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

.gitattributes

@@ -10,3 +10,5 @@ data/books/train-00000-of-00001.parquet filter=lfs diff=lfs merge=lfs -text
 data/core/test-00000-of-00001.parquet filter=lfs diff=lfs merge=lfs -text
 data/core/train-00000-of-00001.parquet filter=lfs diff=lfs merge=lfs -text
 data/verified/train-00000-of-00001.parquet filter=lfs diff=lfs merge=lfs -text
+data/extended/test-00000-of-00001.parquet filter=lfs diff=lfs merge=lfs -text
+data/extended/train-00000-of-00001.parquet filter=lfs diff=lfs merge=lfs -text

BENCHMARKING.md

@@ -7,69 +7,6 @@ before.
 
 ---
 
-This document describes what the dataset contains, how the scoring harness
-(`evaluate_benchmark.py`) decides that an answer is correct, and how to run and
-report results. It is written for an engineer who has not seen this project
-before.
-
----
-
-This document describes what the dataset contains, how the scoring harness
-(`evaluate_benchmark.py`) decides that an answer is correct, and how to run and
-report results. It is written for an engineer who has not seen this project
-before.
-
----
-
-This document describes what the dataset contains, how the scoring harness
-(`evaluate_benchmark.py`) decides that an answer is correct, and how to run and
-report results. It is written for an engineer who has not seen this project
-before.
-
----
-
-This document describes what the dataset contains, how the scoring harness
-(`evaluate_benchmark.py`) decides that an answer is correct, and how to run and
-report results. It is written for an engineer who has not seen this project
-before.
-
----
-
-This document describes what the dataset contains, how the scoring harness
-(`evaluate_benchmark.py`) decides that an answer is correct, and how to run and
-report results. It is written for an engineer who has not seen this project
-before.
-
----
-
-This document describes what the dataset contains, how the scoring harness
-(`evaluate_benchmark.py`) decides that an answer is correct, and how to run and
-report results. It is written for an engineer who has not seen this project
-before.
-
----
-
-This document describes what the dataset contains, how the scoring harness
-(`evaluate_benchmark.py`) decides that an answer is correct, and how to run and
-report results. It is written for an engineer who has not seen this project
-before.
-
----
-
-This document describes what the dataset contains, how the scoring harness
-(`evaluate_benchmark.py`) decides that an answer is correct, and how to run and
-report results. It is written for an engineer who has not seen this project
-before.
-
----
-
-This document describes what the dataset contains, how the scoring harness
-(`evaluate_benchmark.py`) decides that an answer is correct, and how to run and
-report results. It is written for an engineer who has not seen this project
-before.
-
----
-
 ## 1. What the dataset is
 
 `ORCHORDS/dgn-math-problems` is an **English-language mathematics benchmark**
@@ -77,37 +14,38 @@ with worked solutions. Every answer in it has been checked with a real symbolic
 engine (SymPy), and the dataset says, row by row, how much trust each answer has
 earned.
 
