# Finding Orchestration — Sessions × Models × Review Gates

**Updated:** 2026-05-31
**Purpose:** a structured plan to work through every audit finding across
**multiple short sessions**, each run by the **model best suited** to the work,
with an **external Opus reviewer session after every implementation session**.
This lets you pick up any "Session" below cold, hand it to the named model, and
know exactly what it covers and how its output gets validated.

> Companion: the per-finding detail lives in the 11 audit documents in this
> folder (see [`README.md`](README.md)). This file is the *meta-plan* — the
> order, the model assignment, and the review cadence.

---

> **Ready-to-paste prompts** for every pending session (S3–S6 + the review gate)
> live in [`session-prompts.md`](session-prompts.md) — copy one block, set the
> named model, go.

## How to use this

1. Pick the next **⬜ pending** session from the [sequence](#session-sequence).
2. Start a session with the **assigned model**, point it at the listed findings
   in their audit docs (each finding has `file:line`, fix, acceptance criteria).
3. When it finishes, start the paired **🔍 Opus review session** — it validates
   the diff (correctness, value-identity, tests, no parity regression) and only
   then is the batch "done".
4. Mark the session ✅ here and move on.

Rationale for the cadence: implementation models (Sonnet/Haiku) are cheaper and
fast for well-specified work; Opus is reserved for (a) findings that need real
numerical/architectural judgement and (b) the **review gate**, because an
independent high-capability pass catches subtle parity/numerics regressions that
a self-review from the implementing model tends to miss.

---

## Model-assignment heuristic

| Model | Take findings that are… | Examples |
|---|---|---|
| **Haiku** | mechanical, local, low-risk; docs, citations, renames, named-constant extraction | M-series, N4/N6, A1–A3, doc files |
| **Sonnet** | normal coding with a clear acceptance criterion; tests, error-handling, CI, small API changes | V-series, C-series, I-series, H-series |
| **Opus** | numerics, math correctness, architecture, public-API/irreversible decisions — **and every review gate** | B1-port, N1/N3/N5/N7, H2 refactor, A4/A5, all 🔍 reviews |

> Decision rule isn't "how severe" but "how much must be *understood* to get it
> right." A 🔴 one-line switch can be Sonnet; a 🟡 numerical reformulation is Opus.

---

## Master finding table

Status: ✅ done · ⬜ open (actionable) · ⏸ deferred (intentional) · ⛔ blocked (G0) · 👤 needs human expert

| ID | Audit | Sev | Status | Model | Session |
|----|-------|-----|--------|-------|---------|
| B1 (HyperIdeal) | api-perf | 🔴 | ✅ | Sonnet | S1 |
| B1 (Inv-Dist port) | api-perf | 🔴 | ✅ | Opus | S1 |
| V3 | input-val | 🟡 | ✅ | Sonnet | S1 |
| C1 | test-cov | 🔴 | ✅ | Sonnet | S1 |
| N4, N6 | numerics | 🟡/🔵 | ✅ | Haiku | S1 |
| M1, M2, M4 | math-cite | 🟡/🔵 | ✅⚠️ | Haiku → re-fix 2026-06-04 | S1 + nachkorrigiert |
| C2, C3 | test-cov | 🔴 | ✅ | Sonnet | S1 |
| V1, V2, V4 | input-val | 🟡 | ✅ | Sonnet | S1 |
| I2, I3, I4 | test-cov | 🟡 | ✅ | Sonnet | S1 |
| A1, A2, A3 | api-perf | 🔴/🟡 | ✅ | Haiku | S1 |
| N5 | numerics | 🟡 | ✅ | Opus | S1 |
| N3 | numerics | 🟡 | ✅ | Opus | S1 |
| H2, B2, B3, B4, B5 | test-cov/api-perf | 🔵/🟡 | ✅ | Opus | S1 |
| I1 | test-cov | 🟡 | ✅ | Opus | S2 |
| H1 | test-cov | 🔵 | ✅ | Opus | S2 |
| N7 | numerics | 🔵 | ✅ | Opus | S2 |
| **H3** | test-cov | 🔵 | ✅ | Sonnet→🔍Opus | **S3** |
| **H4** | test-cov | 🔵 | ✅ | Sonnet→🔍Opus | **S3** |
| **H5** | test-cov | 🔵 | ✅ | Sonnet→🔍Opus | **S3** |
| **V5, V6** | input-val | 🔵 | ✅ | Sonnet→🔍Opus | **S3** |
| **N2** | numerics | 🟡 | ⬜ | Haiku→🔍Opus | **S4** |
| **thread-safety doc** | thread-safety | 🟡 | ⬜ | Haiku→🔍Opus | **S4** |
| **M3** | math-cite | 🟡 | ⬜ | Haiku→🔍Opus | **S4** |
| **I5** | test-cov | 🟡 | ⬜ | Sonnet→🔍Opus | **S5** |
| A4, A5 | api-perf | 🟡 | ⏸ | Opus | S6 (after G0/G1) |
| N1 | numerics | 🔴 | ✅* | — | (subsumed by B1; doc note folds into N2/S4) |
| G1–G12 | cgal | ⛔/🔴 | ⛔ | Opus | (after G0) |
| D1, D2 | dep-license | 🔴 | ⛔ | Opus | (after G0) |
| M5 | math-cite | 🔵 | 👤 | — | human domain expert |
| G0 | cgal | ⛔ | 🔄 in progress | owner | **author contacted by email — awaiting reply** |

