docs(roadmap): add phase-orchestration + phase-prompts (forward plan & prompts)

Mirror the audit system's structure for the forward pipeline:
- phase-orchestration.md ← finding-orchestration.md: the roadmap DAG as a status
  board (phase × type port/research × status × prerequisites × role/model × chain
  × effort), the ready-set, the recommended waves (0 quick wins / A Phase 12 /
  B genus-g spine), and the per-item gates (spike go/no-go, validation battery,
  review).
- phase-prompts.md ← session-prompts.md: ready-to-paste blocks for the ready-set
  (9g.1, 9h, 9d.3, Phase 12 two-step, 9b-analytic) plus reusable research-spike
  and math-review gate prompts, and the DAG-gated Chain B / G0-blocked notes.
Cross-linked from feature-dev-agentic-system.md.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

doc/roadmap/phase-orchestration.md

@@ -0,0 +1,132 @@
+# Phase Orchestration — DAG × Models × Gates (forward pipeline)
+
+**Forward counterpart** of [`../reviewer/finding-orchestration.md`](../reviewer/finding-orchestration.md).
+Where that file schedules *audit findings*, this one schedules the **roadmap phases**
+([`phases.md`](phases.md)) and **research questions** ([`research-track.md`](research-track.md))
+into model-assigned sessions with **spike → go/no-go**, **validation**, and **review** gates.
+
+System design: [`feature-dev-agentic-system.md`](feature-dev-agentic-system.md).
+Ready-to-paste prompts: [`phase-prompts.md`](phase-prompts.md).
+
+> **Two systems, one loop.** Feature-dev (this plan) lands new modules; the audit
+> system re-audits them. Every merge here appends an "audit module X" entry to the
+> audit backlog.
+
+---
+
+## How to use this
+
+1. Compute the **ready-set** = 🔲 phases whose prerequisites are **all ✅** (table below).
+2. Pick one; copy its block from [`phase-prompts.md`](phase-prompts.md); set the named model.
+3. **Port** items go straight to Porter→Validation. **Research** items go
+   Theorist→**Spike (go/no-go)**→Implement→Validation.
+4. Every item ends with a **review gate (Opus)** + the validation battery for its type,
+   then Integrate → CI → human merge → mark ✅ → unblock dependents.
+
+---
+
+## Model / role assignment (forward heuristic)
+
+| Work | Role · Model |
+|---|---|
+| Faithful Java→C++ translation (golden-oracle parity) | **Porter · Sonnet** (Haiku for trivial CLI/glue) |
+| Derive discrete formulas from papers, design validation, LaTeX note | **Theorist · Opus** |
+| Throwaway numeric proof-of-correctness before production | **Prototyper · Opus→Sonnet** |
+| Productionise validated research math | **Research Implementer · Opus→Sonnet** |
+| Test battery (oracle / invariant / convergence / cross-lib) | **Validation · Sonnet** |
+| Math-soundness + parity + correctness gate | **Reviewer · Opus** |
+| `references.md`, math-note polish, user/CLI docs | **Scholar · Haiku** |
+| Branch/PR/CI/rebase/merge | **Integrator · Sonnet** (shared with audit) |
+| Research direction · discretisation sign-off · precision substrate · G0 | **Human** |
+
+Routing rule: **port → cheapest faithful model; research → Opus owns the math, cheaper
+models productionise once the spike says GO.**
+
+---
+
+## Master phase table
+
+Type: 🔌 port (Java oracle) · 🔬 research (papers only) · 🧱 infra
+Status: ✅ done · 🔲 ready/planned · ⏸ planned-blocked-by-prereq · ⛔ blocked (G0)
+
+| Phase | Type | Status | Prerequisites | Role · Model | Chain | Effort |
+|---|---|---|---|---|---|---|
+| 1–7 (special fns → holonomy) | 🔌 | ✅ | — | — | — | done |
+| 9a.1 CP-Euclidean | 🔌 | ✅ | — | — | — | done |
+| 9a.2 inversive-distance | 🔬 | ✅ | — | — | — | done |
+| 9b block-FD HyperIdeal Hessian | 🔬 | ✅ | — | — | — | done |
+| **9g.1 conformal-quality measures** | 🔌 | 🔲 **ready** | none | Porter · Sonnet | quick | ~3 d |
+| **9h.1 CLI --tol/--max-iter** | 🧱 | 🔲 **ready** | none | Haiku/Sonnet | quick | ~30 m |
+| **9h.2 CLI cp/inv-dist models** | 🧱 | 🔲 **ready** | 9a ✅ | Sonnet | quick | 2–4 h |
+| **9d.3 stereographic layout (S²→ℂ)** | 🔌 | 🔲 **ready** | none | Porter · Sonnet | sphere | ~3 d |
+| **9d.4 Möbius-centering functional** | 🔌 | 🔲 **ready** | Phase 7 ✅ | Porter · Sonnet | sphere | ~3 d |