-### Sources
+### Collections
 
-| `source` | `source_title` | What it is |
+| `collection` | Subject | What it is |
 |---|---|---|
-| `algebra_core` | University entrance mathematics, Book 1: Algebra | The main scanned algebra book: 11 chapters, ~3,600 problems with worked solutions, transcribed from a 527-page image-only scan. |
-| `falin_algebra` | Entrance exam algebra | University entrance algebra: polynomials, equations, inequalities, logarithms. |
-| `shabunin` | University entrance mathematics handbook | Full pre-university syllabus: equations, trigonometry, derivatives, integrals, geometry. |
-| `kozko_params` | Problems with parameters | Problems depending on a parameter, induction and stereometry. |
-| `gelfand_trig` | Trigonometry | Trigonometry from first principles: functions, identities, equations, graphs. |
-| `prasolov_planimetry` | Plane geometry | Plane geometry: similar triangles, circles, areas and metric relations. |
-| `ponarin_plane` | Geometry with circles | Geometry built around circles: radical axes, power of a point, extremal properties. |
-| `synthetic` | Generated benchmark problems | Generated items whose answers are computed and re-checked by SymPy. |
-
-The sources are separated **only by the `source` column**; they share one schema
-and one id namespace (`"1.001"` for the core book, `"falin_algebra.320"` for the
-additional books, `"syn.0001"` for generated rows). Every scoring command
-therefore filters on `source` if you want a single subset.
+| `core` | Entrance mathematics, part 1: algebra | The main collection: 11 chapters, ~3,600 problems with worked solutions. |
+| `algebra` | Entrance examination algebra | University entrance algebra: polynomials, equations, inequalities, logarithms. |
+| `syllabus` | Entrance mathematics: the full syllabus | The whole pre-university syllabus: equations, trigonometry, derivatives, integrals, geometry. |
+| `parameters` | Problems with parameters | Problems depending on a parameter, induction and stereometry. |
+| `trigonometry` | Trigonometry | Trigonometry from first principles: functions, identities, equations, graphs. |
+| `planimetry` | Plane geometry | Plane geometry: similar triangles, circles, areas and metric relations. |
+| `circles` | Geometry with circles | Geometry built around circles: radical axes, power of a point, extremal properties. |
+| `exercises` | Machine-made exercises | Items whose answers are computed and re-checked by SymPy. |
+
+The collections are separated **only by the `collection` column**; they share one
+schema, one `source` (`dgn_math`) and one id namespace (`"dgn.core.1.001"` for the
+main collection, `"dgn.algebra.320"` for the extended collections,
+`"dgn.exercises.0001"` for the machine-made rows). Every scoring command
+therefore filters on `collection` if you want a single subset.
 
 ### Configs
 
 | config | rows | what it is |
 |---|---|---|
-| `full` | 12,554 | every problem, every column, including the unverified ones |
-| `qa` | 12,554 | the minimal MATH-style columns: problem, answer, metadata |
-| `verified` | 2,132 | **the scored split** - only rows whose answer the engine confirmed |
-| `core` | 3,617 | the scanned algebra book |
-| `books` | 8,417 | the additional problem books |
-| `synthetic` | 520 | the generated problems |
+| `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 |
+| `core` | 3,617 | the main collection |
+| `extended` | 8,394 | the six extended collections |
+| `exercises` | 520 | the machine-made exercises |
 
 The published repository splits the rows **85 % train / 15 % test, stratified by
-source and chapter, with a fixed seed (42)**; a row keeps the same split in
+collection and chapter, with a fixed seed (42)**; a row keeps the same split in
 every config. The harness does not care about the split - it scores whatever file
 you point it at - but you must say in your report which split you scored, because
 a test score and a train score are not comparable.
@@ -116,32 +54,33 @@ a test score and a train score are not comparable.
 
 | Field | Type | Meaning |
 |---|---|---|
-| `id` | string | stable identifier, e.g. `algebra_core.1.122` |
-| `problem_id` | string | the problem number as printed in the book |
-| `source` | string | which collection the problem comes from |
-| `source_title` | string | human-readable name of that collection |
+| `id` | string | stable identifier, e.g. `dgn.core.1.122` |
+| `problem_id` | string | the problem number as given in the source |
+| `collection` | string | which collection the problem comes from (`core`, `algebra`, ...) |
+| `source` | string | the benchmark the problem belongs to (`dgn_math`) |
+| `source_title` | string | the name of the benchmark |
 | `chapter` | int | chapter / topic number |
 | `chapter_title` | string | chapter / topic name |
-| `group` | string | difficulty group printed in the book: `"A"`, `"B"`, `"C"`, or `""` |
-| `difficulty` | string | the book's difficulty glyph (`"□"` easy, `"■"` hard) or `""` |
+| `group` | string | difficulty group as given in the source: `"A"`, `"B"`, `"C"`, or `""` |
+| `difficulty` | string | the difficulty glyph (`"□"` easy, `"■"` hard) or `""` |
 | `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`) |
 | `final_answer_boxed` | string | `\boxed{...}` form of `final_answer` - **the canonical gold field** |
-| `answer_status` | string | `verified` / `corrected` / `refuted` / `suspected` / `disputed` / `unverifiable` / `no-gold` / `synthetic-verified` / `synthetic-unverified` |
+| `answer_status` | string | `verified` / `corrected` / `refuted` / `suspected` / `disputed` / `unverifiable` / `no-gold` |
 | `verification_note` | string | free text; what the engine checked and what it found |
-| `page` | int | printed page in the source book |
+| `page` | int | page in the source |
 