\* N1 (FD-step vs Newton tol) is largely subsumed by the B1 block-FD work; the
remaining piece is the tolerance-coupling note, folded into N2 (Session S4).

---

## Session sequence

### ✅ S1 — Audit quick-wins + numerics + refactor (DONE, 2026-05-31)
Branch `fix/b1-v3-c1-quick-wins`, 9 commits, 298/298 CGAL tests green.
- **Sonnet:** B1(HyperIdeal)/V3/C1; C2/C3, V1/V2/V4, I2/I3/I4.
- **Haiku:** N4/N6; M1/M2/M4; A1–A3.
- **Opus:** B1 inv-dist port; N5; N3; H2+B2/B3/B4/B5.
- **🔍 Opus review:** validated all Sonnet/Haiku commits (value-identity, error
  handling, coverage gate, alias forwarding) — all correct.

### ✅ S2 — Solver result diagnostics (DONE, 2026-05-31, Opus impl + self-review)
Done directly in the warm post-refactor Opus session (all three findings live in
the just-written `newton_core`/`NewtonResult`/`NewtonLinearSolver`). Commit
`90e966a`; 301/301 CGAL tests green. **I1** status enum + **H1** iteration fix +
**N7** `sparse_qr_fallback_used` / `min_ldlt_pivot` diagnostics. Follow-up **done**
(commit `957f506`): `NewtonStatus` + both diagnostics propagated into the public
CGAL result types (`Conformal_map_result`, `Hyper_ideal_map_result`,
`Circle_packing_result`) via the `CGAL::Newton_status` alias.

<details><summary>original S2 plan</summary>

#### S2 — Solver result diagnostics (Sonnet → 🔍 Opus)
- **I1** — give `NewtonResult` a status enum
  (`Converged`/`MaxIterations`/`LinearSolverFailed`/`LineSearchStalled`). The
  `newton_core` refactor centralised every exit point, so this lands in one
  place now. Update the 5 wrappers + any callers reading `converged`.
- **H1** — `res.iterations` is stale when the solver breaks on `!ok`/stall;
  set it correctly at each `break` in `newton_core`.
- **N7** *(Opus within this session)* — optional conditioning diagnostic
  (smallest LDLT pivot / cheap cond estimate) surfaced in the result; pairs
  naturally with the I1 status enum (near-singular ⇒ a distinct status/flag).
- **🔍 Opus review:** confirm the enum doesn't break the CGAL-layer result
  mapping and that `converged` semantics are unchanged for existing callers.

</details>

### ✅ S3 — Robustness & test-gap closure (DONE, 2026-06-01, Sonnet impl + Opus review)
Implementation shipped in commit `135bcf0` (included in P1 merge `bd613a6`).
Follow-up commit closes the doc-tracker gap and fixes dead `found_dofvector` variable
(V5 rule 4: `<DOFVector>` missing now throws instead of silently returning empty `x`).
- **H3** — `enforce_gauss_bonnet` returns `|deficit|` (both overloads); 3 new tests.
- **H4** — `ReduceToFD_ThrowsForRealAxisBoundary` covers `Im(τ)==0.0` exact boundary.
- **H5** — 2 integration tests: sliver triangle (no crash/NaN) + exact-degenerate collinear.
- **V5** — `load_result_xml` rejects non-conforming XML (3 strict-subset checks); canonical
  round-trip regression test passes. V5 rule 4 (`<DOFVector>` must be present) now enforced.
- **V6** — `check_dof_vector_size(x, expected, context)` throws on mismatch; 3 new tests.
- **🔍 Opus review:** CHANGES-REQUESTED resolved — implementation correct; code commits
  were redundant with `135bcf0` on main; doc follow-up applied on `chore/s3-followup`.

