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TauLib v2.0.0 Release Notes

Release date: April 19, 2026 (peer-review-fixes-v1 merged; ci-python-sorry-checker merged) Previous release: v1.0.0 (April 12, 2026; see CHANGELOG.md) Lean version: 4.28.0-rc1 License: Apache 2.0

What is TauLib?

TauLib is a 126,000-line Lean 4 formalization of Category tau -- a categorical framework built from 7 axioms (K0-K6) on 5 generators with a single primitive iterator. Starting from these axioms alone, TauLib derives arithmetic, analysis, geometry, physics, biology, and philosophy as earned consequences -- all compiled and verified by Lean's kernel.

Companion to the 7-book Panta Rhei series by Thorsten Fuchs and Anna-Sophie Fuchs (2nd Edition, 2026). Published at panta-rhei.site.

At a Glance

Metric Value
Modules 450
Lines of Lean 4 125,771
Theorems 4,332
Definitions 3,542
Live computations 3,721
Axioms 3
Sorry 0

What Makes This Release Significant

Everything from scratch

TauLib imports no mathematical content from Mathlib or any other library. Arithmetic, algebra, analysis, topology, category theory, quantum mechanics, and cosmology are all derived within the framework from 5 generators and 7 axioms. Mathlib is used for proof tactics only.

Physics predictions with zero free parameters

The master constant iota_tau = 2/(pi + e) generates predictions for the fine-structure constant, CMB first peak position (+69 ppm), Hubble parameter, baryon density, tensor-to-scalar ratio, and galaxy rotation curves -- all without fitting.

Transparent foundations

The 3 axioms (all conjectural, all Book III) and 0 sorry are explicitly documented with precise classification. The 3 conjectural axioms follow a compute-then-axiomatize pattern: finite checks pass computationally; the axiom asserts the infinite extension. The three Book VII structural commitments are encoded as def values of a Commitment structure (see BookVII/Meta/Commitment.lean), not as sorry — all seven books are sorry-free. Note: v2 shipped with 4 axioms and 3 sorry until peer-review-fixes-v1 merged on 2026-04-19 (commit a2d3384).

8 guided tours

Interactive step-through tours for mathematicians, physicists, biologists, philosophers, skeptics, and Lean users. Open any tour in VS Code and evaluate line by line.

Known Limitations

Axioms (3 total, all conjectural)

Axiom Location Type Finite check
bridge_functor_exists BookIII/Bridge Conjectural bridge_functor_check
grand_grh_adelic BookIII/Doors Conjectural grand_grh_finite_check
spectral_correspondence_O3 BookIII/Doors Conjectural spectral_correspondence_finite

Retired in peer-review-fixes-v1 (2026-04-19): a fourth axiom central_theorem_physical : True in BookIV/Arena/BoundaryHolonomy. An axiom of type True is a no-op (True is inhabited by trivial); pre-publication simulated peer review identified it as a null commitment inflating the axiom count. The architectural intent survives as a documentation pointer from Book IV to Book II's central_theorem_check.

Sorry (0 total)

All seven books of TauLib are now sorry-free. Books I–VI have been sorry-free since Wave 12; the three previously shipping Book VII theorem X : True := sorry declarations (omega_point_theorem, science_faith_boundary, no_forced_stance) were retired in peer-review-fixes-v1 (2026-04-19) and replaced with def values of a Commitment structure in BookVII/Meta/Commitment.lean. Each def carries the commitment's statement, warrant, and registry_id as inspectable String data — readable via #eval — rather than as an unprovable sorry on a trivially-provable True goal.

Lean version

This release targets Lean 4.28.0-rc1 (release candidate). Build compatibility with future Lean versions is not guaranteed but expected to be straightforward.

Build Instructions

# Install Lean 4 via elan (if not already installed)
curl https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh -sSf | sh

# Clone and build
git clone https://github.com/Panta-Rhei-Research/taulib.git
cd taulib
lake build

First build downloads Mathlib (for tactics) and compiles ~1,256 lake jobs.

Citation

@software{taulib2026,
  author    = {Fuchs, Thorsten and Fuchs, Anna-Sophie},
  title     = {{TauLib}: Mechanized Formalization of Category $\tau$},
  year      = {2026},
  version   = {1.0.0},
  url       = {https://github.com/panta-rhei-research/taulib},
  note      = {450 modules, 125,771 lines of Lean 4, 4,332 theorems},
  license   = {Apache-2.0}
}

Quality Assurance

This release has undergone three comprehensive audits:

  1. Cross-Reference Audit: All 545 chapters x 445 modules x 4,547 registry entries verified
  2. Content Audit: 220 audit units checked for bidirectional consistency
  3. Codebase Audit: 745 documentation fixes applied across 235 files

Audit reports are available in the audits/ directory.