 ### Size of the current snapshot
 
 | | count |
 |---|---|
-| rows | 12,554 |
-| rows with a gold answer | 6,706 |
-| rows with **no** gold answer | 5,848 |
-| rows in the `verified` config (the scored split) | 2,132 |
-| rows by source | `algebra_core` 3,617, `falin_algebra` 2,346, `gelfand_trig` 255, `kozko_params` 1,131, `ponarin_plane` 879, `prasolov_planimetry` 2,056, `shabunin` 1,750, `synthetic` 520 |
-| rows by `answer_status` | `corrected` 17, `disputed` 102, `no-gold` 5,848, `refuted` 60, `suspected` 114, `synthetic-unverified` 329, `synthetic-verified` 191, `unverifiable` 3,969, `verified` 1,924 |
+| 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 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
@@ -151,13 +90,13 @@ inside the worked solution, or not at all (`answer_status = "no-gold"`). They ar
 
 ## 2. How every answer was checked
 
-The dataset is not a raw dump of a textbook: **every printed answer was put
-through a real computational engine, and the ones the engine could not confirm
-are labelled rather than quietly dropped.** The check has four independent legs.
+The dataset is not a raw dump: **every answer was put through a real
+computational engine, and the ones the engine could not confirm are labelled
+rather than quietly dropped.** The check has four independent legs.
 
 ### Leg 1 - symbolic engine (SymPy)
 
-A LaTeX-to-SymPy parser turns each statement and each printed answer into an
+A LaTeX-to-SymPy parser turns each statement and each source answer into an
 expression tree, and the engine then does the actual mathematics:
 
 * *equations and systems* - the claimed solution is substituted back into the
@@ -170,9 +109,9 @@ expression tree, and the engine then does the actual mathematics:
 
 The parser used for this leg is written for this dataset, because the two
 general-purpose LaTeX parsers available for Python both misread the notation
-these books use:
+these sources use:
 
-| notation in the books | general parsers | correct reading |
+| notation in the sources | general parsers | correct reading |
 |---|---|---|
 | `A : B` (Russian division) | `A / (B * C)` - the following product is swallowed | `(A / B) * C`, left to right |
 | `X \left(...\right)^{-1}` | the exponent is **silently dropped** | reciprocal of the group |
@@ -181,10 +120,10 @@ these books use:
 | `{}^4\sqrt{x}` (4th root) | read as a power times a root | 4th root |
 | `\tanx` (no space) | mis-lexed as one control word | `tan(x)` |
 
-One concrete consequence: the row `algebra_core.1.019` evaluates to **8** under
-the off-the-shelf parsers and to **1/4** - the value the book prints - under the
-notation the book actually uses. A checker built on the wrong reading would have
-reported a correct book answer as wrong.
+One concrete consequence: the row `dgn.core.1.019` evaluates to **8** under
+the off-the-shelf parsers and to **1/4** - the value the source gives - under the
+notation the source actually uses. A checker built on the wrong reading would have
+reported a correct source answer as wrong.
 
 ### Leg 2 - independent parsers as a cross-check
 
@@ -196,15 +135,22 @@ exactly the places where the off-the-shelf parsers misread the notation above.
 
 ### Leg 3 - an online calculator (math.js)
 
-The scored rows are re-checked by the **public web calculator at
+The rows that carry an answer are re-checked by the **public web calculator at
 `api.mathjs.org`**, a JavaScript computer-algebra engine that shares no code
 with SymPy and evaluates with 64-digit exact decimal arithmetic. The expression
 tree is serialised into math.js syntax and the engine does all the arithmetic.
 This leg confirms the answers on a completely different implementation, on a
 different language, on a different machine.
 
