fix: align modular forms with the Fuchsian roadmap

[Paul-Lez]

🤖 Companion to #282.

• Makes ModularForms consume the Fuchsian quotient, cusp compactification, and generic degree and Riemann--Hurwitz APIs.
• Keeps congruence arithmetic, analytic Riemann--Roch, automorphy sheaves, and dimension formulas in ModularForms.

[CBirkbeck]

Part of the third adversarial review of the reusable-roadmap split (#279–#284) and companion roadmaps (#288, #81, #250), reviewed 26 August 2026 against the current heads. This section covers #288 — ModularForms companion revision.

Head reviewed: 125fb08030a324b62f3c448483f5f76a1b038bf6

What is good

The companion revision now says the right things:

• FuchsianOrbifolds owns the analytic quotient and compactification;
• ModularForms owns congruence-subgroup arithmetic, automorphy sheaves, analytic Riemann–Roch and dimension formulas;
• no second quotient carrier is introduced in ModularForms.

Remaining issue: the dependency graph is still cyclic at roadmap level

FuchsianOrbifolds Layer 6 consumes from ModularForms:

• the normalized level-one j;
• modular invariance;
• the q-expansion;
• exact elliptic orders.

ModularForms Layer 10 consumes from FuchsianOrbifolds:

• the compactified quotient;
• genus;
• local multiplicity and degree;
• Riemann–Hurwitz.

This can be implemented acyclically, but the roadmaps do not yet specify the module split. Suggested.lean for ModularForms still imports only Mathlib and does not #check the Fuchsian contracts.

Pin the dependency as something like

ModularForms/LevelOne/JInputs
        ↓
FuchsianOrbifolds/LevelOne
        ↓
FuchsianOrbifolds/RiemannSurface/Degree
        ↓
ModularForms/DimensionFormula

or move the level-one j application into a separate consumer module. The essential condition is that no single ModularForms module imports Fuchsian while being imported by the Fuchsian module it consumes.

After #282 lands, add literal imports and #checks for the exact contracts in the higher ModularForms module.

Verdict

Changes requested.

---

Cross-roadmap dependency recommendation — Analytic geometry chain

Acyclic implementation order:

ComplexManifolds
    ├── ComplexTori
    ├── AnalyticToricGeometry
    └── FuchsianOrbifolds core

ModularForms.LevelOne.JInputs
    └── FuchsianOrbifolds.LevelOne

RiemannSurface.Degree  (independent lower module)
    ├── FuchsianOrbifolds applications
    └── ModularForms.DimensionFormula

The generic degree/genus module must not depend on the higher ModularForms Riemann–Roch module.

Recommended disposition (all nine PRs)

1. Merge after routine CI: #279, #280, #281.
2. Small focused repairs: #283, #81.
3. Coordinate and repair together: #282 and #288.
4. Rewrite the representative architecture before merge: #284.
5. Complete the class-field endpoint and state the global-function-field scope: #250.

[Paul-Lez]

🤖 Addressed in 678e6ea, stacked on the coordinated #282 contract commit 4f13956. The README now pins the literal acyclic split: lower ModularForms.LevelOne.JInputs points to Fuchsian.LevelOne; independent RiemannSurface.Degree points to both Fuchsian applications and the higher ModularForms.DimensionFormula; only that higher module imports the Fuchsian compactification. Suggested.lean now imports the stacked Fuchsian contract file and literally #checks the compactification, finite-map, genus, local-multiplicity, degree, divisor-pullback, degree-one, and Riemann–Hurwitz declarations. Focused verification: lake build TauCetiRoadmap.ModularForms.Suggested completed successfully (8703 jobs). Once #282 merges, its files disappear from this PR diff while these import checks remain.