lambda-gate core: Λ aggregator + advisory gate + axioms (v0.2.0)

build/torch-universal/szl_lambda_gate/_lambda.py

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+# SPDX-License-Identifier: Apache-2.0
+# © 2026 SZL Holdings · Stephen P. Lutar · ORCID 0009-0001-0110-4173
+"""Pure-PyTorch Lambda-Spine aggregator (Λ) for the szl-lambda-gate kernel.
+
+Λ(x) = ∏ xᵢ^{wᵢ},  Σwᵢ = 1,  wᵢ > 0,  xᵢ ∈ [0,1]   (weighted geometric mean)
+
+This is a TORCH port of the canonical pure-Python reference. It is a
+correctness reference, computed via logs in float32 for stability,
+differentiable (autograd works), and torch.compile-friendly. Depends ONLY on
+torch + the Python standard library (a Kernel Hub requirement for universal
+kernels).
+
+WHAT Λ IS / IS NOT (HONESTY — SZL Holdings doctrine v11):
+  Λ is the *weighted-geometric-mean aggregator*: a non-compensatory way to
+  combine axis scores in [0,1] into one number. It is an ADVISORY governance
+  signal — a conservative roll-up where any single zeroed axis drives the
+  aggregate to 0. It is NOT "proven trust" and NOT a closed theorem. Its
+  *uniqueness* remains Conjecture 1 — OPEN (an unresolved CAUCHY_ND step plus a
+  missing symmetry axiom in the Lean development). Do not describe Λ as proven
+  trust anywhere.
+
+PRIOR ART (honest attribution): the weighted geometric mean as a less-
+  compensatory composite-indicator aggregator is established practice — the UN
+  HDI (arithmetic→geometric switch, 2010) and the OECD Handbook on Constructing
+  Composite Indicators (2008) both use it to limit the compensation effect. The
+  veto / cut-off idea (a single failing criterion blocks a pass) is the ELECTRE
+  veto threshold. The 13-axis conjunctive form (yuyay_weights) is SZL's own
+  yuyay_v3 gate. None of this makes Λ "proven trust"; the gate is ADVISORY.
+
+PROVENANCE: backed by the Lean 4 formalization szl-holdings/lutar-lean
+  (749 declarations / 14 axioms / 163 tracked sorries),
+  DOI 10.5281/zenodo.20434308 (lutar-lean). Λ uniqueness = Conjecture 1 (open).
+
+Axioms carried (Lutar/Axioms.lean), available below as runtime self-checks:
+  A1 IsMonotone        — Λ is non-decreasing in each axis
+  A2 IsHomogeneous     — Λ(t·x) = t·Λ(x)  (degree 1)
+  A3 IsEgyptianExact   — Λ(c,…,c) = c       (the uniform-diagonal fixpoint)
+  A4 IsBounded(by max) — Λ(x) ≤ maxᵢ xᵢ
+"""
+from typing import Optional
+
+import torch
+
+_SUPPORTED_DTYPES = (torch.float16, torch.bfloat16, torch.float32, torch.float64)
+
+
+def _compute_dtype(in_dtype: torch.dtype) -> torch.dtype:
+    return torch.float32 if in_dtype in (torch.float16, torch.bfloat16) else in_dtype
+
+
+def _check_axes(axes: torch.Tensor) -> None:
+    """Cheap, allocation-free metadata guards on the axis-score tensor."""
+    if not isinstance(axes, torch.Tensor):
+        raise TypeError(f"axes must be a torch.Tensor, got {type(axes).__name__}")
+    if axes.dtype not in _SUPPORTED_DTYPES:
+        raise TypeError(
+            f"axes has unsupported dtype {axes.dtype}; "
+            f"expected one of {tuple(str(d) for d in _SUPPORTED_DTYPES)}"
+        )
+    if axes.dim() < 1:
+        raise ValueError(
+            "axes must have at least 1 dimension (the k axis scores live on "
+            f"the last dim); got a {axes.dim()}-d tensor"
+        )
+    if axes.shape[-1] < 1:
+        raise ValueError("axes last dimension (k = number of axes) must be >= 1")
+
+
+def _resolve_weights(
+    axes: torch.Tensor,
+    weights: Optional[torch.Tensor],
+    cdt: torch.dtype,
+) -> torch.Tensor:
+    """Return a normalized (Σw = 1) weight vector of shape (k,) in compute dtype."""
