SFIT Stochastic-Braid Substrate: Part III - Finite-Carrier Record Formation and the Conditions for Born-Weighted Outcomes: A Structural Analysis
Year: 2026
Type: preprint
Abstract: This deposit contains the manuscript and the three analysis scripts (with outputs and SHA-256 hashes) for Part III of the SFIT Stochastic-Braid Substrate series. The paper separates three objects that are often conflated in attempts to obtain quantum measurement statistics from a classical substrate: (i) the substrate configuration (positions, velocities, helicities of the Part I defects), (ii) the channel population \(x_k \ge 0\), \(\sum_k x_k = 1\), and (iii) the record probability \(P(k)\), i.e. the probability that a physical record names channel \(k\). The Born rule relates (iii) to (ii); it says nothing by itself about how (ii) arises from (i). The paper asks three questions and reports the status of each: 1. Can a shared, finite carrier enforce exclusive records? In a coupled-mode model with explicit local detectors, detector-local back-reaction lowers the gated coincidence parameter from \(\alpha = 1.00\) to \(\alpha = 0.57\text{–}0.60\) at the strongest back-reaction tested, but only when detector thresholds are comparable to the carrier energy. At thresholds one-twentieth of the carrier energy, \(\alpha\) stays at \(0.96\text{–}1.00\). Strong exclusion (\(\alpha < 0.1\)) was not reached in any of 136 configurations. Result: partial suppression only. 2. Under what conditions does record selection reproduce Born weights? Two sufficient routes are identified, each with a precisely quantified fragility. Route 1: exactly memoryless (exponential) detector thresholds give Born frequencies by a common-time-change argument; gamma thresholds of shape 2 depart by TV distance \(0.08\text{–}0.15\). Route 2: a bounded martingale for channel populations absorbed at a vertex gives Born weights for any functional form of the exchange law; a first-passage bound and a converse are proved (given absorption, zero conditional drift is necessary), and a biased exchange kernel is shown to follow the Kimura fixation formula, so zero drift must hold to order \(1/M\) in the number of exchange units. Common-mode noise on the shared carrier cannot substitute for detector-local randomness: with fixed thresholds the largest channel fires first in every run, at every reversal rate. 3. Does Part I supply these conditions? No. The Part I helicity representation acts by permutation matrices, and no permutation action yields zero conditional drift for any filtration unless it is the identity (for pairwise-distinct populations). Measured on the Part I crossing process, the drift is nonzero at every test state, and populations are rearranged but never concentrated; sector populations are exactly invariant. This identifies braiding as neutral with respect to record selection. Scope and caveats. No derivation of the Born rule or of quantum superposition from the substrate is claimed. The internal state \(\psi\) is an input; the exchange kernel of Route 2 is global and postulated; memoryless detector thresholds (Route 1) are assumed; strong exclusion was not achieved; and the first-passage record of Proposition 3 (\(\alpha = 0\) by conservation) has not been combined with local detectors in simulation. Real amplitudes suffice for the single-system statistics studied, but real-amplitude quantum theory is experimentally distinguishable from complex quantum theory in network scenarios. Each result in the manuscript is tagged [DERIVED], [ASSUMED], or [TESTED]. Three scripts produce every number in the paper; each states its model, metrics, controls, predictions and decision rules in its header, fixed before the runs reported. The scripts were not preregistered; this deposit supplies them together with their outputs and hashes to support reproducibility.
Author: Puodzius, Luiz Claudio
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225083704