In a few words
In a few words
Short texts to enter Persistence Theory without reading the full monograph. Each starts in plain mode, pushes one notch deeper in standard mode, and links to the precise results for the rest.
The idea in 5 minutes
PT starts from a simple question: what persists when a structure passes through constraints? The sieve, physics, and chemistry then become places where that principle can be computed.
Fundamental questions PT addresses
A plain-language map of the questions PT explains, reframes, or dissolves: time, relativity, cosmology, chemistry, nuclear physics, and the Standard Model, with epistemic status.
PT predictions
The registry of predictions, explanatory reconstructions, and negative predictions: neutrinos, Higgs, g−2, αs, superheavy elements, chemistry, nuclear physics, and emerging signals.
Being and having, addition and multiplication
The being / having dyad is more than a metaphor: it is inscribed in arithmetic itself. Additive position vs multiplicative factorisation, and PT as a cosmology of the passage between the two.
The Principles of PT
Why is Persistence Theory so rigid? This page collects the methodological rules that block tuning: no fitted parameters, justified coefficients, unique routes, negative predictions, and PT-derived corrections.
Persistence Theory through geometry
A pedagogical reading of the PT chain: the sieve as a filter, primes as resonance points, and geometric form as the carrier of space, time, and observables.
Primes are the waves that persist
Each integer is a discrete wave on the circles Z/pZ. The primes are the self-coherent superpositions that survive the sieve’s interference. An intuitive reading of BA5, T1 and L0 — with a guard-rail against a common mistake.
Why three dimensions?
Space does not have three dimensions by accident. PT gives an arithmetic reason: there are exactly three active primes at the reduced attractor — $\{3, 5, 7\}$ — and each opens one direction.
Life is a filter of the cascade
A living being is not a thing in which life happens. It is a structure that persists: a localised node of the informational landscape that resists dispersion by stacking several layers of filters. And the moment that filter starts looking at itself, something changes.
Where does $\alpha_{\mathrm{EM}} = 1/137$ come from?
The fine-structure constant is not measured in PT, it is computed. Three sines squared, one product, one dressing. Here are the three steps.
Where does s = 1/2 come from?
Why the only input of the model, the fundamental symmetry s = 1/2, is not a choice but a forced arithmetic consequence. A guided tour of theorem T1 (mod-3 forbidden transitions).
Why does the periodic table have this shape?
The sequence 2, 8, 8, 18, 18, 32, 32 is not merely memorized in PT: it is derived from s, p, d, f channels, spin, and sieve depth.
The q⁺ / q⁻ bifurcation: why two branches?
At μ* = 15, the sieve splits into two natural branches: q⁺ for couplings (vertex, leptons, α_EM), q⁻ for geometry (propagator, quarks, metric). Why this bifurcation is unavoidable and what it separates.
What is persistence?
The word "persistence" has a precise technical meaning in PT: it is the structured part of information, in bits, that resists mixing. Here is how it is defined and why it is conserved.
Where does gravity come from?
Gravity is not an attractive force — it is the slope of an informational landscape. To understand this, you first need to know what an information is, then what a persistence landscape is, and then see that its relief is exactly what Einstein's equations describe.
What is an echo prime?
At μ* = 15, the primes {3, 5, 7} are active and shape physics. But what about {11, 13}? They stay: they dress α_EM and supply what ΛCDM calls "dark matter".
Ramanujan, Mihailescu, and the $p = 3$ channel
Ramanujan's famous nested radical for 3 hides a unique arithmetic singularity: its first level is a Catalan identity. Mihailescu's theorem (2002) guarantees this is the only case in the whole family. And PT uses exactly the same brick to force N_gen = 3.
Why three fermion generations?
We observe three families of quarks and leptons, not two, not four. The Standard Model takes that 3 as given. PT derives it.
The 28 PT predictions in 5 minutes
A quick read of the Tier-1 register: 4 fundamental predictions, 6 numerical, 5 negative, 13 advanced. Each prediction has an explicit refutation criterion and an experiment that will test it within ten years.
What is a bridge in PT?
A fundamental theory must say where pure theorem ends and physical identification begins. PT bridges exist precisely to keep that boundary visible.
Quasi-Perelman: PT as Asymptotic Expanding Soliton
PT's Fisher–Bianchi metric is a quasi-soliton expanding Ricci soliton whose constant $\lambda(\mu) = -1/\mu^4 + O(1/\mu^5)$ vanishes asymptotically (coefficient $-1$ exact, pair-independent). This nonzero residue co-occurs with the entropic arrow of PT-time — two independent signatures of the same dynamical non-triviality of the sieve.
The persistence curve: when arithmetic selects a unique geometry
There exists one and only one algebraic curve in the Kontsevich–Norbury class satisfying PT's three arithmetic coherence conditions. This is the **persistence curve**, of genus $\mu^* - 1 = 14$ — PT's first non-trivial topological invariant, derived without any tuned parameter.
After the bit: why the future of computing will be continuous
Binary will not disappear. It will change status: no longer the primitive atom of computation, but the stable point where a continuous dynamics becomes readable. A PT-inspired hypothesis about analog chips, attractor-based computing, and artificial self-reflection.