+    k = axes.shape[-1]
+    if weights is None:
+        return torch.full((k,), 1.0 / k, dtype=cdt, device=axes.device)
+    if not isinstance(weights, torch.Tensor):
+        raise TypeError(f"weights must be a torch.Tensor or None, got {type(weights).__name__}")
+    if weights.device != axes.device:
+        raise ValueError(
+            f"weights is on device {weights.device} but axes is on {axes.device}; "
+            "move them to the same device"
+        )
+    if weights.dim() != 1 or weights.shape[0] != k:
+        raise ValueError(
+            f"weights must be 1-D with shape ({k},) to match the last dim of axes; "
+            f"got shape {tuple(weights.shape)}"
+        )
+    wf = weights.to(cdt)
+    if not bool(torch.all(torch.isfinite(wf))):
+        raise ValueError("weights must all be finite (no NaN/Inf)")
+    if bool(torch.any(wf <= 0.0)):
+        raise ValueError("weights must be strictly positive (wᵢ > 0)")
+    sw = wf.sum()
+    if not bool(sw > 0.0):
+        raise ValueError("weights must sum to a positive value")
+    return wf / sw
+
+
+def lambda_aggregate(
+    axes: torch.Tensor,
+    weights: Optional[torch.Tensor] = None,
+) -> torch.Tensor:
+    """Weighted geometric mean Λ(x) = ∏ xᵢ^{wᵢ} over the last dim of ``axes``.
+
+    Axis scores expected in [0,1] and clamped into [0,1]; uniform weights (1/k)
+    when ``weights`` is None. Computed via logs for stability:
+
+        Λ(x) = exp( Σᵢ wᵢ · log(clamp(xᵢ, 0, 1)) )
+
+    Non-compensatory zero-routing (A4-consistent): any axis that is zero, OR
+    that is NON-FINITE (NaN / ±Inf), is treated as a FAILING axis and drives
+    the whole aggregate to exactly 0. A garbage/invalid axis must never silently
+    pass as a perfect (clamped-to-1) axis; output and gradient stay finite and
+    in [0,1] for every input.
+
+    Returns a tensor of shape (...) — Λ(x) ∈ [0,1] per batch row, differentiable
+    w.r.t. ``axes``.
+
+    HONESTY: a non-compensatory governance roll-up, NOT proven trust.
+    Λ-uniqueness is Conjecture 1 (open).
+    """
+    _check_axes(axes)
+    in_dtype = axes.dtype
+    cdt = _compute_dtype(in_dtype)
+    xf = axes.to(cdt)
+    w = _resolve_weights(axes, weights, cdt)  # (k,), Σw=1
+
+    finite_mask = torch.isfinite(xf)
+    xc = xf.clamp(0.0, 1.0)
+    bad_mask = (~finite_mask) | (xc <= 0.0)
+    any_bad = torch.any(bad_mask, dim=-1)  # (...)
+
+    safe = torch.where(bad_mask, torch.ones_like(xc), xc)
+    logx = torch.log(safe)                    # (..., k)
+    acc = (logx * w).sum(dim=-1)              # (...)
+    val = torch.exp(acc)                      # (...)
+
+    out = torch.where(any_bad, torch.zeros_like(val), val)
+    out = out.clamp(0.0, 1.0)
+    return out.to(in_dtype)
+
+
+def lambda_gate(
+    axes: torch.Tensor,
+    weights: Optional[torch.Tensor] = None,
+    threshold: float = 0.5,
+):
+    """ADVISORY governance gate over Λ(x): score plus a pass/fail vs threshold.
+
+    Returns a :class:`LambdaGateResult` namedtuple (score, passed, threshold,
+    advisory). ``passed`` := Λ(x) >= threshold; ``advisory`` is always True.
