TauLib · API Book III

TauLib.BookIII.Arithmetic.TowerAssembly

TauLib.BookIII.Arithmetic.TowerAssembly

Enrichment Tower Assembly: E₀ ⊊ E₁ ⊊ E₂ assembled.

Registry Cross-References

  • [III.T40] Enrichment Tower Assembly – tower_assembly_check

Mathematical Content

III.T40 (Tower Assembly): The tower E₀ ⊊ E₁ ⊊ E₂ is assembled with coherent bi-square scaling chain and complete Millennium coverage:

  • E₀: RH + Poincaré (pure mathematics)

  • E₁: NS + YM + Hodge (physics)

  • E₁→E₂: BSD + Langlands (arithmetic mirror)

  • E₂: P vs NP (computation)

The tower is strict (E₀ ⊊ E₁ ⊊ E₂), each level has its bi-square, and the scaling chain is coherent: algebraic → topological → enriched.

Tau.BookIII.Arithmetic.tower_strict_check

source def Tau.BookIII.Arithmetic.tower_strict_check :Bool

[III.T40] Tower strictness: E₀ ⊊ E₁ ⊊ E₂. Each level is a proper subset of the next (enrichment adds genuine content). Equations

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Tau.BookIII.Arithmetic.millennium_coverage_check

source def Tau.BookIII.Arithmetic.millennium_coverage_check :Bool

[III.T40] Millennium coverage: all 8 problems are assigned to levels. Equations

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Tau.BookIII.Arithmetic.scaling_chain_check

source def Tau.BookIII.Arithmetic.scaling_chain_check (bound db : Denotation.TauIdx) :Bool

[III.T40] Bi-square scaling chain: all three bi-squares have the same structural shape (CRT roundtrip + BNF decomposition + sector products). Equations

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Tau.BookIII.Arithmetic.scaling_chain_check.crt_roundtrip_go

source@[irreducible]

def Tau.BookIII.Arithmetic.scaling_chain_check.crt_roundtrip_go (x k bound db fuel : ℕ) :Bool

Algebraic: CRT roundtrip. Equations

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Tau.BookIII.Arithmetic.scaling_chain_check.bnf_decomposition_go

source@[irreducible]

def Tau.BookIII.Arithmetic.scaling_chain_check.bnf_decomposition_go (x k bound db fuel : ℕ) :Bool

Topological: BNF decomposition. Equations

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Tau.BookIII.Arithmetic.tower_assembly_check

source def Tau.BookIII.Arithmetic.tower_assembly_check (bound db : Denotation.TauIdx) :Bool

[III.T40] Tower assembly: tower is strict, coverage is complete, and scaling chain is coherent. Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIII.Arithmetic.tower_strict

source theorem Tau.BookIII.Arithmetic.tower_strict :tower_strict_check = true

Tau.BookIII.Arithmetic.millennium_coverage

source theorem Tau.BookIII.Arithmetic.millennium_coverage :millennium_coverage_check = true

Tau.BookIII.Arithmetic.scaling_chain_15_3

source theorem Tau.BookIII.Arithmetic.scaling_chain_15_3 :scaling_chain_check 15 3 = true

Tau.BookIII.Arithmetic.tower_assembly_15_3

source theorem Tau.BookIII.Arithmetic.tower_assembly_15_3 :tower_assembly_check 15 3 = true

Tau.BookIII.Arithmetic.e0_lt_e1

source theorem Tau.BookIII.Arithmetic.e0_lt_e1 :Enrichment.EnrLevel.E0.lt Enrichment.EnrLevel.E1 = true

[III.T40] Structural: E₀ < E₁.

Tau.BookIII.Arithmetic.e1_lt_e2

source theorem Tau.BookIII.Arithmetic.e1_lt_e2 :Enrichment.EnrLevel.E1.lt Enrichment.EnrLevel.E2 = true

[III.T40] Structural: E₁ < E₂.

Tau.BookIII.Arithmetic.e2_lt_e3

source theorem Tau.BookIII.Arithmetic.e2_lt_e3 :Enrichment.EnrLevel.E2.lt Enrichment.EnrLevel.E3 = true

[III.T40] Structural: E₂ < E₃.

Tau.BookIII.Arithmetic.eight_problems

source theorem Tau.BookIII.Arithmetic.eight_problems :[Doors.problem_level Doors.MillenniumProblem.RH, Doors.problem_level Doors.MillenniumProblem.Poincare, Doors.problem_level Doors.MillenniumProblem.NS, Doors.problem_level Doors.MillenniumProblem.YM, Doors.problem_level Doors.MillenniumProblem.Hodge, Doors.problem_level Doors.MillenniumProblem.BSD, Doors.problem_level Doors.MillenniumProblem.Langlands, Doors.problem_level Doors.MillenniumProblem.PvsNP].length = 8

[III.T40] Structural: all 8 problems covered.