Republish the benchmark with one unified id namespace and one headline total

BENCHMARKING.md

@@ -37,11 +37,11 @@ therefore filters on `collection` if you want a single subset.
 
 | config | rows | what it is |
 |---|---|---|
-| `full` | 12,531 | every problem, every column, including the unverified ones |
-| `qa` | 12,531 | the minimal MATH-style columns: problem, answer, metadata |
-| `verified` | 2,157 | **the scored split** - only rows whose answer the engine confirmed |
+| `full` | 12,592 | every problem, every column, including the unverified ones |
+| `qa` | 12,592 | the minimal MATH-style columns: problem, answer, metadata |
+| `verified` | 2,755 | **the scored split** - only rows whose answer the engine confirmed |
 | `core` | 3,617 | the main collection |
-| `extended` | 8,394 | the six extended collections |
+| `extended` | 8,455 | the six extended collections |
 | `exercises` | 520 | the machine-made exercises |
 
 The published repository splits the rows **85 % train / 15 % test, stratified by
@@ -61,8 +61,8 @@ a test score and a train score are not comparable.
 | `source_title` | string | the name of the benchmark |
 | `chapter` | int | chapter / topic number |
 | `chapter_title` | string | chapter / topic name |
-| `group` | string | difficulty group as given in the source: `"A"`, `"B"`, `"C"`, or `""` |
-| `difficulty` | string | the difficulty glyph (`"□"` easy, `"■"` hard) or `""` |
+| `group` | string | group of the problem inside its chapter as given in the source: `"A"`, `"B"`, `"C"`, or `""` |
+| `difficulty` | string | difficulty mark of the problem (`"□"` easy, `"■"` hard) or `""` when the source prints none |
 | `problem` | string | English statement, LaTeX in `$...$` / `$$...$$` |
 | `solution` | string | English worked solution, ending in the boxed answer |
 | `final_answer` | string | short gold answer as bare LaTeX (no `$`, no `\boxed`) |
@@ -75,12 +75,12 @@ a test score and a train score are not comparable.
 
 | | count |
 |---|---|
-| rows | 12,531 |
-| rows with a gold answer | 6,703 |
-| rows with **no** gold answer | 5,828 |
-| rows in the `verified` config (the scored split) | 2,157 |
-| rows by collection | `algebra` 2,344, `circles` 876, `core` 3,617, `exercises` 520, `parameters` 1,130, `planimetry` 2,048, `syllabus` 1,745, `trigonometry` 251 |
-| rows by `answer_status` | `corrected` 19, `disputed` 97, `no-gold` 5,828, `refuted` 61, `suspected` 250, `unverifiable` 4,138, `verified` 2,138 |
+| rows | 12,592 |
+| rows with a gold answer | 7,407 |
+| rows with **no** gold answer | 5,185 |
+| rows in the `verified` config (the scored split) | 2,755 |
+| rows by collection | `algebra` 2,327, `circles` 853, `core` 3,617, `exercises` 520, `parameters` 1,287, `planimetry` 2,000, `syllabus` 1,751, `trigonometry` 237 |
+| rows by `answer_status` | `corrected` 50, `disputed` 85, `no-gold` 5,185, `refuted` 68, `suspected` 271, `unverifiable` 4,228, `verified` 2,705 |
 
 Rows without a gold answer are rows where the source page prints the result only
 inside the worked solution, or not at all (`answer_status = "no-gold"`). They are
@@ -196,9 +196,9 @@ not a description of the method.
 
 | leg | what it covered | outcome |
 |---|---|---|
-| 1 - SymPy | 6,703 published rows that carry an answer | 2,157 confirmed, the rest labelled |
-| 2 - independent parsers | 60,985 LaTeX fragments of the published dataset | **0 disagreements** with the third-party parser |
-| 3 - math.js web calculator | 6,703 published rows that carry an answer | 1,114 could be evaluated; **805 of the 2,157 scored rows were independently confirmed and 0 were contradicted** |
+| 1 - SymPy | 7,407 published rows that carry an answer | 2,755 confirmed, the rest labelled |
+| 2 - independent parsers | 61,152 LaTeX fragments of the published dataset | **0 disagreements** with the third-party parser |
+| 3 - math.js web calculator | 6,703 published rows that carry an answer | 1,114 could be evaluated; **805 of the 2,755 scored rows were independently confirmed and 6 were contradicted** |
 | 4 - third page read | every one of the 336 flagged answers | 336 covered |
 