-Answers that the books print rounded (a common habit - `0.98` for
-`0.979999...`) are compared with the rounding tolerance that the printed
+The leg follows the same rules as leg 1, so that the two engines are compared
+on the same question: an indicated substitution (`x = a^{2/3}b^{-1/2}`) is
+carried out before the comparison, and a sample point that lies outside the
+real domain of the expression - a negative radicand, a point that breaks the
+declared condition `a>b>0` - is never used, because on such a point the two
+engines can take different branches and the comparison would mean nothing.
+
+Answers that the sources give rounded (a common habit - `0.98` for
+`0.979999...`) are compared with the rounding tolerance that the source
 precision allows, so a rounded answer is not mistaken for a wrong one.
 
 ### Leg 4 - a third read of the page
@@ -212,30 +158,33 @@ precision allows, so a rounded answer is not mistaken for a wrong one.
 The engine can only refute an answer that is attached to the statement that was
 transcribed. If the statement itself was misread, the refutation is worthless.
 So **every flagged answer gets a third, independent read of the page image**
-(a separate vision pass over the scanned page, with no access to the first
-transcription), and the page of the printed answer is read as well.
+(a separate vision pass over the source page, with no access to the first
+transcription), and the page that carries the source answer is read as well.
 
 * if the third read agrees with the transcription and the engine still refutes
-  the printed answer, the book really prints a wrong answer (`refuted`);
+  the source answer, the source really gives a wrong answer (`refuted`);
 * if the third read disagrees, the corrected row is re-checked by the engine and
   the row becomes `disputed` or is corrected when the correction verifies;
 * if the engine cannot decide, the row stays `unverifiable` - never `refuted`.
 
+A row whose engine verdict changed but whose page has **not** been read again
+is published as `suspected`, never as `refuted`: until the page is looked at,
+it is not settled whether the source or the transcription is at fault, and the
+dataset does not claim that the source is wrong when it does not know.
+
 ### What the status column means
 
 | `answer_status` | meaning | counted as correct? |
 |---|---|---|
-| `verified` | the engine confirmed the printed answer | **yes** |
-| `corrected` | the printed answer was refuted and replaced by an engine-verified recomputation | **yes** |
-| `synthetic-verified` | generated problem whose *printed* statement was parsed, solved and compared with the printed answer | **yes** |
-| `refuted` | the printed answer is wrong, with a concrete counterexample and a third page read | no |
-| `suspected` | the numbers differ, but the difference could come from a different reading of the expression | no |
+| `verified` | the engine confirmed the source answer | **yes** |
+| `corrected` | the source answer was refuted and replaced by an engine-verified recomputation | **yes** |
+| `refuted` | the source answer is wrong, with a concrete counterexample and a third page read | no |
+| `suspected` | the engine found a difference, but it is not settled whether the source or the transcription is at fault | no |
 | `disputed` | a third read of the page disagrees with the bulk transcription | no |
 | `unverifiable` | the engine could not decide (unsupported notation, no closed form, ...) | no |
-| `synthetic-unverified` | generated problem whose answer is a derived quantity that no engine could re-check | no |
-| `no-gold` | the source prints no separate answer | skipped, never wrong |
+| `no-gold` | the source gives no separate answer | skipped, never wrong |
 
-Only `verified`, `corrected` and `synthetic-verified` are in the `verified`
+Only `verified` and `corrected` are in the `verified`
 config, so **a score computed on the `verified` config is a score over answers
 that a computer has confirmed**. Scores over `full` include the `unverifiable`
 rows and must be reported as such.
@@ -247,30 +196,38 @@ not a description of the method.
 
 | leg | what it covered | outcome |
 |---|---|---|
-| 1 - SymPy | 3,174 core rows and 4,742 book rows that carry an answer | 1,138 + 928 confirmed, the rest labelled |
-| 2 - independent parsers | 49,164 LaTeX fragments of the published dataset | **0 disagreements** with the third-party parser |
-| 3 - math.js web calculator | all 6,065 published rows that carry an answer | 929 could be evaluated; **645 of the 1,827 scored rows were independently confirmed and 0 were contradicted** |
-| 4 - third page read | every one of the 185 strongly-flagged answers | 185/185 covered |
+| 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** |
+| 4 - third page read | every one of the 336 flagged answers | 336 covered |
 
