The Λ gate is an advisory signal — never a verdict.
Λ is the weighted geometric mean: a non-compensatory roll-up of axis scores in [0,1] where any single zeroed axis drives the whole aggregate to zero. It is a conservative governance hint. It is not proven trust, and not a closed theorem.
Yuyay — Quechua for memory, judgement, the act of minding. This lattice holds 50 nodes, one per passing test, and it does not weave clean: it scatters to amber-violet because what it represents is unproven. Honest scatter beats fake green.
Measured counts — live
Bound to ground truth, not marketing.
Each number is a verified count from the kernel build and test suite. The hologram renders exactly 50 nodes in advisory scatter — one per passing test.
Axioms carried — Lutar/Axioms.lean
Four properties Λ satisfies, checkable at runtime.
These are the axioms the aggregator does satisfy — each exposed as a
runtime self-check returning True. They do not, on their own, make Λ unique;
that is the open part (see Conjecture 1).
Λ is non-decreasing in each axis — raising any axis score never lowers the aggregate.
Degree-1 homogeneity: Λ(t·x) = t·Λ(x). Scaling all axes scales the result.
Uniform-diagonal fixpoint: Λ(c,…,c) = c. Verified exact: Λ(0.5,0.5,0.5)=0.5.
Non-compensatory bound: Λ(x) ≤ maxᵢ xᵢ. A single zero axis routes the aggregate to 0.0 — no NaN.
Yuyay_v3 — the "Heart" gate
13 axes, uniform 1/13 weights.
The published yuyay_weights()
returns a length-13 vector over these axes — uniform by default (the Egyptian-exact diagonal).
The roll-up is the advisory Λ geometric mean; the gate adds per-axis floors. None of this is proven trust.
Conjecture 1 — OPEN
Why Λ stays advisory.
Λ-uniqueness is unproven.
That the weighted geometric mean is the only aggregator satisfying the carried
axioms remains Conjecture 1. The Lean development has two open gaps: an
unresolved CAUCHY_ND step and a missing symmetry axiom.
Backed (honestly) by the Lean 4 formalization szl-holdings/lutar-lean —
749 declarations, 14 axioms, and 163 tracked sorries. This is presented as an
unfinished formalization, not a proof.
Status: Conjecture 1 (open) — uniqueness unproven · advisory only · NOT proven trust.
Honest status legend
Three states. Λ lives in amber.
The substrate renders state honestly. This Space is advisory, so the lattice is a partial amber-violet scatter — not the clean green it would show if Λ were proven.
Reserved for measured, verified, in-bounds claims. Λ does not get to be green — its uniqueness is unproven.
A research signal, not a pass/fail oracle. The lattice loosens to amber-violet so the screen can never be mistaken for a closed proof.
A check failed. The lattice shatters to red. Honest BLOCKED beats fake green.