DTAB follow-ups: integral lifts of tied-class profiles & MCG-equivariance of the tower decomposition

[harryd-b]

Ledger: notes/QUESTIONS-2026-07-19.md §I item 8

Two follow-ups left open by the DTAB paper (data/DTAB-PAPER.md):

1. Integral lifts of the tied-class profiles — the paper works over 𝔽 = ℤ/2 except where stated; lift the tied-class (displaced-tower) results to ℤ coefficients.
2. MCG-equivariance of the tower decomposition — establish how the mapping class group acts on the Λ*H¹(Σ) tower decomposition. (This feeds the framed-dictionary decoration in the wider program, but is a clean equivariance question on its own.)

Relevant material: data/DTAB-PAPER.md, data/DTAB-DATA-2026-07-19.md, scripts/dtab*_calc.py.