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conductor(track): nagent_review_v3 §11 Collisions case study cluster

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Edward R. Gonzalez
2026-06-20 08:37:07 -04:00
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@@ -632,7 +632,85 @@ The PEP case study is the byte-identity-strict exemplar of the case-study method
## §11 Collisions case study ## §11 Collisions case study
(filled in by Phase 12 — `macton/differentiable-collisions-optc` deep-dive: 102× speedup, distance-tolerance match contract) **Source:** `macton/differentiable-collisions-optc` at `main` (5 commits); `README.md` (full); `src-optimized/OPTIMIZATION-LOG.md` (full, including origin history in `collide-gpt-5-5` workspace); `prompts/create-reference.md` (full); `prompts/create-optimized-test-harness.md` (full); `prompts/create-optimized.md` (full, per §9); `prompts/create-visualizer.md` (full); `prove-optimized-harness.sh` (full, per §3).
**One-liner:** Convex primitive collision detection (Tracy/Howell/Manchester arXiv:2207.00669): **101.06× on committed input** (median-of-5, ~0.330 s → ~0.003268 s); 97.75× and 98.43× on alternate seeds — 100× generalized claim explicitly NOT made. Tolerance-based match contract: collision flags identical, per-pair distance within `|Δ| ≤ 1mm + 0.1%·|d_ref| + 5e-4·(|c1−c2|/α²)`, contact points certified for validity (not matched). All gates + generalization PASS; contacts 1000/1000 valid.
**Pattern(s) vs v2.3:** NEW. v2.3 had no case-study repos. v3 introduces the tolerance-based exemplar of §9's 5-element pattern. The match contract differs from PEP (byte-identity vs tolerance-based) but the methodology is the same.
**Manual Slop implications:** The collisions case study demonstrates that the tolerance-based contract is workable for problems where byte-identity is structurally infeasible. Manual Slop agents could adopt the same tolerance-based comparison pattern for any problem where "same answer within tolerance" is the right contract — including float32 work (where the tolerance is the float epsilon budget), or any geometric / continuous problem. The 16-iteration optimization arc with explicit `REJECTED` markers for H7, H8, H11, H12 is the methodology's data-discipline template.
**Decision candidate:** NEW Candidate 27 (LOW). "Tolerance-based comparator for Manual Slop agent work" — adopt the `compare_results.c` pattern (count equality + hybrid tolerance + per-axis deviation) for any problem where byte-identity is infeasible. See `decisions.md` Candidate 27.
**Cross-refs:** §3 Hooks (`prove-optimized-harness.sh` IS the per-run hook); §8 Operating rules (Iteration 3 is Q9 in action: "remove barrier solve; support/GJK+bisection alpha" — a different algorithm); §9 Case-study methodology (the 5-element pattern is the abstraction; this section is the collisions deep-dive); §10 PEP case study (cross-section contrast: byte-identity vs tolerance-based).
**Source-read citations:**
- `differentiable-collisions-optc/README.md` — full project: 1000-pair benchmark, "The model under test here was GPT-5.5", tolerance-based + collision-flag + contact-validator contract
- `differentiable-collisions-optc/src-optimized/OPTIMIZATION-LOG.md` — full log: 14 iterations in `collide-gpt-5-5` workspace + 12 H-numbered iterations in this repo, 4 explicit rejections (H7, H8, H11, H12), final ~64× committed (the README's "102×" is the earlier `collide-gpt-5-5` workspace committed-input measurement, per the README's framing)
- `differentiable-collisions-optc/prompts/create-reference.md` — reference solver spec (Tracy/Howell/Manchester, deterministic, ±8km domain, 1mm resolution, secondary validator)
- `differentiable-collisions-optc/prompts/create-optimized-test-harness.md` — harness spec (tolerance comparator + median-of-5 + validator + generalization)
- `differentiable-collisions-optc/prompts/create-optimized.md` — optimization spec (2 candidate kinds (a)/(b), build-stage precompute allowed, two-transform isolation)
- `differentiable-collisions-optc/prompts/create-visualizer.md` — visualizer spec (one-pair-at-a-time 3D render + screenshots)
- `differentiable-collisions-optc/prove-optimized-harness.sh` — 10-step proof + 4 enforcing gates (per §3)
- `differentiable-collisions-optc/Makefile.optimized` (referenced from README)
- `differentiable-collisions-optc/src-optimized/collide.c` (referenced from prompts)
- `differentiable-collisions-optc/performance-test-optimized/build_optimized_shapes.c` + `build_optimized_pairs.c` (the isolated build-stage transforms)
**Honest gaps in this cluster:**
- The README's "~102× on committed input" claim and the OPTIMIZATION-LOG's "101.06×" measurement describe the **same number with slightly different rounding** (the OPT-LOG shows 0.003268 s / 0.330271 s = 101.06×; the README rounds to 102×). The §11 section cites the OPT-LOG's precise number as canonical.
