| ---
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| tags:
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| - kernel
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| - governance
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| - lambda
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| - gate
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| - provenance
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| - doi:10.5281/zenodo.19944926
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| library_name: kernels
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| license: apache-2.0
|
| ---
|
|
|
| <p align="center">
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| <a href="https://huggingface.co/SZLHOLDINGS/szl-lambda-gate/tree/main/build/torch-universal/szl_lambda_gate"><img src="https://img.shields.io/badge/kernel%20hub-torch--universal-5b8dee?style=flat-square" alt="kernel hub"></a>
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| <a href="https://huggingface.co/SZLHOLDINGS/szl-lambda-gate/blob/main/MODEL_PROVENANCE.json"><img src="https://img.shields.io/badge/provenance-MODEL_PROVENANCE.json-3af4c8?style=flat-square" alt="provenance"></a>
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| <a href="https://huggingface.co/SZLHOLDINGS/szl-lambda-gate/blob/main/LICENSE"><img src="https://img.shields.io/badge/license-Apache--2.0-7e8aa3?style=flat-square" alt="license"></a>
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| </p>
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|
|
| # szl-lambda-gate
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|
|
| **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).
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|
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| > 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.
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|
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| ## Interactive demo
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|
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| > **Live demos (in-browser, nothing to install)** — [`lambda-gate-holo`](https://szlholdings-lambda-gate-holo.static.hf.space) (this kernel's holographic gate demo) · [`szl-kernels-live`](https://szlholdings-szl-kernels-live.static.hf.space) (unified suite demo).
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| >
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| > The quickstart above runs fully locally. For a full governed-kernel suite demo, see [szl-kernels](https://huggingface.co/SZLHOLDINGS/szl-kernels). For the live a11oy substrate, see [a11oy Space](https://huggingface.co/spaces/SZLHOLDINGS/a11oy).
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|
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| ## What Λ is — and is NOT (read this first)
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|
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| Λ is the **weighted geometric mean** over axis scores in [0,1]:
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|
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| \[ \Lambda(x) = \prod_i x_i^{w_i}, \quad \sum_i w_i = 1, \; w_i > 0, \; x_i \in [0,1] \]
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|
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| 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.
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|
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| ## Quickstart
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|
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| ```bash
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| pip install kernels torch
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| ```
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|
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| ```python
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| import torch
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| from kernels import get_kernel
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|
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| # Current `kernels` (>=0.15) requires an explicit revision/version + trust flag for org kernels:
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| lg = get_kernel("SZLHOLDINGS/szl-lambda-gate", revision="main", trust_remote_code=True)
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| # (once a tag is published you can pin it, e.g. revision="v0.2.0")
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|
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| axes = torch.tensor([0.9, 0.8, 0.95]) # axis scores in [0,1]
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| score = lg.lambda_aggregate(axes) # Λ(x) ∈ [0,1]
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| res = lg.lambda_gate(axes, threshold=0.5)
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| print(res.score, res.passed, res.advisory) # advisory is always True
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|
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| print(lg.selfcheck()) # empirical A1–A4 checks + version
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| ```
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|
|
| ## API
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| | Function | Notes |
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| |---|---|
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| | `lambda_aggregate(axes, weights=None)` | Λ over the last dim. Differentiable, batched, torch.compile-friendly. |
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| | `lambda_gate(axes, weights=None, threshold=0.5)` | Advisory gate → `LambdaGateResult(score, passed, threshold, advisory)`. |
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| | `lambda_gate_batch(candidates, weights=None, threshold=0.5)` | Score many candidate vectors `(..., N, k)` in one call; returns the advisory pass mask. |
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| | `selfcheck()` | Empirical A1–A4 axiom checks + adversarial falsification search + version. NOT a uniqueness proof. |
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| | `is_monotone / is_homogeneous / is_egyptian_exact / is_bounded_by_max` | The four carried axioms as real runtime checks. |
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| | `yuyay_weights()`, `YUYAY_AXES`, `YUYAY_FLOORS` | Canonical 13-axis Yuyay preset (advisory). |
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| | layers: `LambdaGate`, `LambdaAggregate` | Pure `nn.Module` for the Kernel Hub layer-mapping mechanism. |
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|
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| ## Carried axioms (verifiable, not a proof)
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|
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| - **A1 IsMonotone** — Λ is non-decreasing in each axis.
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| - **A2 IsHomogeneous (deg 1)** — Λ(t·x) = t·Λ(x).
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| - **A3 IsEgyptianExact** — Λ(c,…,c) = c.
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| - **A4 IsBounded** — Λ(x) ≤ maxᵢ xᵢ.
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| `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).
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|
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| ## Provenance
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| 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).
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|
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| ## Honesty
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| - Pure-Python universal kernel — a correctness reference, not a CUDA speed record. No fabricated benchmarks (50 passing tests).
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| - Λ is advisory; never "proven trust."
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| - 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.
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|
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| ## Compatibility
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|
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| Python 3.9+, `torch>=2.5`, standard library + torch only.
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|
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| ## License
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|
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| Apache-2.0. Copyright 2026 SZL Holdings.