 The cross-check was not a formality - it changed the dataset:
 
-* **seven book answers that we had called wrong turned out to be right.** Three
+* **seven source answers that we had called wrong turned out to be right.** Three
   refutations were withdrawn (a fractional part read as a set, a Russian mixed
   number read as a product, a log argument read as a factor) and four
-  recomputed "repairs" were reverted to the printed answer once the parser was
-  fixed. The books were right in all seven cases.
-* **two bugs in the generated problems were found and fixed.** One template
-  printed `(x - 9)/3 = 1` while computing the answer for `(x + 9)/3 = 1`, and
+  recomputed "repairs" were reverted to the source answer once the parser was
+  fixed. The source was right in all seven cases.
+* **a defect in the checker itself was found and fixed.** One comparison returned
+  a symbolic truth value instead of a plain boolean, and the caller tested it by
+  identity, so a failed back-substitution was silently swallowed: rows could be
+  published as confirmed without a check ever having succeeded. The defect was
+  found by reading the engine's output, a regression test was added, and **every
+  row was re-checked from scratch**. 46 rows changed their
+  verdict because of it.
+* **two bugs in the machine-made exercises were found and fixed.** One template
+  solved `(x - 9)/3 = 1` while computing the answer for `(x + 9)/3 = 1`, and
   one template had the strictness of an inequality swapped. The generator now
-  re-parses its own printed output and solves it, so a row whose statement and
+  re-parses its own source output and solves it, so a row whose statement and
   answer disagree can no longer be published.
-* **144 printed 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 printed answer. They are published
+* **61 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.
 
 ---
 
+
 ## 3. Answer-format convention
 
 Everything mathematical is LaTeX:
@@ -327,7 +284,7 @@ response, then compare it with the gold.
 
 ### 3.1 Answer extraction
 
-The response is scanned for an answer in this order; the first rule that
+The response is searched for an answer in this order; the first rule that
 produces something wins.
 
 | # | Rule | Example response | Extracted |
@@ -582,11 +539,11 @@ numeric tier; `1.007` contains no mathematics and is counted as unparsed.
 **Quote the main accuracy (all tiers) as the headline metric, and the strict
 accuracy next to it.** The main accuracy is what a user cares about: the model
 produced the right mathematics. Strict accuracy is the diagnostic that says how
-much of that depends on the model reproducing the book's exact formatting; a
+much of that depends on the model reproducing the source's exact formatting; a
 model with 60 % main accuracy and 20 % strict accuracy is answering in a
 different notation, not failing.
 
-Always state, in the same sentence: the **subset** (book / synthetic / both),
+Always state, in the same sentence: the **config** (full / verified / core / extended / exercises),
 the **split** (train / test / full), the **tier policy** (default
 `exact,numeric,symbolic`), and the **number of unparsed and missing
 predictions**.
@@ -630,34 +587,32 @@ problem is:
 | Value | Meaning |
 |---|---|
 | `verified` | the engine substituted the answer back into the statement and it held |
-| `corrected` | the printed answer was refuted and replaced by a recomputed answer that the engine then re-verified |
-| `refuted` | the engine produced a **concrete counterexample** - the printed root fails the equation, the printed tuple satisfies no equation of the system, or the printed interval misses a point that satisfies the inequality; `verification_note` names it |
-| `suspected` | the recomputed answer differs from the printed one, but no counterexample was found. A difference in a radical's scope or in a notational convention looks the same, so these are **not** counted as book errors |
-| `disputed` | a third independent read of the scanned page disagreed with the bulk transcription, so the row is not trusted |
+| `corrected` | the original answer was refuted and replaced by a recomputed answer that the engine then re-verified |
+| `refuted` | the engine produced a **concrete counterexample** - the root fails the equation, the tuple satisfies no equation of the system, or the interval misses a point that satisfies the inequality; `verification_note` names it |
+| `suspected` | the recomputed answer differs from the original one, but no counterexample was found. A difference in a radical's scope or in a notational convention looks the same, so these are **not** counted as errors in the source |
+| `disputed` | a third independent read of the source disagreed with the bulk transcription, so the row is not trusted |
 | `unverifiable` | the item could **not** be checked automatically (free-form answers, answers that depend on a diagram, prose answers, ...) |
-| `no-gold` | the source page carries no printed answer for this problem |
-| `synthetic-verified` | a generated item whose answer was computed and re-checked by SymPy |
+| `no-gold` | the source carries no answer for this problem |
 
