KTLean

KTLean is a Lean 4 formalization of Kosmoplex Theory.

At the current Draft 1 checkpoint, the repository contains:

• 1,992 theorem and lemma declarations
• No sorry
• No sorryAx
• A successful full lake build
• A successful clean-clone build on an independent physical drive
• An explicit axiom audit of the principal capstone theorems

Project website: https://thektproject.org

What KTLean formalizes

The current verified structural spine proceeds through:

triadic closure
    →
canonical 42-glyph spectrum
    →
spinorial double-cover boundary
    →
visible projection with recoverable escrow
    →
four directed views per glyph
    →
168 monads
    →
exact structural inverse-alpha invariant 137

A conditional physical layer then develops:

action, causal, and gravity tokens
    →
Planck mass, length, and time
    →
four candidate dimensionless projection-state grammars
    →
explicit canonical-state selection obligation
    →
exact interval-certification architecture for projected alpha

The principal navigational capstone is:

MainTheoremChain.ktlean_structural_spine

Clone and build

Requirements:

• Git
• Lean 4 through elan
• Lake

Clone the repository:

git clone https://github.com/KosmoNexus/KTLean.git
cd KTLean
lake build

The first build may take time because Lake downloads Mathlib and its pinned dependencies.

A successful build ends with output similar to:

Build completed successfully

Repository integrity checks

Check for unfinished proofs:

grep -RniE '\bsorry\b|sorryAx' KTLean --include='*.lean'

A clean repository should return no output.

Count theorem and lemma declarations:

grep -RhoE '^[[:space:]]*(theorem|lemma)[[:space:]]+[A-Za-z0-9_′]+' KTLean \
  --include='*.lean' | wc -l

At the current Draft 1 checkpoint, the count is:

1992

Check repository state:

git status

Where to begin

New readers should start with:

1. KTLean/MainTheoremChain.lean
2. KTLean/AxiomAudit.lean
3. KTLean/GlyphSpectralCompleteEmergence.lean
4. KTLean/OMBTLocalityGeneration.lean
5. KTLean/OMBTMonadEmergence.lean
6. KTLean/PhysicalAlphaInvariant.lean
7. KTLean/PhysicalPlanckScale.lean
8. KTLean/PhysicalCanonicalStateCount.lean
9. KTLean/PhysicalAlphaCertifiedValue.lean

Claim status

The repository distinguishes carefully among:

• proved structural results
• explicit hypotheses
• finite computational certificates
• conditional physical constructions
• open formal obligations

The current corpus does not claim that every physical consequence of Kosmoplex Theory has already been derived.

In particular, the following remain open or conditional:

• a unique physical criterion selecting the canonical projection-state count
• exact certification of the claimed projected decimal value of alpha
• a full Bell/Tsirelson reconstruction in the KT setting
• a full Hurwitz classification at the octonionic boundary
• derivation of the full Standard Model parameter set

These boundaries are stated explicitly rather than hidden in implementation details.

Axiom audit

The audited capstones contain:

• no sorryAx
• no undeclared KT-specific axiom
• standard Lean logical dependencies such as:
  • propext
  • Classical.choice
  • Quot.sound
• visible native_decide certificates for selected finite computations

See:

KTLean/AxiomAudit.lean

Project guide

A public PDF introducing the project, module architecture, glossary, theorem tour, open problems, and dependency structure is available at:

https://thektproject.org

Constructive criticism and collaboration

Independent verification, constructive criticism, alternate formalizations, and serious collaboration are welcome.

The aim of KTLean is not to insulate Kosmoplex Theory from criticism. It is to make the theory precise enough that its claims can be inspected, reproduced, challenged, and extended in a common formal language.

Repository

https://github.com/KosmoNexus/KTLean

License

KTLean is released under the MIT License.

Citation and archived release

KTLean Draft 1 — Formal Spine is permanently archived at Zenodo:

https://doi.org/10.5281/zenodo.21610428