---
tags:
- kernel
library_name: kernels
license: apache-2.0
---

# 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](https://huggingface.co/SZLHOLDINGS).

> Companion to [`szl-governed-norm`](https://huggingface.co/SZLHOLDINGS/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**](https://huggingface.co/spaces/SZLHOLDINGS/lambda-gate-holo) — the Λ gate visualized: zero any axis and watch the whole lattice fail (non-compensatory veto).
- 🔮 [**lambda-aggregator-live**](https://huggingface.co/spaces/SZLHOLDINGS/lambda-aggregator-live) — Λ aggregation across many candidate vectors, advisory pass mask in real time.
- 🔮 [**szl-substrate**](https://huggingface.co/spaces/SZLHOLDINGS/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

```python
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](https://github.com/szl-holdings/lutar-lean) (749 declarations / 14 axioms / 163 tracked sorries), DOI [10.5281/zenodo.20434308](https://doi.org/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.

---

<sub><b>SZL Holdings</b> · Λ governance aggregator · advisory, not proven trust · <a href="https://a11oy.net">a11oy.net</a> · <a href="https://github.com/szl-holdings">github.com/szl-holdings</a> · <a href="https://huggingface.co/SZLHOLDINGS">huggingface.co/SZLHOLDINGS</a></sub>