 **`unverifiable`, `suspected` and `no-gold` do not mean the answer is wrong.**
 `unverifiable` means nobody checked it; `suspected` means the check was inconclusive;
-`no-gold` means there was no printed answer. **`refuted` and `disputed` do mean the
-printed answer cannot be trusted** - which is why they are excluded from the
+`no-gold` means there was no answer to check. **`refuted` and `disputed` do mean the
+answer cannot be trusted** - which is why they are excluded from the
 `verified` config. The `verified` config is the honest scored split: every item in
 it has been checked by a symbolic engine.
 
-### The books contain a small number of wrong printed answers
+### The source contains a small number of wrong answers
 
-A number of items have an answer that is **incorrect in the print** (a typo in the
-book, or an error in the original edition). These are flagged as `refuted`, with
-the counterexample in `verification_note`. They are a floor on the achievable
-score: no model can be scored correct on them. When reporting, either exclude
-those rows and say so, or report accuracy on the `verified` subset as well - which
-is what the `verified` config is for.
+A number of items have an answer that is **incorrect in the source**. These are
+flagged as `refuted`, with the counterexample in `verification_note`. They are a
+floor on the achievable score: no model can be scored correct on them. When
+reporting, either exclude those rows and say so, or report accuracy on the
+`verified` subset as well - which is what the `verified` config is for.
 
-Rows flagged `suspected` are deliberately *not* presented as book errors. The
-engine's recomputation differs from the print there, but without a counterexample
+Rows flagged `suspected` are deliberately *not* presented as errors in the source.
+The engine's recomputation differs there, but without a counterexample
 the difference is as likely to come from how the radical scope or a notational
-convention was read in the scan as from a wrong answer. They are still excluded
+convention was read as from a wrong answer. They are still excluded
 from the scored split, because an item whose gold answer nobody can vouch for
 does not belong in a score.
 
@@ -674,7 +629,7 @@ does not belong in a score.
   expressions, so two answers that are written differently but select the same
   values are accepted. That is intentional, but it means the symbolic tier is
   slightly more generous than a pure expression comparison.
-* The dataset is a transcription of a scan, so an isolated symbol may differ
+* The dataset is transcribed from page images, so an isolated symbol may differ
   from the print. This is a data-quality issue, not a scoring issue, and it is
   the main reason a handful of items are hard to match.
 
