THM0190canonicalv1S-Duality Transport
S-duality transport for Eisenstein series at τ = iι_τ. The modular transformation E_{2k}(−1/τ) = τ^{2k}E_{2k}(τ) with i⁴=+1 and i⁶=−1 gives E₄·ι⁴ = 1+240q' (2.4 ppm) and E₆·ι⁶ = −(1−504q') (5.1 ppm). Closes OQ.09 (E₄/E₆ fixed point). The S-dual nome q' = e^{−2π/ι_τ} < e^{−18} is exponentially suppressed.
Payload
S-Duality Transport
S-duality transport for Eisenstein series at τ = iι_τ. The modular transformation E_{2k}(−1/τ) = τ^{2k}E_{2k}(τ) with i⁴=+1 and i⁶=−1 gives E₄·ι⁴ = 1+240q’ (2.4 ppm) and E₆·ι⁶ = −(1−504q’) (5.1 ppm). Closes OQ.09 (E₄/E₆ fixed point). The S-dual nome q’ = e^{−2π/ι_τ} < e^{−18} is exponentially suppressed.
S-Duality Transport
Summary
S-duality transport for Eisenstein series at τ = iι_τ. The modular transformation E_{2k}(−1/τ) = τ^{2k}E_{2k}(τ) with i⁴=+1 and i⁶=−1 gives E₄·ι⁴ = 1+240q’ (2.4 ppm) and E₆·ι⁶ = −(1−504q’) (5.1 ppm). Closes OQ.09 (E₄/E₆ fixed point). The S-dual nome q’ = e^{−2π/ι_τ} < e^{−18} is exponentially suppressed.
Statement
No manuscript statement was extracted in this pilot run.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 212 - Manuscript source: not matched
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.ConfinementBridge - Name:
Tau.BookIII.Spectral.ConfinementBridge.sdual_exponent_large
Dependencies
- Canonical: III.D80
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
III.T55s-duality-transportthm:sduality-transportRelease lines
corpus_v3_workingcorpus_v2Relations
Appears in (1)
Sources
Version & History
Status disclaimer
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