Publish v1.0.2 difficulty definition and audit

Documentation-only release relative to v1.0.1. Adds a pinned, source-grounded Tdoku difficulty definition, quantitative raw-pool audit, source-confounding analysis, and reproducibility limitations. The seven raw CSV files and four processed Parquet splits are byte-identical to v1.0.1.

README.md

@@ -25,10 +25,14 @@ configs:
 # Sudoku DLM Reasoning
 
 `stwistzz/Sudoku_DLM_Reasoning` is a deterministic 9x9 Sudoku benchmark for studying masked
-diffusion language models, depth, and iterative decoding. Version 1.0.1
+diffusion language models, depth, and iterative decoding. Version 1.0.2
 trains only on `original`, `r0`, and `r1_4`; `r5_19` is held out for adjacent
 difficulty extrapolation.
 
+Version 1.0.2 is a documentation-only update relative to v1.0.1.
+The seven raw CSV files and all four released Parquet splits are byte-identical;
+only the difficulty definition, audit, and version metadata were added or updated.
+
 ## Repository layout
 
 - `raw/`: complete 1,415,420-row candidate snapshot used by this protocol
@@ -36,6 +40,7 @@ difficulty extrapolation.
 - `metadata/`: source/release hashes, split specification, and audits
 - `scripts/`: deterministic builder and independent verifier
 - `docs/BUILDING.md`: end-to-end reconstruction instructions
+- `docs/DIFFICULTY.md`: operational difficulty definition and quantitative audit
 
 Files under `raw/` are explicitly source data and are not loaded as extra splits.
 Only the four `data/*.parquet` paths declared in the card metadata form the
@@ -57,9 +62,16 @@ small number of already-selected configurations; it is not a tuning split.
 
 ## Difficulty
 
-`r0`, `r1_4`, and `r5_19` use the number of tdoku backtracks. Higher values are
-harder. `original` comes from a separate easy Sudoku collection and is not on the
-same numeric scale.
+`r0`, `r1_4`, and `r5_19` use an upstream Tdoku search measurement. In public
+Tdoku commit `af426180dc53aef89b82868e7b3fdfcf42165654`, the counter increments when the
+solver expands a binary band/stack-configuration decision after constraint propagation.
+It is therefore best interpreted as visited search decision nodes, not recursion
+depth, failed undo count, clue count, or human difficulty. `original` comes from
+a separate easy collection and has no official rating on this scale.
+
+See `docs/DIFFICULTY.md` for the DFS root, propagation and branch semantics,
+bucket formulas, full raw-pool statistics, source confounding, and the upstream
+rating-provenance limitation.
 
 The evaluation sample deliberately covers subranges:
 

docs/BUILDING.md

@@ -29,7 +29,7 @@ machine-readable audits.
 Verify the result independently:
 
 ```bash
-python scripts/verify_dataset.py rebuilt-release --expected-version 1.0.1
+python scripts/verify_dataset.py rebuilt-release --expected-version 1.0.2
 ```
 
 The expected processed split hashes are recorded in `metadata/manifest.json`.