 The cross-check was not a formality - it changed the dataset:
@@ -220,7 +220,7 @@ The cross-check was not a formality - it changed the dataset:
   one template had the strictness of an inequality swapped. The generator now
   re-parses its own source output and solves it, so a row whose statement and
   answer disagree can no longer be published.
-* **61 source answers are reported as wrong.** Each of those has a
+* **68 source answers are reported as wrong.** Each of those has a
   concrete counterexample from the engine *and* a third, independent read of the
   page that agrees with our transcription of the source answer. They are published
   as `refuted`, not silently replaced.

README.md

@@ -76,7 +76,7 @@ configs:
 
 # DGN Math Benchmark
 
-**12,531 mathematics problems, built and machine-verified by us.** 2,157 of them carry an
+**12,592 mathematics problems, built and machine-verified by us.** 2,755 of them carry an
 answer that a symbolic engine confirmed, and those form the scored split.
 
 > Every answer in this dataset was put through a real computational engine (SymPy).
@@ -89,23 +89,25 @@ answer that a symbolic engine confirmed, and those form the scored split.
 ## What this is
 
 An English-language mathematics benchmark for evaluating language models on
-problem solving. Problems are given in LaTeX, every item carries a worked
-solution, and the final answer is stored in the standard MATH convention
+problem solving. Problems are given in LaTeX, 5,105 of the 12,592 items
+carry a worked solution, and the final answer is stored in the standard MATH convention
 (`\boxed{...}`), so the dataset drops straight into the usual math harnesses.
 
 ## Configs
 
 | config | rows | what it is |
 |---|---|---|
-| `full` | 12,531 | every problem, every column, including the unverified ones |
-| `qa` | 12,531 | the minimal MATH-style columns: problem, answer, metadata |
-| `verified` | 2,157 | **the scored split** - only rows whose answer the engine confirmed |
+| `full` | 12,592 | every problem, every column, including the unverified ones |
+| `qa` | 12,592 | the minimal MATH-style columns: problem, answer, metadata |
+| `verified` | 2,755 | **the scored split** - only rows whose answer the engine confirmed |
 | `core` | 3,617 | the main collection: algebra, trigonometry, progressions, logarithms, inequalities |
-| `extended` | 8,394 | the extended collections: entrance algebra, the full syllabus, parameters, trigonometry, plane geometry |
+| `extended` | 8,455 | the extended collections: entrance algebra, the full syllabus, parameters, trigonometry, plane geometry |
 | `exercises` | 520 | machine-made exercises whose answers are computed and re-checked |
 
 Each config has a deterministic 85/15 train/test split (seed 42), stratified by
-collection and chapter.
+collection and chapter. A problem that is printed more than once - in two chapters
+of one collection or in two collections - keeps all of its copies in the same half,
+so no problem of the test half was in the train half.
 
 ## Columns (`full`)
 
@@ -118,10 +120,10 @@ collection and chapter.
 | `source_title` | string | the title of the benchmark |
 | `chapter` | int | chapter / topic number |
 | `chapter_title` | string | chapter / topic name |
-| `group` | string | difficulty group of the problem (A / B / C) |
-| `difficulty` | string | the difficulty glyph of the problem (`□` easy, `■` hard) |
+| `group` | string | group of the problem inside its chapter, as printed in the source (`A`, `B`, `C`); empty when the source names no group |
+| `difficulty` | string | difficulty mark of the problem (`□` easy, `■` hard); empty when the source prints no difficulty mark |
 | `problem` | string | the statement, LaTeX, inline `$...$` and display `$$...$$` |
-| `solution` | string | the worked solution, ending in the boxed answer |
+| `solution` | string | the worked solution; where the row carries an answer it ends in the boxed answer |
 | `final_answer` | string | the gold answer as bare LaTeX (no `$`, no `\boxed`) |
 | `final_answer_boxed` | string | the same answer as `\boxed{...}` |
 | `answer_status` | string | `verified` / `corrected` / `refuted` / `suspected` / `disputed` / `unverifiable` / `no-gold` |
@@ -132,13 +134,13 @@ collection and chapter.
 
