exact method implementation below.

Returns: int

Method implementation

    def cardinality(self) -> int:
        return self.max_half_degree

View source ↗

originmethod

origin(self) -> int

See the class contract above and the exact method implementation below.

Returns: int

Method implementation

    def origin(self) -> int:
        return 1

View source ↗

neighborsmethod

neighbors(self, candidate: Candidate) -> Sequence[int]

See the class contract above and the exact method implementation below.

Parameters

Name	Type & default	Contract
candidatepositional-or-keyword	CandidateRequired	See the operation contract and implementation below.

Returns: Sequence[int]

Method implementation

    def neighbors(self, candidate: Candidate) -> Sequence[int]:
        value = int(candidate)  # type: ignore[arg-type]
        out: list[int] = []
        if value > 1:
            out.append(value - 1)
        if value < self.max_half_degree:
            out.append(value + 1)
        return out

View source ↗

scoremethod

score(self, candidate: Candidate) -> int

See the class contract above and the exact method implementation below.

Parameters

Name	Type & default	Contract
candidatepositional-or-keyword	CandidateRequired	See the operation contract and implementation below.

Returns: int

Method implementation

    def score(self, candidate: Candidate) -> int:
        return -int(candidate)  # type: ignore[arg-type]

View source ↗

checkmethod

check(self, candidate: Candidate) -> ExactCheck | None

See the class contract above and the exact method implementation below.

Parameters

Name	Type & default	Contract
candidatepositional-or-keyword	CandidateRequired	See the operation contract and implementation below.

Returns: ExactCheck | None

Executed regression · sos template planted hits

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_sos_template_planted_hits() -> None:
    family = SosTemplateFamily()
    result = run_discovery(family.statement, family, "score_guided", budget=4)
    assert result.status == "PROVED"
    assert result.check is not None
    assert result.check.payload["honesty"]["no_condition_exists_claim"] is False
    assert result.check.payload["honesty"]["discovered_by_omnibias"] is True

python -m pytest "packages/omnibias-sos/tests/test_conditions.py::test_sos_template_planted_hits" -q

Method implementation

    def check(self, candidate: Candidate) -> ExactCheck | None:
        half = int(candidate)  # type: ignore[arg-type]
        if not 1 <= half <= self.max_half_degree:
            return None
        cert = certify_sos(self.polynomial, half_degree=half)
        ok = cert.status == "proved"
        return ExactCheck(
            ok=ok,
            payload={
                "half_degree": half,
                "status": cert.status,
                "honesty": {
                    "discovered_by_omnibias": ok,
                    "unproven_claim": False,
                },
            },
        )

View source ↗

Read the implementation

class SosDegreeFamily:
    """Candidate = half-degree; check = existing ``certify_sos`` on a planted poly."""

    polynomial: Polynomial = field(default_factory=planted_sum_of_squares)
    max_half_degree: int = 2
    name: str = "sos_degree_search"
    complete: bool = True
    statement: Statement = field(
        default_factory=lambda: Statement(
            name="sos_degree_search",
            obligation="the planted polynomial is SOS at some half-degree in the box",
            parent="global nonnegativity",
            parent_status="already_true",
        )
    )

    def cardinality(self) -> int:
        return self.max_half_degree

    def origin(self) -> int:
        return 1

    def neighbors(self, candidate: Candidate) -> Sequence[int]:
        value = int(candidate)  # type: ignore[arg-type]
        out: list[int] = []
        if value > 1:
            out.append(value - 1)
        if value < self.max_half_degree:
            out.append(value + 1)
        return out

    def score(self, candidate: Candidate) -> int:
        return -int(candidate)  # type: ignore[arg-type]

    def check(self, candidate: Candidate) -> ExactCheck | None:
        half = int(candidate)  # type: ignore[arg-type]
        if not 1 <= half <= self.max_half_degree:
            return None
        cert = certify_sos(self.polynomial, half_degree=half)
        ok = cert.status == "proved"
        return ExactCheck(
            ok=ok,
            payload={
                "half_degree": half,
                "status": cert.status,
                "honesty": {
                    "discovered_by_omnibias": ok,
                    "unproven_claim": False,
                },
            },
        )

Related APIsomnibias.core.proof.ExactCheck↗omnibias.core.proof.Statement↗omnibias.sos.certify_sos↗

FUNCTION

planted_sum_of_squares

omnibias.sos.families.planted_sum_of_squaresSource ↗

planted_sum_of_squares() -> Polynomial

The module contract describes the context for this operation. Its signature, explicit validation, return expressions, and implementation are recorded below.

ReturnsPolynomial

Executed regression · sos template planted hits

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_sos_template_planted_hits() -> None:
    family = SosTemplateFamily()
    result = run_discovery(family.statement, family, "score_guided", budget=4)
    assert result.status == "PROVED"
    assert result.check is not None
    assert result.check.payload["honesty"]["no_condition_exists_claim"] is False
    assert result.check.payload["honesty"]["discovered_by_omnibias"] is True

python -m pytest "packages/omnibias-sos/tests/test_conditions.py::test_sos_template_planted_hits" -q

Read the implementation

def planted_sum_of_squares() -> Polynomial:
    x = Polynomial.variable(0, 2)
    y = Polynomial.variable(1, 2)
    one = Polynomial.constant(1.0, 2)
    return x * x + y * y + one

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