szl-lambda-gate

Λ — a governance aggregator as a Hugging Face kernel. A differentiable, torch.compile-friendly weighted-geometric-mean aggregator with an ADVISORY non-compensatory gate and runtime axiom self-checks, from SZL Holdings.

Companion to szl-governed-norm. Where that kernel makes a normalization auditable, this one makes a governance decision computable and checkable at the tensor layer.

See it live (holographic Spaces)

This kernel powers two live, 3D-holographic Spaces — the lattice renders violet/advisory, never a fake green:

• 🔮 lambda-gate-holo — the Λ gate visualized: zero any axis and watch the whole lattice fail (non-compensatory veto).
• 🔮 lambda-aggregator-live — Λ aggregation across many candidate vectors, advisory pass mask in real time.
• 🔮 szl-substrate — the hub tying the whole governed-AI substrate together.

What Λ is — and is NOT (read this first)

Λ is the weighted geometric mean over axis scores in [0,1]:

[ \Lambda(x) = \prod_i x_i^{w_i}, \quad \sum_i w_i = 1, ; w_i > 0, ; x_i \in [0,1] ]

It is a non-compensatory, ADVISORY roll-up: any single zeroed (or non-finite) axis drives the whole aggregate to 0 — a conservative "one bad axis fails the gate" signal. Λ is NOT "proven trust" and NOT a closed theorem. Its uniqueness (that the weighted geometric mean is the only aggregator satisfying the carried axioms) remains Conjecture 1 — OPEN. A gate "pass" is an advisory signal, never a guarantee. We label this honestly everywhere.

Quickstart

import torch
from kernels import get_kernel

# Current `kernels` (>=0.15) requires an explicit revision/version + trust flag for org kernels:
lg = get_kernel("SZLHOLDINGS/szl-lambda-gate", revision="main", trust_remote_code=True)
# (once a tag is published you can pin it, e.g. revision="v0.2.0")

axes = torch.tensor([0.9, 0.8, 0.95])      # axis scores in [0,1]
score = lg.lambda_aggregate(axes)          # Λ(x) ∈ [0,1]
res   = lg.lambda_gate(axes, threshold=0.5)
print(res.score, res.passed, res.advisory) # advisory is always True

print(lg.selfcheck())                      # empirical A1–A4 checks + version

API

Function	Notes
lambda_aggregate(axes, weights=None)	Λ over the last dim. Differentiable, batched, torch.compile-friendly.
lambda_gate(axes, weights=None, threshold=0.5)	Advisory gate → LambdaGateResult(score, passed, threshold, advisory).
lambda_gate_batch(candidates, weights=None, threshold=0.5)	Score many candidate vectors (..., N, k) in one call; returns the advisory pass mask.
selfcheck()	Empirical A1–A4 axiom checks + adversarial falsification search + version. NOT a uniqueness proof.
is_monotone / is_homogeneous / is_egyptian_exact / is_bounded_by_max	The four carried axioms as real runtime checks.
yuyay_weights(), YUYAY_AXES, YUYAY_FLOORS	Canonical 13-axis Yuyay preset (advisory).
layers: LambdaGate, LambdaAggregate	Pure nn.Module for the Kernel Hub layer-mapping mechanism.

Carried axioms (verifiable, not a proof)

• A1 IsMonotone — Λ is non-decreasing in each axis.
• A2 IsHomogeneous (deg 1) — Λ(t·x) = t·Λ(x).
• A3 IsEgyptianExact — Λ(c,…,c) = c.
• A4 IsBounded — Λ(x) ≤ maxᵢ xᵢ.

selfcheck() verifies these empirically on sampled inputs and runs a random falsification search. A clean run is evidence, not proof — Λ-uniqueness is Conjecture 1 (open).

Provenance

Backed by the Lean 4 formalization szl-holdings/lutar-lean (749 declarations / 14 axioms / 163 tracked sorries), DOI 10.5281/zenodo.20434308. Λ uniqueness = Conjecture 1 (open).

Honesty

• Pure-Python universal kernel — a correctness reference, not a CUDA speed record. No fabricated benchmarks (50 passing tests).
• Λ is advisory; never "proven trust."
• Prior art honestly attributed: the weighted geometric mean as a less-compensatory composite indicator is established practice (UN HDI 2010, OECD Composite Indicators Handbook 2008); the veto/cut-off idea is ELECTRE. The 13-axis conjunctive form is SZL's own yuyay_v3 gate.

Compatibility

Python 3.9+, torch>=2.5, standard library + torch only.

License

Apache-2.0. Copyright 2026 SZL Holdings.

---

_{SZL Holdings · Λ governance aggregator · advisory, not proven trust · a11oy.net · github.com/szl-holdings · huggingface.co/SZLHOLDINGS}