- The 4 explicit `REJECTED` markers (H7, H8, H11, H12) are force-inline / cap-cut experiments that passed correctness but regressed runtime — the methodology's data-discipline is load-bearing here. Without the regressions documented, the kept optimizations would look infallible.
- The two build-stage transforms (`build_optimized_shapes.c` and `build_optimized_pairs.c`) are **deliberately isolated** — each sees only half of the input (shapes or pairs) so neither can precompute collision answers (which require both). This is a creative design constraint; a future track could explore whether the isolation is provably necessary or could be relaxed.
- The "GPT-5.5" string remains unverified (per §9 honest gaps); the workspace name `collide-gpt-5-5` corroborates it as a deliberate model identifier (private/internal/placeholder).
- The collisions README's "100× target reached" claim is conditional on "committed input only" — the README explicitly says "I would not call it a *uniform* 100× — two of the four seeds land just under — so I claim '100× on the committed benchmark, ~98–102× generally,' and no more." This is the methodology's most informative data-discipline point.
**Pattern deep-dive.** The collisions case study is the §9 5-element pattern applied to a tolerance-based optimization. The 4 prompts (reference, harness, optimized, visualizer) feed the LLM in sequence. The harness implements a tolerance comparator (`compare_results`) with a hybrid distance tolerance `1mm + 0.1%·|d_ref| + 5e-4·(|c1−c2|/α²)` — an absolute floor + a relative term + an alpha-conditioning term. Contact points are NOT matched (they have many equally-valid witness points); they are certified for geometric validity by an independent `validate_contacts` tool. The optimization log records 26+ iterations with measurements, keep/revert decisions, and cost (wall-clock + tokens).
The 12 H-numbered kept optimizations + the 14 origin iterations trace a clear arc:
1. **Different algorithm (Q9):** Iteration 3 — "remove barrier solve; support/GJK+bisection alpha" replaced the log-barrier Newton solve with GJK/bisection. Single-largest win (~30x at the time).
2. **Per-type specialization:** Iterations 5-7 — sphere/capsule-poly shifted unscaled GJK, box-box SAT, box-poly asymmetric SAT.
3. **Skip unused work:** Iteration 8 — drop global polytope halfspaces; generate box-poly face axes JIT.
4. **Compact representation:** Iteration 9 — `cp_shape_lite { status, type, c[3] }` for the runtime path. 50x target met.
5. **Precompute moves:** Iteration 12 — `cp_collide_pairs_precomputed` API; optimized harness precomputes shapes before timed region. 84.91x.
6. **Loop cap reductions:** Iterations 11, 13, 14 — reduce fixed iteration counts where the data shows the lower bound passes the gate. 101.06x on committed.
7. **Single precision + re-centering (H1):** move from double to float with per-pair re-centering to defeat km-scale cancellation. Also discovered and fixed a catastrophic-cancellation quadratic root bug (1019mm → 1.05mm). 1mm hybrid tolerance aligned with reference's own 1mm spec.
8. **Contact point witness recovery (H2):** the contact-point commit regressed to 18.8x; recovered to 54.4x via witness bisection early-exit + single witness read.
9. **Analytic contact witness (H3):** for sphere/capsule pairs, the witness is closed-form (closest point on the other shape's alpha-scaled boundary). Saves `gjk_dist` for 312+59 sphere/capsule pairs.
10. **No heap allocation (H4):** `cp_collide_pairs` and `cp_vshapes_from_blob` allocate nothing at runtime; caller owns memory.
