Verify Verification Surface Canonical mathematics Verification for the mathematical layer of the τ-framework — Books I–III: kernel, holomorphy, central theorem, Yoneda enrichment, master constant ι_τ. Lean-formalized with the strongest formalization ratio of any domain.
Verification SurfaceCanonical

Mathematics Verification

Verification for the mathematical layer of the τ-framework — Books I–III: kernel, holomorphy, central theorem, Yoneda enrichment, master constant ι_τ. Lean-formalized with the strongest formalization ratio of any domain.

Public Lean · 284 modules · 5002/7617 formalized Mode · Formal + Empirical Bridge · Moderate (65%)
In plain language

Mathematics is where the τ-framework's formalization is strongest. Books I–III are the foundational kernel: definitions, theorems, holomorphy results, the Yoneda-as-theorem under self-enrichment, and the central theorem that pins τ's categoricity. Verification here means checking that every load-bearing theorem actually compiles in Lean 4, that the registry's claim of "formalized" matches the source, and that bridges into standard mathematics (Mathlib) hold. Three load-bearing checks: the categoricity of τ (Book II), the Yoneda enrichment ladder (Book II), and the Hyperfactorization theorem (Book I). Anything claiming "formalized" status here should resolve to a Lean theorem you can read.

At a glance

Books

I · II · III

Foundational kernel · holomorphy · enrichment + categoricity · spectral / Riemann.

TauLib modules

284

70685 lines of Lean 4 across mathematics-domain modules.

Lean coverage

5002 / 7617

Formalized declarations · 65% formal · 0 sorries.

Custom axioms

3

Beyond Mathlib's standard base. All disclosed in the Custom Axiom Inventory.

Per-book Lean coverage

| Book | Modules | Lines | |------|--------:|------:| | Book I | 147 | 35469 | | Book II | 66 | 18183 | | Book III | 71 | 17033 |

Inspection routes

Formalization

TauLib Status

Per-module formalization ratios, declaration counts, and source-line coverage for the mathematics layer.

 Bridge

Bridge Verification

How internal τ-categorical structure transfers to standard mathematics (Mathlib, classical results).

 Axioms

Custom Axiom Inventory

The 3 declared custom axioms, their finite-checked support, and what specialist review would close.

 TCB

Trust Budget

What Lean's kernel trusts, where TauLib uses native_decide, and which theorems carry the extension.

 Audit

How to Verify (Mathematician)

Reviewer route for category theorists, model theorists, complex analysts, and number theorists.

 Results

Mathematics Results Hub

Landmark theorems, world readout, and recovery targets for the mathematics layer.

Verification levels

Kernel integrity

Does each Lean module compile cleanly relative to the stated formalization scope? Do theorem dependencies close, and does the registry’s formalized flag match the source?

Surfaces: TauLib, Formalization Status, Release Manifest.

Standard-foundation alignment

Can selected hinge theorems be re-established in standard foundational settings (Mathlib, ZFC, classical category theory) by independent specialists?

Surfaces: hinge companion pages, Formal Methods audit route, and selected corpus objects.

Bridge adequacy

Do recovery and transfer claims into standard mathematics support the downstream use being made of them in physics, life, and metaphysics?

Surfaces: Custom Axiom Inventory, TCB Disclosure, Bridge Verification.

Accountability statement

Any theorem claimed as formally certified is certified in the precise sense stated: relative to the relevant proof infrastructure, declared assumptions, and stated scope. Mathematical verification establishes internal proof discipline; it does not by itself settle bridge adequacy into every standard foundation, the program’s downstream physics/life/metaphysics consequences, or external review.

Key glossary terms

MathG-D01-iota-tau Master constant ι_τ MathG-K01-universe-postulate The Universe Postulate (K0) MathG-T04-central-theorem Central theorem at rank (3, 15) MathG-D04-yoneda-as-theorem Yoneda-as-theorem under self-enrichment MathG-T06-prime-polarity Prime Polarity Theorem MathG-D06-truth4-logic Truth4 Logic MathG-T07-split-complex-forced Split-Complex Forced MathG-D07-4-plus-1-sector 4+1 Sector Decomposition

Cross-domain bridges

This verification surface intersects glossary terms that bridge to other domains. The τ-framework's cross-domain pivots are the structural junctions where verification claims meet the empirical, life, and metaphysical readouts.

See also

Results · Mathematics Hub for mathematics-domain results, world readout, and recovery targets. Corpus Registry The 4,547 registry items underpinning the formal layer. Formal Verification Stack Cross-domain explanation of the four formal-verification layers. How to Verify (all roles) Pick your reviewer route — formal methods, mathematician, physicist, philosopher, prior-art, or generalist.

Save or share this page for inspection

Download a portable dossier, copy a reviewer note, or send this page to someone who can inspect it.

Email to expert