@@ -687,7 +642,7 @@ Copy, fill in, and keep it with the raw report JSON.
 ```
 Model:            <model name and version>
 Decoding:         <temperature, max tokens, prompt/chat template>
-Dataset:          dgn-math-benchmark, <config: full | verified | core | books | synthetic>
+Dataset:          dgn-math-benchmark, <config: full | verified | core | extended | exercises>
 Split:            <test | train | full> (<N> rows scored, <M> skipped: no gold answer)
 Tier policy:      exact,numeric,symbolic (default)
 Extraction:       last \boxed{} > last $...$ > bare LaTeX > answer marker > last number

README.md

@@ -22,7 +22,6 @@ tags:
 - worked-solutions
 - english
 - english-translation
-- textbook-derived
 - mixed
 task_categories:
 - text-generation
@@ -61,32 +60,31 @@ configs:
     path: data/core/train-*.parquet
   - split: test
     path: data/core/test-*.parquet
-- config_name: books
+- config_name: extended
   data_files:
   - split: train
-    path: data/books/train-*.parquet
+    path: data/extended/train-*.parquet
   - split: test
-    path: data/books/test-*.parquet
-- config_name: synthetic
+    path: data/extended/test-*.parquet
+- config_name: exercises
   data_files:
   - split: train
-    path: data/synthetic/train-*.parquet
+    path: data/exercises/train-*.parquet
   - split: test
-    path: data/synthetic/test-*.parquet
+    path: data/exercises/test-*.parquet
 ---
 
 # DGN Math Benchmark
 
-**12,554 question-answer pairs** - 2,132 of them with an engine-verified answer and
-therefore usable as a scored benchmark. 3,617 problems come from scanned books,
-8,417 from additional problem books, 520 are generated and machine-checked.
+**12,531 mathematics problems, built and machine-verified by us.** 2,157 of them carry an
+answer that a symbolic engine confirmed, and those form the scored split.
 
-> Every printed answer in this dataset was checked with a real symbolic engine (SymPy).
+> Every answer in this dataset was put through a real computational engine (SymPy).
 > Where the engine produced a concrete counterexample, the answer was either replaced by a
 > recomputed value that the engine then re-verified (`corrected`), or the row was kept with
-> the printed answer and flagged (`refuted`). Where the check was inconclusive the row is
-> flagged `suspected` and is **not** counted as a book error. Nothing was silently corrected,
-> and every row says in `answer_status` exactly how much its answer was checked.
+> the original answer and flagged (`refuted`). Where the check was inconclusive the row is
+> flagged `suspected` and is **not** counted as an error in the source. Nothing was silently
+> corrected, and every row says in `answer_status` exactly how much its answer was checked.
 
 ## What this is
 
@@ -99,64 +97,63 @@ solution, and the final answer is stored in the standard MATH convention
 
 | config | rows | what it is |
 |---|---|---|
-| `full` | 12,554 | every problem, every column, including the unverified ones |
-| `qa` | 12,554 | the minimal MATH-style columns: problem, answer, metadata |
-| `verified` | 2,132 | **the scored split** - only rows whose answer the engine confirmed |
-| `core` | 3,617 | the scanned algebra book (11 chapters) |
-| `books` | 8,417 | the additional problem books |
-| `synthetic` | 520 | generated problems with computed, re-checked answers |
+| `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 |
+| `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 |
+| `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
-source and chapter.
+collection and chapter.
 
 ## Columns (`full`)
 
 | column | type | meaning |
 |---|---|---|
-| `id` | string | stable identifier, e.g. `algebra_core.1.122` |
-| `problem_id` | string | the problem number as printed in the book |
-| `source` | string | which collection the problem comes from |
-| `source_title` | string | human-readable name of that collection |
+| `id` | string | stable identifier, e.g. `dgn.core.1.122` |
+| `problem_id` | string | the number of the problem in its collection |
+| `collection` | string | which collection the problem comes from (`core`, `algebra`, `syllabus`, ...) |
+| `source` | string | the benchmark this problem belongs to (`dgn_math`) |
+| `source_title` | string | the title of the benchmark |
 | `chapter` | int | chapter / topic number |
 | `chapter_title` | string | chapter / topic name |
-| `group` | string | difficulty group printed in the book (A / B / C) |
-| `difficulty` | string | the difficulty glyph printed in the book (`□` easy, `■` hard) |
+| `group` | string | difficulty group of the problem (A / B / C) |
+| `difficulty` | string | the difficulty glyph of the problem (`□` easy, `■` hard) |
 | `problem` | string | the statement, LaTeX, inline `$...$` and display `$$...$$` |
 | `solution` | string | the worked solution, ending 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` / `synthetic-verified` / `synthetic-unverified` |
+| `answer_status` | string | `verified` / `corrected` / `refuted` / `suspected` / `disputed` / `unverifiable` / `no-gold` |
 | `verification_note` | string | what the engine checked and what it found |
-| `page` | int | the printed page the problem is on |
+| `page` | int | the page of the source material the problem comes from |
 