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|
|
| ---
|
|
|
| ## SZL Kernels Suite
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|
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| Part of the [`szl-kernels`](https://huggingface.co/SZLHOLDINGS/szl-kernels) governed-kernel suite — the hub links every member, and each member links back to the hub so no leaf is orphaned:
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| | Kernel | Lane |
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| |---|---|
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| | [`szl-kernels`](https://huggingface.co/SZLHOLDINGS/szl-kernels) | **hub** — unified suite, cross-kernel `UnifiedReceiptChain` |
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| | [`szl-governed-norm`](https://huggingface.co/SZLHOLDINGS/szl-governed-norm) | RMSNorm/LayerNorm + SHA3-256 receipts |
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| | **`szl-lambda-gate`** (this repo) | **advisory Λ gate (Conjecture 1, OPEN)** |
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| | [`governed-inference-meter`](https://huggingface.co/SZLHOLDINGS/governed-inference-meter) | MEASURED-joule energy accounting (NVML) |
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| | [`szl-govsign`](https://huggingface.co/SZLHOLDINGS/szl-govsign) | signed governance attestation (DSSE / in-toto) |
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| | [`szl-blocked`](https://huggingface.co/SZLHOLDINGS/szl-blocked) | honest-BLOCKED state + EU AI Act Annex IV DRAFT |
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| | [`szl-provctl`](https://huggingface.co/SZLHOLDINGS/szl-provctl) | provenance-DAG verify + in-toto/SLSA interop |
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|
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| **Live Spaces:** [a11oy](https://huggingface.co/spaces/SZLHOLDINGS/a11oy) · [hatun-mcp](https://huggingface.co/spaces/SZLHOLDINGS/hatun-mcp).
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|
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| **Related — Governed Kernels collection:** [Governed Kernels — verifiable AI building blocks](https://huggingface.co/collections/SZLHOLDINGS/governed-kernels-verifiable-ai-building-blocks-6a41d3936cfce4fba83ce378) groups the whole family in one page. **Live console:** [a11oy](https://szlholdings-a11oy.hf.space) · [a-11-oy.com](https://a-11-oy.com) · [llm-router](https://szlholdings-llm-router-live.hf.space) · [receipt verifier](https://szlholdings-governed-receipt-verifier.static.hf.space) · [receipt spec (hub)](https://github.com/szl-holdings/governed-receipt-spec).
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|
|
|
|
| ---
|
|
|
| <sub><b>SZL Holdings</b> · Λ governance aggregator · advisory, not proven trust · <a href="https://a-11-oy.com">a-11-oy.com</a> · <a href="https://github.com/szl-holdings">github.com/szl-holdings</a> · <a href="https://huggingface.co/SZLHOLDINGS">huggingface.co/SZLHOLDINGS</a></sub>
|
|
|
| ---
|
|
|
| [](https://doi.org/10.5281/zenodo.19944926)
|
|
|
| ## Citation
|
|
|
|
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| **Cite this.** Part of the SZL Holdings *Ouroboros Thesis* (Governed Post-Determinism).
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| Concept DOI (always-latest): [10.5281/zenodo.19944926](https://doi.org/10.5281/zenodo.19944926).
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| Author: Stephen P. Lutar Jr. · [ORCID 0009-0001-0110-4173](https://orcid.org/0009-0001-0110-4173) · License CC-BY-4.0.
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| Full DOI-pinned lineage (v1→v26) + the 8 papers: [szl-papers PAPERS_INDEX](https://github.com/szl-holdings/szl-papers/blob/main/PAPERS_INDEX.md).
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| No artifact-specific DOI is minted for this model; the concept DOI above covers the program.
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|
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| Honesty (Doctrine v11): Λ unconditional uniqueness is **Conjecture 1** (machine-checked FALSE as stated) — never a theorem; conditional uniqueness is **Theorem U** (axiom-free). Locked-proven formulas = **exactly 8** {F1,F4,F7,F11,F12,F18,F19,F22}; ~185 experimental theorems are a separate CI-green tier; Khipu BFT safety = Conjecture 2. Trust never 100%.
|
|
|
| ```bibtex
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| @misc{lutar_szl_ouroboros,
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| author = {Lutar, Stephen P., Jr.},
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| title = {SZL Holdings --- The Ouroboros Thesis (Governed Post-Determinism)},
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| year = {2026},
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| publisher = {Zenodo},
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| doi = {10.5281/zenodo.19944926},
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| url = {https://doi.org/10.5281/zenodo.19944926},
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| note = {Concept DOI --- always resolves to the latest version. ORCID 0009-0001-0110-4173. CC-BY-4.0.}
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| }
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| ```
|
|
|
| *Signed-off-by: Stephen Lutar <stephenlutar2@gmail.com>*
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|
|
| ## Files in this repo
|
|
|
| | Path | What it is |
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| |---|---|
|
| | `build/torch-universal/szl_lambda_gate/__init__.py` | public API — `lambda_aggregate`, `lambda_gate`, `selfcheck()` |
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| | `build/torch-universal/szl_lambda_gate/_lambda.py` | the weighted-geometric-mean aggregator + A1–A4 empirical checks |
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| | `build/torch-universal/szl_lambda_gate/layers.py` | `nn.Module` wrapper |
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| | `build.toml` · `metadata.json` | Kernel Hub build/metadata manifests |
|
| | `LICENSE` · `SECURITY.md` | Apache-2.0 · security policy |
|
|
|
| ---
|
|
|
| <p align="center">
|
| <a href="https://huggingface.co/SZLHOLDINGS">SZL Holdings</a> ·
|
| <a href="https://a-11-oy.com">a-11-oy.com</a> ·
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| <a href="https://huggingface.co/SZLHOLDINGS/szl-kernels">szl-kernels</a>
|
| </p>
|
|
|
| <p align="center"><sub>SLSA: L1 honest · L2 attested · L3 roadmap. Λ = Conjecture 1. Trust ceiling 0.97.</sub></p>
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|
|
