docs/reconstruction.md

# Reconstructing problem text

This release contains **no upstream problem text, gold answers, reference
solutions, or answer options** (see `docs/license_audit.md`). Every table keys on
stable identifiers instead. This document explains how to attach the text
yourself from the upstream sources, under those sources' own licenses.

## The two identifier columns

Every per-problem table carries both:

- `problem_id` — the canonical, cross-solver identifier. Use this to join the
  same problem across the gpt-oss-120b and Gemma-4-31B-it settings.
- `source_problem_id` — the identifier exactly as it appeared in that setting's
  own run artifacts. **This is what you match against upstream.**

They differ because the two solver campaigns were exported under different
naming schemes. For OmniMath and LAB-Bench the two solvers used *different*
`source_problem_id` namespaces for the very same problems:

| Benchmark | gpt-oss-120b `source_problem_id` | Gemma-4-31B-it `source_problem_id` | canonical `problem_id` |
|---|---|---|---|
| omnimath2 | `omni2_1` | `omni2:t01:1` | `omni2_...` |
| labbench | `labbench_cloningscenarios_000001` | `lab-bench:CloningScenarios:00540e26-...` | `labbench_...` |
| jeebench | `jeebench:JEE Adv 2016 Paper 1:1` | same | same |
| scibench | `scibench:atkins:e1.1(a)(a)` | same | same |

Both solvers cover an identical canonical problem set in every paired setting
(verified: symmetric difference is empty for all five pairs). Always join on
`problem_id`, never on `source_problem_id`, when comparing solvers.

`data/problems.csv` carries both columns for all 6,803 released problems, plus a
`legacy_tier_id` column for OmniMath (`omni2:tNN:idx`) that matches the Gemma
namespace and the primary-split identifiers.

## Per-benchmark reconstruction

### Omni-MATH-2 (4,181 problems)
Upstream: <https://huggingface.co/datasets/martheballon/Omni-MATH-2> (Apache-2.0).

The released slice is a filtered exact-answer subset built locally; it is not a
contiguous upstream range, so you cannot slice it by index. Use
`data/problems.csv` (`source`, `difficulty`, `difficulty_tier`, `domain`) to
identify rows, then match against the upstream corpus. The `legacy_tier_id`
column encodes the project's own tier partition: `omni2:tNN:idx` is the
`idx`-th problem of difficulty tier `NN`. Tier sizes are in
`registry/release_manifest.json` under `coverage.omnimath_tier_counts`.

Caveat: reconstructing this slice exactly requires the project's filtering
script, which is not part of this dataset release. It is in the code repository
at <https://github.com/ChihHsuan-Yang/EMNLP_Cost-Aware-Protocol-Routing>.

### JEEBench (515 problems)
Upstream: <https://github.com/dair-iitd/jeebench> (MIT).

`source_problem_id` has the form `jeebench:<paper>:<index>`, e.g.
`jeebench:JEE Adv 2016 Paper 1:1`. Split on `:` to recover the upstream paper
name and 1-based question index. All 515 public problems are covered.

### SciBench (565 problems)
Upstream: <https://github.com/mandyyyyii/scibench> (MIT).

`source_problem_id` has the form `scibench:<textbook>:<problem_id>`, e.g.
`scibench:atkins:e1.1(a)(a)`. The textbook segment names the JSON file under
`dataset/original/`. The project's text-only slice holds 574 rows carrying 571
distinct identifiers (three identifiers are reused, see below); 565 of those 571
were executed under all four protocols and are released. The six unexecuted
identifiers are all from the `thermo` textbook: `scibench:thermo:1.3`,
`1.6`, `2.13`, `6.10`, `9.9`, and `14.5`. Why those six were not run is not
recorded in the artifacts this release was built from.

Three SciBench source identifiers are ambiguous upstream — `scibench:quan:2.13`,
`scibench:stat:5.8-5`, and `scibench:stat:Problem 1.1.1` each name two distinct
problems. The canonical `problem_id` disambiguates them with a content-hash
suffix (`...#<12 hex>`); the plain `source_problem_id` does not. When
reconstructing those three, expect two upstream candidates and disambiguate by
content.

### LAB-Bench (1,542 problems, in two nested slices)
Upstream: <https://huggingface.co/datasets/futurehouse/lab-bench>
(CC-BY-SA-4.0), revision `5c77cec648430f30611808808861eb86f81d5eaa`, `train`
split.

Two slices are released, and the smaller is a strict subset of the larger:

- `llm_strict` (741): subsets `CloningScenarios` (33), `ProtocolQA` (108),
  `SeqQA` (600).
- `text_no_tool` (1,542): the strict slice plus `DbQA` (520), `LitQA2` (199),
  `SuppQA` (82).

`FigQA` (181) and `TableQA` (244) are excluded upstream-side because they require
image assets. There are no row-level exclusions within the included subsets.

The Gemma-namespace `source_problem_id` embeds the upstream UUID directly:
`lab-bench:<Subset>:<uuid>`. The gpt-oss namespace
(`labbench_<subset>_<zero-padded index>`) does not; use `problem_id` and
`data/problems.csv` (`subset` column) to bridge.

**Answer-option order.** The runs used a deterministically shuffled option order
derived from the upstream row id and ideal answer, and the gold label in the
runs is the *shuffled* letter. If you reconstruct from upstream you will get the
upstream option order, and your letter labels will not match. This release does
not contain the shuffle, so per-option correctness is not reconstructible from
this release alone. The per-problem correctness flags here are unaffected — they
record whether the protocol's chosen option was the correct one.

**Do-not-train request.** LAB-Bench ships a canary and an upstream request not to
train on it. This release contains no LAB-Bench content, only identifiers. Do not
use these identifiers to assemble a training corpus that would violate that
request.

## What you cannot reconstruct from this release

- **Raw model generations.** No protocol produced text is included. Per-protocol
  correctness is the finest-grained outcome released.
- **Baseline final answers.** The confidence probe's prompt included the
  baseline's final answer as untrusted input. That answer text is not in this
  release, so `data/probe_inputs.jsonl` carries `baseline_final_answer: null`.
  The probe is therefore **not re-runnable** from this release alone; see
  `docs/schema.md`.
- **Per-protocol token/call/wall-time costs for the nine non-primary settings.**
  Cost accounting is released only through the aggregate tables. The primary
  OmniMath 423-problem held-out analysis in `data/aggregate/
  main_routing_heldout.csv` reports costs, but the per-problem cost columns
  behind it are not staged here.