+| **9e circle-pattern layout** | 🔌 | 🔲 **ready** | 9a.1 ✅ | Porter · Sonnet | — | ~1 wk |
+| **9d.1 ConesUtility (Euclidean)** | 🔌 | 🔲 **ready** | none | Porter · Sonnet | cones | ~1 wk |
+| **9b-analytic HyperIdeal Hessian (Schläfli)** | 🔬 | 🔲 **ready** | 9b ✅ | Theorist · Opus | — | 10–14 d |
+| **9f polygon Laplacian** | 🔬 | 🔲 **ready** | none | Theorist · Opus | — | ~3 wk |
+| **Phase 12 decorated DCE + transition** | 🔬 | 🔲 **ready** | landed code only | Theorist · Opus | **A** | medium |
+| 9d.2 non-Euclidean cones | 🔬 | 🔲 ready | 9d.1 | Theorist · Opus | cones | medium |
+| 9g.2 period-matrix convergence study | 🔬 | 🔲 ready | period_matrix ✅ | Validation · Sonnet | — | ~3 d |
+| 9c 4g-gon fundamental domain | 🔌+🔬 | ⏸ | high-precision substrate | Theorist+Porter · Opus | **B** | ~5 wk |
+| holonomy-bug fix (+`cpp_dec_float_50`) | 🔬 | ⏸ | — (architecture call) | Opus + Human | **B** | ~1 wk |
+| 10a DEC layer + 1-forms | 🔌+🔬 | ⏸ | 9c | Porter+Theorist · Opus | **B** | ~6 wk |
+| 10b Siegel period matrix Ω | 🔬 | ⏸ | 10a | Theorist · Opus | **B** | ~1 wk |
+| 10c Fuchsian-group / H²/Γ | 🔬 | ⏸ | 10a+10b+9c | Theorist · Opus | **B** | large |
+| 13 canonical tessellations (capstone) | 🔬 | ⏸ | 9c+10a+10b+10c+holonomy(+12) | Theorist · Opus | **B** | very large |
+| Phase 8 CGAL packaging | 🧱 | ⛔ | **G0** (porting rights) | Opus+Human | — | large |
+| 11a/11b/11c, 10d–10g, GC-1/2/3 | 🔬 | ⏸/opt | various | Theorist · Opus | later | large |
+
+> **Ready-set right now** (no open prerequisites): **9g.1, 9h.1, 9h.2, 9d.3, 9d.4, 9e,
+> 9d.1, 9b-analytic, 9f, Phase 12, 9g.2.** The Chain-B spine and Phase 8 stay ⏸/⛔.
+
+---
+
+## Recommended sequence
+
+### Wave 0 — quick wins (Porter/Haiku, parallel, build confidence)
+**9g.1** (quality measures) · **9h.1+9h.2** (CLI) · **9d.3** (stereographic). All 🔌/🧱,
+no theory, golden-oracle or trivial validation. Land fast, exercise the forward pipeline
+cheaply, strengthen the genus-0/1 validation story.
+
+### Wave A — first research (Chain A, the spike gate's debut)
+**Phase 12 decorated DCE.** Theorist (Opus) derives the Penner-coordinate decoration as a
+*reparametrisation* of the shipped inversive-distance/hyper-ideal/spherical functionals →
+**spike**: round-trip `I_ij ↔ (r_i,r_j,ℓ)` + κ-transition invariant → Research Implementer
+→ invariant/GB battery. Builds on landed code only; **no genus-g dependency.**
+
+### Wave B — research on shipped modules (parallel with A)
+**9b-analytic** (Schläfli analytic HyperIdeal Hessian, with `doc/math/` LaTeX note,
+FD-vs-analytic cross-check against today's block-FD) · **9f** (polygon Laplacian) ·
+**9e / 9d.1 / 9d.4** (further Java ports).
+
+### Wave C — the genus-g≥2 spine (Chain B, strictly DAG-gated)
+**holonomy-bug fix + `cpp_dec_float_50`** → **9c** → **10a (+DEC layer)** → **10b** →
+**10c** → **Phase 13** capstone. The Orchestrator keeps each ⏸ until its prereqs are ✅;
+**13 never dispatches early.** Land **Phase 12** first so the Penner machinery exists.
+
+### Blocked
+**Phase 8 (CGAL packaging)** — ⛔ until **G0** (authors emailed, awaiting reply).
+
+---
+
+## Per-item gates (what "done" requires)
+
+- **Spike go/no-go** (research only): numeric correctness on a `spike/**` branch *before*
+  production code. A NO-GO is a recorded result, not a failure.
+- **Validation battery** (by type — see `feature-dev-agentic-system.md` §4):
+  - 🔌 port → Java golden values bit-for-bit + FD-gradient + Gauss–Bonnet.
+  - 🔬 with cross-impl → geometry-central agreement after normalisation.
+  - 🔬 no oracle → analytic-limit match + invariant conservation (GB, ∏[aᵢ,bᵢ]=Id) +
+    FD-vs-analytic + convergence-under-refinement.
+- **Review gate (Opus)**: math sound? parity intact (HardJava-style defaults)? public
+  surface intentional + documented? precision-prerequisite respected?
+- **Integrate**: PR with `/test-cgal` (+ `/quality-gates` where relevant); model
+  attribution in commits; mark ✅ here; append audit-backlog handoff.
+
+---
+
+## Status log
+
+- **2026-06-01:** plan created. Ready-set open (Wave 0/A/B). Chain B + Phase 8 gated.
+  Audit system delivered S1+S2 (`finding-orchestration.md`); its Integrator/CI/review
+  machinery is reused here.