PT mathematics
Mathematical atlas of persistence
These pages show the mathematical mechanics of PT: the constrained continuum, persistence points, the sieve, GFT, prime cycles, thresholds, and informational applications.
We often picture the numbers as a straight line unfolding forward. PT reads them differently: as soon as residues modulo prime numbers are taken seriously, that line closes into cycles. At increasing depth, the bare line gives way to phase mechanics: discrete points are the remarkable, stable, readable traces of that continuum under constraint.
From principle to demonstrators
The proposed order starts from the general mechanics of survivors, moves through GFT and prime channels, then opens toward visualizations and mathematical/informational applications.
Each page keeps its status visible: identity, theorem, derivation, exploration, or tool. This is deliberate: the site must be clear about what is proved and what is still a research path.
logical map
Mechanics of survivors
How a continuous mechanics of constraints makes remarkable persistence points appear.
Prime gaps and survivor gaps
Reading prime gaps as a limiting case of gaps between sieve survivors.
Why prime numbers?
Why primes appear as irreducible channels of persistence.
The sieve as a dynamics
Reading the sieve not as a mere algorithm, but as a filtration dynamics.
GFT as a mathematical first principle
Understanding $\log_2(m)=D_{KL}+H$ as exact conservation of the information budget.
Discrete-continuous bridge
Why PT does not simply say that the continuum emerges from the discrete.
CRT, holonomy, and cyclic phase
How CRT and cyclic phase force channel products.
Anomalous dimensions
Why $\gamma_p$ measures channel sensitivity and selects active channels.
Riemann and zeta in PT reading
Presenting the PT reading of Riemann as a research programme without overselling a closed proof.
Prime spirals
Using Ulam, Sacks, or Archimedean spirals as visualizations of prime survivors.
Cryptography and one-way functions
Reading easy/hard asymmetry as controlled loss of persistent structure.
Compression and information
Compression as extracting what persists and rejecting what is entropic.
ZKP: proving without revealing
Why zero-knowledge proofs naturally speak about persistence of structure.
Atlas of PT theorems
A reading map distinguishing identities, theorems, bridges, derivations, and validations.
Persistence calculator
Directly manipulating the GFT partition between entropy and persistent information.