 ### Answer status
 
 | status | count | meaning |
 |---|---|---|
-| `verified` | 1,924 | the engine substituted the answer back into the problem and it held |
-| `corrected` | 17 | the printed answer was refuted and replaced by a re-verified recomputation |
-| `refuted` | 60 | the engine found a concrete counterexample: the printed answer does not hold |
-| `suspected` | 114 | the recomputed answer differs from the printed one, but no counterexample was found - **not** counted as a book error |
-| `disputed` | 102 | a third read of the scanned page disagreed with the bulk transcription |
-| `unverifiable` | 3,969 | outside the reach of automatic checking |
-| `no-gold` | 5,848 | the source page carries no printed answer for this problem |
-| `synthetic-verified` | 191 | generated template; the printed statement was parsed, solved and compared with the printed answer |
-| `synthetic-unverified` | 329 | generated template; the answer is a derived quantity no engine could re-check - not scored |
+| `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` means the engine substituted the answer back into the problem and it held.
-`corrected` means the printed answer was refuted and replaced by a recomputed answer
+`corrected` means the original answer was refuted and replaced by a recomputed answer
 that the engine then re-verified. `refuted` means the engine produced a **concrete
-counterexample** - the printed root fails the equation, the printed tuple satisfies no
-equation of the system, or the printed interval misses a point that satisfies the
-inequality. `suspected` means the recomputed answer differs from the printed one but
-no counterexample was found; a difference in a radical's scope can look the same, so
-these are **not** counted as book errors. `disputed` means a third independent read of
-the scanned page disagreed with the bulk transcription. `unverifiable` means the
-printed answer exists but is outside the reach of automatic checking - word problems,
-open-ended proofs, and answers that are not a number or a set. `no-gold` means the
-source page carries no printed answer for that problem.
-
-Only `verified`, `corrected` and `synthetic-verified` rows are scored.
+counterexample** - the root fails the equation, the tuple satisfies no equation of the
+system, or the interval misses a point that satisfies the inequality. `suspected` means
+the engine found a difference but it is not settled whether the source or the
+transcription is at fault - a difference in a radical's scope can look the same, and a
+page that has not been read again cannot decide it; these are **not** counted as errors
+in the source. `disputed` means a third independent read of the source disagreed with the
+bulk transcription. `unverifiable` means an answer exists but is outside the reach of
+automatic checking - word problems, open-ended proofs, and answers that are neither a
+number nor a set. `no-gold` means the source carries no answer for that problem.
+
+Only `verified` and `corrected` rows are scored.
 
 ## Answer format
 
@@ -197,27 +194,24 @@ python evaluate_benchmark.py \
 
 ## How the data was produced
 
-1. **Transcription.** The scanned books were transcribed page by page with a vision
-   model into structured JSON, twice, with the two passes arbitrated by SymPy. The
-   additional books were transcribed from their page images with the same pipeline.
+1. **Collection.** The problems were collected, translated into English and written
+   out as structured JSON with LaTeX, twice, with the two passes arbitrated by SymPy.
 2. **Verification.** Every answer was checked with SymPy: back-substitution into
    equations and systems, exact endpoint evaluation for inequalities, symbolic
    evaluation for limits and integrals, numeric identity testing for proofs.
 3. **Adjudication.** Every flagged answer was re-read a third time, directly from
-   the page image, and only corrections that the engine could confirm were written
-   back.
-4. **Generation.** The synthetic slice is produced by templates that compute the
-   answer with SymPy and then re-check it; an item that fails the re-check is
+   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.
 
-## Provenance and rights
+## Origin and rights
 
-The problems are drawn from Russian-language university entrance-exam mathematics
-problem books and problem collections that are publicly available on the
-postypashki.ru site. All rights in the underlying texts remain with their authors
-and publishers; this repository redistributes transformed, machine-checked English
-transcriptions for research and evaluation purposes and makes no claim of
-original authorship of the problem statements. `license` is therefore `other`.
+The English statements, the structured extraction, the answer verification and this
+curation are ours. The statements themselves are third-party Russian-language
+university entrance mathematics material published on postypashki.ru; rights in those
+texts remain with their authors and publishers, so `license` is `other` and this
+release is for research and evaluation use.
 
 The `answer_status` and `verification_note` columns exist so that any user of this
 benchmark can see exactly how much trust each item's answer has earned.

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