 | status | count | meaning |
 |---|---|---|
-| `verified` | 2,138 | the engine substituted the answer back into the problem and it held |
-| `corrected` | 19 | the original answer was refuted and replaced by a re-verified recomputation |
-| `refuted` | 61 | the engine found a concrete counterexample: the answer does not hold |
-| `suspected` | 250 | the engine found a difference, but it is not settled whether the source or the transcription is at fault - **not** counted as an error in the source |
-| `disputed` | 97 | a third read of the source disagreed with the bulk transcription |
-| `unverifiable` | 4,138 | outside the reach of automatic checking |
-| `no-gold` | 5,828 | the source carries no answer for this problem |
+| `verified` | 2,705 | the engine substituted the answer back into the problem and it held |
+| `corrected` | 50 | the original answer was refuted and replaced by a re-verified recomputation |
+| `refuted` | 68 | the engine found a concrete counterexample: the answer does not hold |
+| `suspected` | 271 | the engine found a difference, but it is not settled whether the source or the transcription is at fault - **not** counted as an error in the source |
+| `disputed` | 85 | a third read of the source disagreed with the bulk transcription |
+| `unverifiable` | 4,228 | outside the reach of automatic checking |
+| `no-gold` | 5,185 | the source carries no answer for this problem |
 
 `verified` means the engine substituted the answer back into the problem and it held.
 `corrected` means the original answer was refuted and replaced by a recomputed answer
@@ -163,7 +165,8 @@ harnesses:
 * inline mathematics is written `$...$`, display mathematics `$$...$$`
 * the gold answer is stored twice: `final_answer` holds the bare LaTeX
   (`\frac{3}{4}`), `final_answer_boxed` holds `\boxed{\frac{3}{4}}`
-* the `solution` column ends with the boxed answer, so a harness that extracts the
+* the `solution` column of every row that carries an answer ends with the boxed
+  answer, so a harness that extracts the
   last `\boxed{...}` from the solution gets the same string
 * decimals use a point, never a comma
 * there is no mixing of `\(...\)` and `$...$` delimiters
@@ -203,7 +206,36 @@ python evaluate_benchmark.py \
    the source, and only corrections that the engine could confirm were written back.
 4. **Exercises.** The machine-made exercises are produced by templates that compute
    the answer with SymPy and then re-check it; an item that fails the re-check is
-   dropped.
+   dropped. A second, independent verifier per topic re-derives every answer from
+   the published statement without using the generator, and a negative test makes
+   sure that a perturbed answer is rejected.
+
+## What was left out, and what is still missing
+
+An item is only published when it is an exercise with a statement that can be read
+off the page. 358 printed items were left out because they are not
+exercises at all - a figure and its caption, a section heading, a table of contents,
+a page of exposition, or the answer key of a chapter, whose answers are published
+with the exercise they belong to. 3 further items were left out
+because their statement could not be recovered with certainty.
+
+Four limitations are worth knowing about:
+
+* a statement that runs over the foot of a page was recovered by reading the page
+  again; where the missing words could not be read with certainty, the item was
+  left out rather than published with a guessed question;
+* a page of the source can print two exam variants side by side, and the two
+  blocks use the same numbers. Where that happened, one of the two blocks was
+  kept and the other left out, so around sixty printed exercises are not in this
+  release;
+* a printed exam variant carries the statements of all of its tasks in one place
+  and their answers in one numbered key. Every such variant was split into its
+  own tasks, so that each task carries its own answer. Where the key could not
+  be read off the page with certainty, the tasks are published without an answer
+  rather than with the answer of a neighbouring task;
+* two collections contain a handful of items whose statement stands in two
+  collections. They are kept in the same half of the split, so no problem of the
+  test half was in the train half.
 
 ## Origin and rights
 

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