The General Law of Navigability Perception as Clustering of Recursive Possibility in the Architecture of Freedom Intelligence (A recursive path-space theory of perception)

Abstract

One sentence has been proposed as a law reaching across physics, biology, cognition, collective behaviour and artificial agency: everything follows the lightest path according to its perception. This paper takes the sentence literally, gives each of its words a measurable form, and puts the result under examination. Perception becomes a field over a path space: a normalised, multiplicatively composed distortion carried by every continuation available at a state. Freedom becomes the relation the framework states in full, Perception over Distortion carried to the recursive identity. The perception funnel becomes clustering in phases: a perceiver reads one perception at a time, clusters the options by it, keeps the light cluster, and reads again until one option is left, seeking more perception whenever a reading leaves the set whole. Light closes in one phase, over 20,000 candidate paths, in 200 of 200 runs; a person choosing among forty hospitals closes in three, reading quality, then distance, then whether a doctor is already known. Across sets from three options to three thousand, the number of phases rises by itself from 1 to 7, the option chosen lands within 1.00 to 1.15 times the lightest, and the perceiver reads 20 to 32 per cent of what a full evaluation would read. Seeking more perception brings the median choice to 1.00 times the lightest against 1.36 for a perceiver that guesses, and options held in doubt are clustered like the rest and cost readings rather than accuracy. Twenty perceivers, from a photon to a clinician, are drawn phase by phase. Four further findings follow, each from code that estimates the field before the world runs. Freedom read at the source orders what happens afterwards: across 420 instances, Spearman rho reaches −0.374 against realised distortion and +0.475 against agreement with the realised path, and realised distortion falls from 4.30 times the lightest in the lowest Freedom quintile to 1.51 times in the highest. Lightest names a set rather than a point: two perceivers reading the same state name different lightest continuations in 63.8 per cent of instances, their orderings agree at a Kendall coefficient of 0.467, and the maximal set surviving both readings averages 2.09 members against the single element a total order returns by construction. The perception funnel widens exactly as the plural reading requires, from a mean competitive width of 1.57 at one perceiver to 2.96 at eight. And following redraws the tree: a plan made on the static projection of a history-dependent possibility set stays unfollowable in 89.5 per cent of instances, where the history-carrying recursion stays followable throughout. Set beside these, the scalar reading of lightness reduces to a classical shortest-path computation, which is stated here as a boundary on that reading rather than on the law. Applied unchanged to twenty systems from light crossing an interface to a collective decision, the architecture holds in eleven, strains in six, and reaches its limit in three; each limit is named, including one where a field settled before any agent moves selects the other branch in 400 of 400 simulated trials. A further twenty perceivers, from a photon to a clinician, are read through the same apparatus on one notation of levels, which places a school of fish and a hospital ward on the same scale; and two measurements bound how much of a field a perceiver has to hold, since half a field captures 90 per cent of the improvement the whole field offers and a group of seven carrying no memory reaches on its first pass what a memory-carrying traveller needs eight passes to reach. The verdict is structural universality carrying measured predictive content, with the ordering reading of the law standing where the scalar reading gives way. How every number here was obtained. The perception field is settled from quantities recorded before the first step, the prediction is written down and sealed, and only afterwards does the world run and the realised path arrive. The inference this path occurred, so it was the lightest stays outside the paper entirely. Where a system resists an estimate made in advance, it is recorded as a system awaiting instruments rather than as a system the framework accounts for. The question A claim of universality earns attention in proportion to what would overturn it. The claim examined here reaches across light in vacuum, a bacterium in a gradient, a slime mould on a lattice, a footballer wi Author ORCID: 0009-0008-6255-7724. License: Creative Commons Attribution 4.0 International.