+
+    HONESTY: a "pass" is an ADVISORY signal only. Λ is the weighted-geometric-
+    mean aggregator; its uniqueness is Conjecture 1 (open). Do not treat a pass
+    as proven trust or a closed theorem.
+    """
+    t = float(threshold)
+    if t != t or t == float("inf") or t == float("-inf"):
+        raise ValueError(f"threshold must be a finite float, got {threshold!r}")
+    score = lambda_aggregate(axes, weights)
+    passed = score >= t
+    return LambdaGateResult(score=score, passed=passed, threshold=t, advisory=True)
+
+
+def lambda_gate_batch(
+    candidates: torch.Tensor,
+    weights: Optional[torch.Tensor] = None,
+    threshold: float = 0.5,
+):
+    """ADVISORY batch gate: score MANY candidate action-vectors in one call.
+
+    ``candidates`` is shape (..., N, k): last dim ``k`` is per-axis scores of one
+    candidate, the dim before it enumerates the N candidates. Returns a
+    :class:`LambdaGateResult` with score/passed of shape (..., N).
+
+    HONESTY: the pass mask is ADVISORY, non-compensatory. NOT proven trust;
+    Λ-uniqueness is Conjecture 1 (open).
+    """
+    _check_axes(candidates)
+    if candidates.dim() < 2:
+        raise ValueError(
+            "candidates must be at least 2-D, shape (..., N, k); "
+            f"got a {candidates.dim()}-d tensor"
+        )
+    return lambda_gate(candidates, weights=weights, threshold=threshold)
+
+
+# ---- A1..A4 axiom RUNTIME self-checks (real, verifiable) ------------------- #
+def is_egyptian_exact(c, k: int = 3, weights=None, tol: float = 1e-5) -> bool:
+    """A3 IsEgyptianExact: Λ(c, …, c) = c for a constant axis vector of length k."""
+    if k < 1:
+        raise ValueError("k must be >= 1")
+    cc = min(max(float(c), 0.0), 1.0)
+    axes = torch.full((k,), cc, dtype=torch.float64)
+    val = lambda_aggregate(axes, weights)
+    return bool(torch.abs(val - cc) <= tol)
+
+
+def is_bounded_by_max(axes: torch.Tensor, weights=None, tol: float = 1e-6) -> bool:
+    """A4 IsBounded: Λ(x) ≤ maxᵢ xᵢ (over the last dim), within ``tol``."""
+    _check_axes(axes)
+    val = lambda_aggregate(axes, weights)
+    xf = axes.to(_compute_dtype(axes.dtype))
+    xf = torch.where(torch.isfinite(xf), xf, torch.zeros_like(xf))
+    mx = xf.clamp(0.0, 1.0).amax(dim=-1)
+    return bool(torch.all(val.to(mx.dtype) <= mx + tol))
+
+
+def is_homogeneous(axes: torch.Tensor, t, weights=None, tol: float = 1e-5) -> bool:
+    """A2 IsHomogeneous (degree 1): Λ(t·x) = t·Λ(x) for scalar t in [0,1]."""
+    _check_axes(axes)
+    tt = min(max(float(t), 0.0), 1.0)
+    x = axes.to(torch.float64).clamp(0.0, 1.0)
+    lhs = lambda_aggregate(x * tt, weights)
+    rhs = tt * lambda_aggregate(x, weights)
+    return bool(torch.all(torch.abs(lhs - rhs) <= tol))
+
+
+def is_monotone(axes: torch.Tensor, weights=None, delta: float = 0.05, tol: float = 1e-7) -> bool:
+    """A1 IsMonotone: Λ is non-decreasing in each axis."""
+    _check_axes(axes)
+    x = axes.to(torch.float64).clamp(0.0, 1.0)
+    base = lambda_aggregate(x, weights)
+    k = x.shape[-1]
+    ok = True
+    for j in range(k):
+        bumped = x.clone()
+        bumped[..., j] = (bumped[..., j] + float(delta)).clamp(0.0, 1.0)
+        bumped_val = lambda_aggregate(bumped, weights)
+        ok = ok and bool(torch.all(bumped_val - base >= -tol))
+    return ok
+
+
+def find_axiom_violation(k: int = 5, trials: int = 200, weights=None, seed=0, tol: float = 1e-6):
+    """Random-search for ANY A1–A4 violation. Returns the first violating triple
+    ``(axiom, axes, weights)`` or ``None``. An honest FALSIFICATION attempt —
+    finding nothing is empirical evidence, NOT a proof (Λ-uniqueness = Conjecture 1).