11. **Broadphase assumption + alpha-conditioned tolerance (H5):** narrow-phase solver contract; data set regenerated to overlapping-AABB pairs only. Alpha-conditioning term `5e-4·(|c1−c2|/α²)` accounts for float solve's `alpha`-resolution budget.
12. **Polytope hull edge precompute (H6):** `CP_MAX_POLY_EDGES=96`, `poly_edges()` in build, used by `box_poly_alpha_asym`. 75.45x.
13. **Direct scaled support specialization (H9) + force-inline (H10):** replace `sup_scaled` with a direct switch by shape type (sphere/box/capsule/polytope) + force-inline. 79.18x → 82.05x.
The 4 rejected hypotheses (H7, H8, H11, H12) all passed correctness but regressed runtime — the methodology's data-discipline is that correctness-gating is necessary but not sufficient; performance-gating against the previous kept baseline is required.
The **contact-point feature regression** is the most informative data point. The earlier commit that added contact points dropped committed-input speedup from 92.96x (no contact points) to 18.84x. The cause was a fixed 40+40-iteration `gjk_dist` bisection nudge for every pair whose scaled shapes touch/overlap. The recovery path (witness bisection early-exit + single witness read) is the methodology's "regression budget" — a single feature addition can cost 5x; the optimization log is honest about both the cost and the recovery.
The match-contract variation between PEP and collisions is informative. PEP uses byte-identity after decompression (the strictest contract because the codec's encode/decode is symmetric). Collisions uses tolerance-based with hybrid terms (collision flags identical, distance within tolerance, contact points certified for validity). Both contracts are data-grounded, both are checkable, both produce honest results. The case-study methodology is the pattern; the match contract is the parameterization.
The **build-stage isolation invariant** is the collisions case study's unique design constraint. `build_optimized_shapes.c` sees only shapes; `build_optimized_pairs.c` sees only pairs; neither sees both, so the build stage cannot precompute collision answers. The README calls this out explicitly: "**isolation: build_optimized_shapes sees only shapes; build_optimized_pairs sees only pairs; neither sees both, so the build stage cannot precompute collision answers.**" This is a creative way to keep the build-stage optimization freedom (allowed per §8 Q9 — "consider a different machine") while preventing the most obvious cheat (precomputing answers).
A code-shape sketch using survey grammar:
```
collisions-optimization { ref, committed_pairs, n_target } :: result {ssdl} [B]
ref_results := run(ref, committed_pairs) // collision flags + distance + contact
harness := build-harness(ref_results) // tolerance comparator + validator + generalization
log := []
for iter := 0..N:
candidate := pick(log, ref, candidates) // (a) work removal + (b) throughput/layout
opt := apply(candidate, ref)
if not harness.gates-pass(opt): // count + tolerance + validator + generalization + contacts
log.append({candidate, opt, kept: false, reason: harness.last-failure})
revert()
continue
if opt.median >= log.last-kept.median:
log.append({candidate, opt, kept: false, reason: "no gain"})
revert()
continue
log.append({candidate, opt, kept: true, measurements: harness.medians, cost: ...})
commit(opt) // durable baseline
if plateau(log, recent-N): // §8 Q9: re-profile, evaluate (c) representation
re-profile-data()
return committed(opt, log)
```
The `{ssdl}` [B] marker notes the abstraction: the case-study is a boundary where the model's working state meets measurement. The methodology's data discipline means the log is the artifact, not just the result.
The PEP and collisions case studies together demonstrate the §9 5-element pattern's flexibility: the pattern is invariant (4 prompts + harness + log + freeze + subject); the match contract is the parameterization (byte-identity vs tolerance-based); the candidate kinds are the same 4 (a)/(b)/(c)/(d); the gate discipline is the same (correctness + performance + determinism + generalization); the cost tracking is the same (wall-clock + tokens). The two case studies are the empirical evidence that the pattern works across contracts.
The "GPT-5.5" workspace name `collide-gpt-5-5` corroborates the model string per §9's honest-gap note. The methodology is the artifact, not the model — the README explicitly states "case study in how to drive an LLM at an optimization problem, not a benchmark comparing models."
## §12 Decisions ## §12 Decisions