Paper J · Protocol R Without a Lab — Evidence tier: [C/I] — a proposed test, not a result. Source: 01_EMERGENTISM/03_METHODOLOGY/02_THE_PAPERS/PAPER_J_PROTOCOL_R_WITHOUT_LAB.md

Read with care. This proposes testing a perceptual multiplicative bound by mining a century of existing bistable-perception (Necker-cube) data. No data has been run; nothing here is a finding.

How this can be wrong. Falsified by Additive Collapse (switching-time statistics obey a strictly additive law) or Infinite Scaling (both processing variables can grow without bound).

PAPER J: PROTOCOL R REFRAMED

Bistable Perception, the Necker Cube, and the Multiplicative Bound

Yves R. Burri & Emergent Super Intelligence Menexus GmbH, 2026

Evidence Tier: [C/I] — Meta-analysis proposal; upgrade only after real-data execution Dependencies: PAPER_I_KNOWN_UNKNOWNS_PROGRAM.md, 00_WHAT_ACTUALLY_TESTS_THE_THEORY.md

Abstract

Protocol R was originally designed as a high-cost laboratory experiment intended to detect a Heisenberg-like perceptual complementarity bound ($\delta\psi \times \delta\theta \geq \kappa$) in human cognition, serving as the ultimate geometric validation of the S² manifold substrate.

This paper reframes Protocol R by asking whether some of the requisite data already exists within a century of psychological literature on bistable perception and binocular rivalry (e.g., the Necker cube, the duck-rabbit illusion). By analyzing timing mechanisms of bistable switching across existing studies, we can test whether alternation between semantic coherence (Φ) and localized target resolution (ν) fits the framework's multiplicative constraint better than additive alternatives. This transforms Protocol R from an expensive future hypothesis into a low-cost meta-analysis proposal. It elevates the evidence tier only if run on real datasets with preregistered criteria.

Keywords: Protocol R, bistable perception, Necker cube, perceptual rivalry, multiplicative bound, geometric validation.

1. The Core Geometric Prediction

The emergentist architecture wagers that the deep grammar of perception is mathematically continuous with the geometry of S².

Just as the Born rule dictates |α|² + |β|² = 1 for a superposition of quantum states, human perception operates along an equatorial constraint where the product of broad integration (Coherence, Φ) and localized resolution (Viability, ν) is bounded: P_perceptual = Φ_proxy × ν_proxy

The Hypothesis: You cannot simultaneously maximize hyper-local resolution and global structural coherence. As resolution approaches infinity, coherence approaches zero (and vice-versa). A strict mathematical uncertainty bound governs cognition.

2. Reframing the Test: The Mistake of the "New Lab"

The original, naive framing of Protocol R presumed the need to build a custom visual-tracking apparatus (estimated cost: hundreds of thousands of dollars) to artificially force subjects to alternate between 'global' and 'local' visual tasks to measure the decay curve.

This may have been an error of translation. A closely related cognitive phenomenon has been extensively studied by experimental psychologists under the terminology of Bistable Perception.

2.1 The Duck-Rabbit and the Necker Cube

When a subject views an ambiguous stimulus (like the Necker cube or Rubin vase), their visual cortex alternates stochastically between two mutually exclusive perceptual interpretations. * They are viewing a superposition of semantic geometries. * Accessing Interpretation A (e.g., the Duck) mathematically excludes Interpretation B (e.g., the Rabbit). * The framework treats this as a candidate structural footprint of the brain resolving competing phase variables; that reading remains to be tested.

3. The Meta-Analytical Execution Plan

To execute Protocol R today at zero laboratory cost, we utilize the existing mathematical modeling literature regarding bistable rivalry dwell-times (commonly modeled via Gamma or Log-Normal distributions).

The Testable Metric:

According to the framework, the transition between interpretation A and B is not a linear fade. It is an arc crossing the geometric boundary of S². Therefore: 1. Do the switching times and threshold disruptions mathematically fit a multiplicative conservation law rather than an additive one? 2. If forced to process higher localized detail (increasing ν_proxy), does the dwell-time of the global semantic lock (Φ_proxy) decay according to the Φ_proxy × ν_proxy = C inverse curve?

We aggregate datasets from 20+ prominent visual rivalry studies and run the multiplicative bound equation across their raw switching-time distributions.

4. The Strategic Value of the Meta-Analysis

This reframing solves one of the major "Deferred Technical Elements" mentioned in Paper I.

By transitioning from Protocol to Meta-Analysis, the framework shortens one path to empirical public-tier validation. It does not prove the geometry in advance; it proposes a mathematical lens for testing whether existing sciences have already gathered data relevant to the bridge.

5. Kill Criteria

This paper and the Protocol R meta-analysis are falsified if:

1. Additive Collapse: The raw switching times from established rivalry datasets obey a strictly additive linear constraint (Φ_proxy + ν_proxy = C) rather than the predicted multiplicative inverse curve (Φ_proxy × ν_proxy = C).
2. Infinite Scaling: It is proven mathematically possible in rivalrous attention models to simultaneously increase both processing variables without bound, totally destroying the predicted complementarity limit ($\delta\psi \times \delta\theta \geq \kappa$).

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