UNNS · Unbounded Nested Number Sequences

UNNS Math Foundations

Volume II shows how every persistent orbit of the collective map closes, scales exactly and selects its surviving carry: — full proofs across — registered statements, with — of — machine checks passing.

—Volume II statements in the registry, beside — in Volume I

—checks passing out of —, rerun from the reproducibility package

—statements with a full proof; — recorded as open

—of — sampled orbits enter their cycle inside the proved bound

Five achievements of Volume II

Each one is a chain of registered theorems; the identifiers point into the registry explorer below.

The registry

Every statement in both volumes is a registered record with a standing, a scope and its dependencies.

Standing of the records

Records per volume, by what has been established.

Where the records sit

Records per chapter, Volume I then Volume II.

Transient bounds and the carry staircase

Chapter 7 makes the transient explicit. The reset-descent bound is sharp; the entry bounds are certified but loose.

Reset descent κ(γ₀) is attained

Carries to the first reset against γ₀ (log scale). Each dot is an exact orbit that needs exactly κ carries.

Observed entry against proved bounds

Carries after the first reset, by prime g (log scale). Dots are sampled orbits; lines are the class-counting and polynomial bounds.

Machine checks

Each square is one check of the reproducibility package; hover or focus a square for the statement it tests.

Registry explorer

The 68 Volume II records with their location in the manuscript. Search, filter by standing and sort any column.

Scope and qualifications

What the results do and do not claim.

Registry — · built — · repository —, — · commit —