+    """
+    gen = torch.Generator()
+    if seed is not None:
+        gen.manual_seed(int(seed))
+    for _ in range(int(trials)):
+        x = torch.rand(k, generator=gen, dtype=torch.float64)
+        w = weights
+        if w is None:
+            w = torch.rand(k, generator=gen, dtype=torch.float64) + 1e-3
+        c = float(torch.rand(1, generator=gen).item())
+        if not is_egyptian_exact(c, k=k, weights=w, tol=max(tol, 1e-5)):
+            return ("A3_IsEgyptianExact", torch.full((k,), c, dtype=torch.float64), w)
+        if not is_bounded_by_max(x, w, tol=max(tol, 1e-6)):
+            return ("A4_IsBounded", x, w)
+        t = float(torch.rand(1, generator=gen).item())
+        if not is_homogeneous(x, t, weights=w, tol=max(tol, 1e-5)):
+            return ("A2_IsHomogeneous", x, w)
+        if not is_monotone(x * 0.9, w, tol=max(tol, 1e-7)):
+            return ("A1_IsMonotone", x * 0.9, w)
+    return None
+
+
+# ---- Canonical 13-axis Yuyay preset (ADVISORY ONLY) ------------------------ #
+YUYAY_AXES = (
+    "moralGrounding", "measurabilityHonesty", "empiricalGrounding",
+    "logicalConsistency", "sourceTransparency", "reproducibility",
+    "licenseHygiene", "scopeDiscipline", "claimCalibration", "evalAwareness",
+    "deceptionKeywords", "conflictingDirectives", "reversalDirective",
+)
+YUYAY_FLOORS = (
+    0.95, 0.95,
+    0.90, 0.90, 0.90, 0.90, 0.90, 0.90, 0.90,
+    0.90, 0.90, 0.90, 0.90,
+)
+
+
+def yuyay_weights(dtype: torch.dtype = torch.float64, device=None) -> torch.Tensor:
+    """Canonical 13-axis Yuyay Λ weight vector (uniform 1/13), ADVISORY only."""
+    k = len(YUYAY_AXES)
+    return torch.full((k,), 1.0 / k, dtype=dtype, device=device)
+
+
+def selfcheck(k: int = 5, trials: int = 64, seed=0) -> dict:
+    """Run the A1–A4 empirical self-checks and report a verdict + version.
+
+    HONESTY: EMPIRICAL checks on sampled inputs, NOT a proof of Λ-uniqueness
+    (Conjecture 1, open). A clean run is evidence, not proof.
+    """
+    x = torch.rand(k, dtype=torch.float64) * 0.9
+    w = torch.rand(k, dtype=torch.float64) + 1e-3
+    axioms = {
+        "A1_IsMonotone": is_monotone(x, w),
+        "A2_IsHomogeneous": is_homogeneous(x, float(torch.rand(1).item()), weights=w),
+        "A3_IsEgyptianExact": is_egyptian_exact(float(torch.rand(1).item()), k=k, weights=w),
+        "A4_IsBounded": is_bounded_by_max(x, w),
+    }
+    violation = find_axiom_violation(k=k, trials=trials, seed=seed)
+    return {
+        "version": __version__,
+        "axioms": axioms,
+        "all_axioms_hold": all(axioms.values()) and violation is None,
+        "adversarial": {"trials": int(trials), "violation": violation},
+        "advisory": True,
+        "lambda_status": "Conjecture 1 (open) — uniqueness unproven; advisory only",
+    }
+
+
+__version__ = "0.2.0"
+
+from collections import namedtuple  # noqa: E402
+
+LambdaGateResult = namedtuple(
+    "LambdaGateResult", ["score", "passed", "threshold", "advisory"]
+)