PUH Theorem 362 — The Processing Rate Has a Ceiling as Well as a Floor: A Maximum Cannot Flatten a Rotation Curve but Predicts Where Flatness Ends, at the Baryonic Edge

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-17
DOI
https://doi.org/10.5281/zenodo.22803248
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

PUH Theorem 362 — The Processing Rate Has a Ceiling as Well as a Floor: A Maximum Cannot Flatten a Rotation Curve but Predicts Where Flatness Ends, at the Baryonic Edge

Brian Martell
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

PUH Theorem 362 — The Processing Rate Has a Ceiling as Well as a Floor: A Maximum Cannot Flatten a Rotation Curve but Predicts Where Flatness Ends, at the Baryonic Edge

Brian Martell
preprint en

Abstract

Photonic Universe Hypothesis (PUH) — Narrow Prediction with a Negative Result. WHAT THE ARCHIVE ALREADY HAS. T242 (June 2026) establishes that the substrate's processing rate varies with condition and that at a Planck core it falls toward zero: "its processing rate of change falls toward zero. To the external universe — still folding, still processing … processing rates, not two conflicting durations." THE RATE HAS A FLOOR, AND THAT FLOOR MAKES THE REBOUND TRIGGER WORK. This note asks the symmetric question: does it also have a CEILING? THE PARALLEL IS WITH LIGHT. Light slows in a medium and can in principle be halted, but nothing exceeds its vacuum speed. If the rate of time behaves the same way it is slowest where mass is densest, fastest where mass is scarcest, and bounded above. RESULT 362.1: GENERAL RELATIVITY ALREADY HAS EXACTLY THIS STRUCTURE — the clock rate √(1 + 2Φ/c²) is always below unity and approaches it as the potential approaches zero. The structure is right and it is NOT NEW. So the only claim available beyond relativity is that the ceiling is REACHED at finite distance rather than approached asymptotically. RESULT 362.2 (a ceiling cannot flatten a rotation curve — A NEGATIVE RESULT). Gravity is the gradient of the clock rate, g = c² d(dτ/dt)/dr. WHERE THE RATE SATURATES, THE GRADIENT VANISHES AND GRAVITY VANISHES WITH IT: stars beyond the saturation radius would travel in straight lines and leave. And working backwards is decisive — setting g = v²/r and integrating gives dτ/dt = (v²/c²) ln(r) + constant. A FLAT CURVE REQUIRES THE CLOCK RATE TO GROW AS THE LOGARITHM OF RADIUS, AND A LOGARITHM HAS NO MAXIMUM. A ceiling is therefore the OPPOSITE of what flatness requires. RESULT 362.3 (but it predicts where flatness ENDS). Rotation curves are measured to perhaps 50 kpc and nobody knows what lies beyond. If the processing rate saturates, flatness must terminate, and the saturation radius is where. NEITHER ESTABLISHED ALTERNATIVE PREDICTS THIS: modified dynamics gives curves flat indefinitely; a dark-matter halo gives a gentle decline at a virial radius set by formation history rather than by the visible galaxy. The three predictions differ by an order of magnitude in radius. RESULT 362.4 (the threshold that fits, and the one that fails). If the rate saturates where local matter density becomes negligible, the termination radius is simply where the baryons run out — NO NEW PARAMETER. The Milky Way's disc scale length is ~2.6 kpc and its stellar disc ends at 15–20 kpc; the reported onset of Keplerian decline is at ~19 kpc. THE ALTERNATIVE THRESHOLD — saturation at the cosmic mean density — PREDICTS 2,526 kpc AND IS WRONG BY A FACTOR OF 133. That is informative rather than merely negative: THE LATTICE RESPONDS TO LOCAL MATTER, NOT TO THE COSMIC BACKGROUND. And it makes the test a CORRELATION rather than a number: whether the decline radius tracks the baryonic edge from galaxy to galaxy, answerable with existing catalogues — and a smooth spherical halo has no reason to know where the stars stop. CAUTIONS, STATED IN FULL. (1) THE DECLINE IS CONTESTED: globular clusters, blue horizontal branch stars and K giants at large radii indicate a larger enclosed mass than it allows, and a 2026 review calls this a debate rather than a result. (2) THE METHOD ASSUMES A STATIONARY, SYMMETRIC DISC, while the outer Galactic disc is warped, flared, and carries an unrelaxed vertical disturbance. (3) THE THRESHOLD IS ARGUED, NOT DERIVED — "where the mass runs out" is plausibility, and plausibility is not derivation. (4) THE RELATED GENERAL CLAIM IS DISFAVOURED: Renzo's rule was tested across SPARC in 2025 and NOT confirmed, with an excess of rotation-curve features lacking baryonic counterparts. This note's claim is coarser and survives that objection, but the finer version of the same idea did not. KILL-CONDITIONS: (i) if the Keplerian decline is withdrawn, Result 362.4 loses its only support; (ii) if the decline radius shows no correlation with the baryonic edge across a sample, the threshold is wrong; (iii) if rotation curves remain flat well beyond the optical edge in any well-measured system, the ceiling is refuted outright; (iv) if the processing rate has no ceiling at all, the premise is empty. NOT CLAIMED: that this explains flat rotation curves — IT DOES NOT, AND RESULT 362.2 SHOWS A CEILING CANNOT; that the framework accounts for the missing mass; that the saturation threshold is derived; that the Keplerian decline is established; or that this resolves anything about dark matter. THE NOTE PREDICTS ONE THING: THAT FLATNESS TERMINATES, AND WHERE.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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