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Formalization Status

Per-book statistics, axiom inventory, and sorry inventory for TauLib.

Summary

Metric Value
Total modules 450
Total lines 125,771
Theorems and lemmas 4,332
Definitions 3,542
Structures and types 1,685
Computations (#eval) 3,721
Examples 350
Axioms 4
Sorry 3

Per-Book Breakdown

Book Modules Lines Theorems #eval Axioms Sorry
I — Foundations 94 20,554 ~900 ~700 0 0
II — Holomorphy 65 18,069 ~700 ~500 0 0
III — Spectrum 70 16,807 ~600 ~450 3 0
IV — Microcosm 89 29,730 ~1,000 ~900 1 0
V — Macrocosm 80 28,394 ~900 ~850 0 0
VI — Life 30 5,221 ~200 ~200 0 0
VII — Metaphysics 7 4,278 ~120 ~100 0 3
Tour 8 ~1,850 0 0
Total 450 125,771 ~4,332 ~3,721 4 3

Axiom Inventory

TauLib contains exactly 4 axioms, each explicitly declared and documented.

Conjectural Axioms (3)

These follow the “compute-then-axiomatize” pattern: a decidable check function is verified computationally via native_decide at all tested finite bounds. The axiom asserts the property holds universally.

# Axiom Module What It Asserts
1 bridge_functor_exists BookIII.Bridge.BridgeAxiom The bridge functor from the canonical enrichment ladder to the spectral decomposition exists for all n
2 spectral_correspondence_O3 BookIII.Doors.SpectralCorrespondence The O(3) spectral correspondence holds universally
3 grand_grh_adelic BookIII.Doors.GrandGRH The adelic Generalized Riemann Hypothesis (used for spectral completeness)

Structural Axiom (1)

# Axiom Module What It Asserts
4 central_theorem_physical BookIV.Arena.BoundaryHolonomy The Central Theorem holds in the physical interpretation; references the algebraic proof in Book II

Sorry Inventory

TauLib contains exactly 3 sorry, all in Book VII. Each is typed True := sorry — the goal is trivially True, and the sorry marks a philosophical boundary where formalization itself is the content under discussion.

# Theorem Module Why Sorry
1 omega_point_theorem BookVII.Logos.Sector Involves omega, which is non-diagrammatic by design. The theorem asserts convergence toward the omega-attractor.
2 science_faith_boundary BookVII.Logos.Sector Full convergence claim involves non-computable limits on omega-directed sequences.
3 no_forced_stance BookVII.Final.Boundary Asserts that the lemniscate closure does not force a metaphysical stance. Formalizing it fully would require the framework to step outside itself.

Key property: All three sorry are reachable only through Book VII’s philosophical modules. No mathematical or physical result in Books I-VI depends on any sorry.