IBPCertificate

Symbolica documentation for getting started, symbolic expressions, numerical evaluation, pattern matching, and APIs in Python and Rust.

`IBPCertificate`

class IBPCertificate

Evidence returned by IBPSolution.certify; no public constructor.

Exact identity replay and probabilistic master counts are separate evidence. Neither a stable residual set nor a count-consistent result proves closure or independence of the residual integrals.

Examples

from symbolica import S
from symbolica.community import hepkit as hep
d, k, m2 = S("d", "k", "m2")
kin = hep.Kinematics(d, momenta=[k])
family = hep.IntegralFamily([k], [], [kin.scalar_product(k, k) - m2], kinematics=kin)
ibp = hep.IBPFamily(family, name="T")
solution = ibp.reduce_laporta([[3]], max_depth=1)
certificate = solution.certify(seed=0)
assert certificate.reduction == "verified"

Attributes

Name	Description
`excess_sectors`	Sectors with more residuals than the counted master number.
`identities`	Number of instantiated original identities used during replay
`master_counts`	Generic count per residual sector; None where no verdict is available
`masters`	unchecked, incomplete, no-verdict, or count-consistent.
`no_verdict`	Explanation for sectors without a count verdict.
`reduction`	Exact identity replay status: verified or unchecked.
`replayed_rules`	Number of rules reconstructed from the original exact identities
`residual_counts`	Number of search residuals in each checked sector.
`seed`	Probabilistic counting seed; None when counting was not requested.
`stable_depth`	First depth whose residual set survived two further search depths

`excess_sectors`

IBPCertificate.excess_sectors: list[list[bool]]

Sectors with more residuals than the counted master number.

Examples

Using the setup in the IBPCertificate class example:

assert certificate.excess_sectors == []

`identities`

IBPCertificate.identities: int | None

Number of instantiated original identities used during replay.

None means replay was not requested.

Examples

Using the setup in the IBPCertificate class example:

assert certificate.identities > 0

`master_counts`

IBPCertificate.master_counts: dict[tuple[bool, ...], int | None] | None

Generic count per residual sector; None where no verdict is available.

The whole mapping is None when master counting was not requested.

Examples

Using the setup in the IBPCertificate class example:

assert certificate.master_counts == {(True,): 1}

`masters`

IBPCertificate.masters: str

unchecked, incomplete, no-verdict, or count-consistent.

Examples

Using the setup in the IBPCertificate class example:

assert certificate.masters == "count-consistent"

`no_verdict`

IBPCertificate.no_verdict: dict[tuple[bool, ...], str] | None

Explanation for sectors without a count verdict.

Examples

Using the setup in the IBPCertificate class example:

assert certificate.no_verdict == {}

`reduction`

IBPCertificate.reduction: str

Exact identity replay status: verified or unchecked.

Examples

Using the setup in the IBPCertificate class example:

assert certificate.reduction == "verified"

`replayed_rules`

IBPCertificate.replayed_rules: int | None

Number of rules reconstructed from the original exact identities.

None means replay was not requested.

Examples

Using the setup in the IBPCertificate class example:

assert certificate.replayed_rules > 0

`residual_counts`

IBPCertificate.residual_counts: dict[tuple[bool, ...], int] | None

Number of search residuals in each checked sector.

Examples

Using the setup in the IBPCertificate class example:

assert certificate.residual_counts == {(True,): 1}

`seed`

IBPCertificate.seed: int | None

Probabilistic counting seed; None when counting was not requested.

Examples

Using the setup in the IBPCertificate class example:

assert certificate.seed == 0

`stable_depth`

IBPCertificate.stable_depth: int | None

First depth whose residual set survived two further search depths.

None means no stable depth was recorded; this is not a closure test.

Examples

Using the setup in the IBPCertificate class example:

assert certificate.stable_depth is None

Methods

Name	Description
`__repr__`	Summarize replay, counting, and stability evidence for inspection.

`repr`

IBPCertificate.__repr__() -> str

Summarize replay, counting, and stability evidence for inspection.

Examples

Using the setup in the IBPCertificate class example:

summary = repr(certificate)