The Process That Forgets: Fokker and Planck's Truncated Series, Priced

In 1914 and 1917 Fokker and Planck produced the founding equation of stochastic dynamics: evolve a probability instead of a trajectory, with a drift term and a diffusion term and nothing else. I credit the equation at full strength — where a process is genuinely diffusive it is the physics, and a century of exact service stands behind it. What I evaluate is the derivation status of its two layers: the process is taken Markovian, its future fixed by its present alone, and its transition distribution is truncated at second order, every Kramers-Moyal coefficient above the diffusion term deleted — neither layer derived from the underlying dynamics in 1914/1917. My bench grants the Markov layer for free (its declared birth-death jump process is Markov by construction) and charges the whole value to the truncation: the first deleted coefficient D_3(0) = 0.166667 is 0.333333 of the kept D_2(0) = 0.500000; the truncated stationary law differs from the exact Poisson law by L1 = 0.040395, overstates mu_4 by +0.500000, and parks 0.142877 of its mass on negative counts that cannot exist — nonzero at every finite RHO in the scan, zero only in a limit the papers do not state. Counted plainly: 1 assumed step in 2 layers, 0 derivations in 1914/1917 of either. Grade: REASON FOUND / STILL TURNING — PREMISE-ONLY, explicitly not a kill and not a falsification. Program headline: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-06
DOI
https://doi.org/10.5281/zenodo.24012429
Primary Topic
Probability and Statistical Research
Type
preprint
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preprint

The Process That Forgets: Fokker and Planck's Truncated Series, Priced

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Probability and Statistical Research
preprint

The Process That Forgets: Fokker and Planck's Truncated Series, Priced

William Alexander Aldred
preprint en

Abstract

In 1914 and 1917 Fokker and Planck produced the founding equation of stochastic dynamics: evolve a probability instead of a trajectory, with a drift term and a diffusion term and nothing else. I credit the equation at full strength — where a process is genuinely diffusive it is the physics, and a century of exact service stands behind it. What I evaluate is the derivation status of its two layers: the process is taken Markovian, its future fixed by its present alone, and its transition distribution is truncated at second order, every Kramers-Moyal coefficient above the diffusion term deleted — neither layer derived from the underlying dynamics in 1914/1917. My bench grants the Markov layer for free (its declared birth-death jump process is Markov by construction) and charges the whole value to the truncation: the first deleted coefficient D_3(0) = 0.166667 is 0.333333 of the kept D_2(0) = 0.500000; the truncated stationary law differs from the exact Poisson law by L1 = 0.040395, overstates mu_4 by +0.500000, and parks 0.142877 of its mass on negative counts that cannot exist — nonzero at every finite RHO in the scan, zero only in a limit the papers do not state. Counted plainly: 1 assumed step in 2 layers, 0 derivations in 1914/1917 of either. Grade: REASON FOUND / STILL TURNING — PREMISE-ONLY, explicitly not a kill and not a falsification. Program headline: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.

Zenodo (CERN European Organization for Nuclear Research)
Probability and Statistical Research
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