### ⬜ S4 — Documentation & citations (Haiku → 🔍 Opus)
- **N2** — `doc/math/tolerances.md`: every numerical threshold, its role, and
  the constraints between them (incl. the N1 FD-step ≪ Newton-tol coupling).
- **thread-safety** — document the same-mesh concurrency contract (the code has
  no mutable static state; this is purely the written contract).
- **M3** — re-verify the future-dated / arXiv-only citations against their
  published versions; update `references.md`.
- **🔍 Opus review:** sanity-check the tolerance relationships are stated correctly.

### ⬜ S5 — Coverage truthfulness (Sonnet → 🔍 Opus)
- **I5** — wire `coverage.sh` to the full CGAL suite (not just the 26 fast
  tests, ~9.6%), then remove `SKIP_COVERAGE_GATE=1` so the agreed
  80%/70%/90% gate goes live (C3 ramp-up → enforced).
- **🔍 Opus review:** confirm the measured numbers are honest and the gate fails
  correctly when coverage drops.

### ⏸ S6 — Public CGAL surface + packaging (Opus, **only after G0/G1**)
Gated by the author's reply on porting/relicensing rights.
- **A4, A5** — public entry-point renames + unified `Circle_packing_result`.
- **G1–G12, D1, D2** — license headers, CGAL package layout, concept doc, user
  manual, CGAL test harness, dependency/data provenance.
- **G0 status:** *author contacted by email (2026-05-31), awaiting reply.* No
  public release / submission / relicensing until a written answer exists.

### 👤 Out of model scope
- **M5** — the large hand-derivations need a domain-expert prose review
  (the numerical results are already validated; the prose is not).
- **Alle Zitationen** — alle `references.md`-Einträge müssen von einem
  Fachexperten manuell verifiziert werden (siehe Lektion unten).

---

## ⚠️ Lektion: KI-gestützte Citation-Audits können Fehler einführen

**Datum:** 2026-06-04  
**Befund:** Die M1-Auflösung in S1 (Haiku, 2026-05-31) war selbst fehlerhaft:

- Der Haiku-Audit erkannte korrekt, dass `Kolpakov–Mednykh` in `references.md` fehlt
- Als „Fix" wurde die Zeile mit arXiv:math/0603097 ergänzt — aber **math/0603097 ist Springborn 2008**, nicht Kolpakov–Mednykh
- Das Autorenpaar „Kolpakov & Mednykh" hat **2006 kein gemeinsames Paper veröffentlicht** (früheste Zusammenarbeit: 2010, über Torusknoten, nicht Tetraedervolumen)
- Der falsche Autorenname entstand bereits beim Java→C++-Port; der Audit hat ihn zementiert statt korrigiert

**Nachkorrektur:** 2026-06-04, 7 Dateien korrigiert (Code-Kommentare, references.md, roadmap, architecture-doc, tests-doc, audit-doc).

**Konsequenz für das Projekt:**

> KI-Modelle können bei Citation-Audits plausibel klingende aber falsche  
> Autoren/Jahres-Zuordnungen produzieren — besonders wenn die Primärquelle  
> (Java-Code) nur einen Link ohne Autorennamen enthält.

**Empfehlung:**

Vor jeder öffentlichen Veröffentlichung / CGAL-Submission müssen **alle** Einträge
in `references.md` von einem **Fachexperten (Mensch)** gegen die tatsächlichen
Papiere verifiziert werden:

| Priorität | Was prüfen |
|---|---|
| 🔴 Hoch | Formeln in Code-Kommentaren (`hyper_ideal_utility.hpp`, `hyper_ideal_functional.hpp`) gegen die zitierten Paper |
| 🔴 Hoch | Ushijima 2006 (DOI 10.1007/0-387-29555-0_13) — arXiv math/0309216 — korrigiert: kein Meyerhoff, anderer Titel, anderes Buch |
| 🟡 Mittel | Ob Springborn 2008 (math/0603097) die 12-Term-Lobachevsky-Formel tatsächlich enthält |
| 🟡 Mittel | M3: post-2023 / arXiv-only Zitationen (Bowers-Bowers-Lutz 2026 etc.) |
| 🔵 Niedrig | Alle weiteren `references.md`-Einträge auf Titel/Jahr/DOI-Konsistenz |

---

## Review-gate checklist (what every 🔍 Opus session checks)

- [ ] Builds clean; full CGAL suite green (no count regression).
- [ ] No Java golden-vector / parity test perturbed (HardJava defaults intact).
- [ ] Numeric changes are value-identical where claimed, or justified + tested.
- [ ] New public surface (result types, enums, API) is intentional and documented.
- [ ] Commit message attributes the implementing model
      (`Co-Authored-By: Claude <Model> <noreply@anthropic.com>`).
- [ ] Finding marked ✅ in the master table above with the commit ref.