The Theory of Persistence
What persists is what remains under constraint.
In one sentence: what persists is not what remains by inertia, but what remains after admissible constraints. What dissipates becomes entropy; what persists becomes structure, then observable.
The core idea is simple. Any system can take many forms. Some resist the constraints acting on it; others dissipate. What resists — the structure that survives the constraints — is what PT calls persistence. What dissipates becomes entropy. At every scale, this split is exact: nothing vanishes, everything distributes between these two sides. Physical observables measure that distribution.
PT then tests this principle across three broad registers. In mathematics, persistence appears in the sieve of Eratosthenes: prime numbers and the gaps between them are the minimal survivors of an elementary constraint. In physics, it fixes constants, masses, geometry, and time. In chemistry, it explains periods, shells, ionization energies, and electron affinities. Technical details remain available via the depth selector (bottom right), but the natural entry is the idea: first understand what “persisting” means.
The persistence points
The sieve serves as an exact laboratory: survivors, gaps, GFT, and theorems show how a constraint produces stable structures.
PhysicsThe principle tested
Couplings, masses, angles, time, and geometry: PT compares its persistent structures with physical measurements.
ChemistryShell persistence
The sequence 2, 8, 8, 18, 18, 32, 32 becomes a consequence of persistent channels, spin doubling, and internal shells.
ChemistryIonization energies
PT reconstructs peaks, closures, and relativistic residuals through a continuous reading of channels and radial depth.
ChemistryElectron affinities
EA becomes a capture energy at the channel boundary, with a PT calculator, full table, and three-level depth reading.
Technical note
The formal framework comprises base bridge axioms (BA0–BA2) that identify the dynamical field with the gaps between consecutive primes, then derived bridges (BA3–BA5) promoted or constrained in the chain, and a cascade of seven theorems (T0 → T6) deriving the holonomy angles sin²(θ_p) = δ_p(2 − δ_p) and the anomalous dimensions γ_p, and theorem T5 closing the fixed point μ* = 15 by exact rational exhaustion. The identity log₂(m) = D_KL(P‖U_m) + H(P) (GFT) is the fundamental principle of persistence: total informational capacity is conserved and partitions exactly into persistence and entropy.
T0 → T6, GFT, L0 — complete chain, zero drift across versions.
43 observables, mean error 0.30%, median 0.06%, zero fit.
Canonical registry: 45 companion script entries, 2,522/2,523 passing checks — flagship scripts runnable in the browser.
PT sub-projects
Three public repos applying PT to specific domains.
PT Mathematics (PTM)
Five self-contained articles (M1–M5) on the mathematical foundations of PT — from the sieve of Eratosthenes to the reconstruction of physics.
Each article = one theorem + companion scripts that verify every statement numerically.
PT Physics (PTP)
Computational proof that PT works: 43 Standard Model observables reproduced from the derived symmetry s = 1/2.
Local HTML dashboard + reproducible companion scripts tracked by Appendix F.
PT Chemistry (PTC)
Computational chemistry engine derived entirely from PT. 0 adjustable parameters; constants descend from the symmetry s = 1/2 and the sieve structure.
Dissociation energies, MAE ≈ 2% (200+ molecules) — aromaticity, σ-bonds, NICS.
Cite this work
If you cite PT in a paper, thesis, or post, the recommended BibTeX entry is below.
@book{senez2026persistence,
author = {Senez, Yan},
title = {The Theory of Persistence: From the Sieve to the Standard Model},
year = {2026},
publisher = {Self-published preprint},
url = {https://www.persistencetheory.org}
}Preprint — not peer-reviewed. Critical scrutiny is welcomed.