docs/DIFFICULTY.md

@@ -0,0 +1,165 @@
+# Difficulty definition and quantitative audit
+
+This document defines the difficulty fields used by Sudoku DLM Reasoning release
+`1.0.2`. Difficulty is an operational, solver-relative measurement;
+it is not a human Sudoku grade and is not defined by the number of clues.
+
+## 1. Provenance of the rating
+
+For the Sudoku Extreme rows, the upstream `rating` column is copied into
+`official_rating` and labeled `rating_type = tdoku_backtracks`. The converter
+does not recompute the rating:
+
+- Sudoku Extreme card: https://huggingface.co/datasets/sapientinc/sudoku-extreme
+- Conversion code: https://github.com/hengyuf/diffusion-vs-ar/blob/ba0445f4d0808113bf08a9a9d8c7041086bfdf10/tools/prepare_sudoku_datasets.py
+
+The upstream card describes the value as the number of backtracks required by
+Tdoku. At public Tdoku commit `af426180dc53aef89b82868e7b3fdfcf42165654`, the counter is named
+`num_guesses_` and is incremented whenever the DPLL solver expands a binary
+configuration decision:
+
+- Branch implementation: https://github.com/t-dillon/tdoku/blob/af426180dc53aef89b82868e7b3fdfcf42165654/src/solver_dpll_triad_simd.cc#L539-L559
+- Branch-variable selection: https://github.com/t-dillon/tdoku/blob/af426180dc53aef89b82868e7b3fdfcf42165654/src/solver_dpll_triad_simd.cc#L473-L536
+
+Operationally, `official_rating` is best interpreted as the number of search
+decision nodes visited before the first solution, rather than literal failed
+undo operations.
+
+## 2. Constraint propagation and the DFS root
+
+Tdoku does not begin search from an empty board or from the first empty cell.
+For a standard 81-character puzzle it:
+
+1. loads every given digit;
+2. eliminates incompatible row, column, box, band, and stack configurations;
+3. propagates those eliminations until the initialized state is consistent; and
+4. calls depth-first search on that propagated partial state.
+
+The initialization and call path are visible in that pinned public source:
+
+- Initialization: https://github.com/t-dillon/tdoku/blob/af426180dc53aef89b82868e7b3fdfcf42165654/src/solver_dpll_triad_simd.cc#L612-L634
+- Solve entry point: https://github.com/t-dillon/tdoku/blob/af426180dc53aef89b82868e7b3fdfcf42165654/src/solver_dpll_triad_simd.cc#L680-L693
+
+Propagation applies only logical consequences of the current givens or branch
+assumption. It makes no new hypothesis and is not counted by the rating. It can
+end in a complete solution, a contradiction, or a fixed point that still has
+multiple configurations.
+
+This matters because two puzzles can both have rating zero while requiring very
+different amounts of propagation.
+
+## 3. What one branch means
+
+For one digit in a three-row band (or a three-column stack), there are six
+possible global placements across the three boxes. Tdoku represents these as
+band configurations. When propagation leaves multiple configurations, the
+branching heuristic selects:
+
+1. the unresolved band or stack with the fewest configurations; then
+2. the digit in that band or stack with the fewest configurations.
+
+It then creates a binary decision:
+
+- left branch: force the first remaining configuration;
+- right branch: exclude that configuration and retain the others.
+
+The counter increases once for this binary split. If the left branch fails and
+the right branch immediately solves the puzzle, the count for that decision is
+still one. A later split of the remaining configurations increases it again.
+Therefore the rating is not the recursion depth, the number of filled cells, the
+number of contradictions, or a human solving-step count.
+
+## 4. Bucket definitions
+
+The source converter applies these thresholds:
+
+| release label | operational rule | interpretation |
+|---|---:|---|
+| `original` | no Tdoku rating | separate easy collection; not numerically calibrated to Extreme |
+| `r0` | rating = 0 | propagation resolves the puzzle without a search decision |
+| `r1_4` | 1 <= rating < 5 | 1--4 visited decision nodes |
+| `r5_19` | 5 <= rating < 20 | 5--19 visited decision nodes |
+
+The upstream converter also defines `r20_49`, `r50_99`, and `r100_plus`, but
+those buckets are outside this v1 candidate pool. Thus `r5_19` is an adjacent
+held-out difficulty band, not the hardest part of the upstream corpus.
+
+## 5. Quantitative audit of the raw candidate pool
+
+The following statistics were computed over all 1,415,420 rows included under
+`raw/`. Rating and clue statistics use the full pool.
+
+| bucket | rows | rating mean / median | clue mean / median | clue range |
+|---|---:|---:|---:|---:|
+| `original` | 101,000 | not rated | 33.813 / 34 | 29--37 |
+| `r0` | 614,136 | 0 / 0 | 26.282 / 26 | 17--37 |
+| `r1_4` | 588,453 | 1.976 / 2 | 25.604 / 26 | 17--31 |
+| `r5_19` | 111,831 | 11.776 / 12 | 24.932 / 25 | 17--30 |
+
+Clue count is not a substitute for this rating. Within `r1_4`, the Pearson
+correlation between rating and clues is -0.035; within `r5_19` it is 0.002.
+
+As an independent diagnostic, standard row/column/box naked-single propagation
+was run over all 101,000 original rows and deterministic 20,000-row reservoir
+samples of each Extreme bucket. The reservoir seeds were `20260816` for `r0`,
+`20260817` for `r1_4`, and `20260818` for `r5_19`:
+
+| bucket | rows checked | solved by naked singles |
+|---|---:|---:|
+| `original` | 101,000 | 100,959 (99.959%) |
+| `r0` | 20,000 | 3,691 (18.455%) |
+| `r1_4` | 20,000 | 0 |
+| `r5_19` | 20,000 | 0 |
+
+The 41 original rows that stalled under naked singles were all solved after
+adding hidden-single propagation. This independent audit describes basic Sudoku
+logic, not Tdoku's own internal propagation, which is configuration-based and
+stronger.
+
+## 6. Released train and evaluation distributions
+
+The three training buckets are equal in size, but exact ratings inside `r1_4`
+retain the upstream proportions:
+
+| exact rating | train rows |
+|---:|---:|
+| 1 | 29,584 |
+| 2 | 16,809 |
+| 3 | 10,244 |
+| 4 | 8,899 |
+
+The main `r1_4` test allocation instead uses 250 rows at each exact rating 1,
+2, 3, and 4. The `r5_19` test allocation uses 250 rows from each of `[5,8)`,
+`[8,12)`, `[12,16)`, and `[16,20)`; `test_ood_confirm` uses 1,000 per range.
+This supports per-rating or per-range reporting rather than only a bucket-wide
+average.
+
+## 7. Source confounding
+
+Difficulty and source collection are not independent in the raw pool:
+
+- `r0`: 77.40% `puzzles1_unbiased`, 16.28% `puzzles0_kaggle`, and 6.30%
+  `puzzles2_17_clue`;
+- `r1_4`: 85.02% `puzzles1_unbiased`, 9.70%
+  `puzzles4_forum_hardest_1905`, and 3.40% `01_file1`;
+- `r5_19`: 68.19% `puzzles4_forum_hardest_1905`, 28.15% `01_file1`, and only
+  2.18% `puzzles1_unbiased`.
+
+Consequently, an `r5_19` result combines a Tdoku-rating shift, a held-out
+training-exposure shift, and a source-distribution shift. It must not be
+interpreted as a pure causal effect of search count.
+
+Recommended reporting includes exact rating or subrange, source collection, and
+clue count. A source- and clue-matched diagnostic set is appropriate when the
+goal is to isolate the rating axis.
+
+## 8. Reproducibility limitation
+
+The public Sudoku Extreme card does not pin the Tdoku commit, build flags,
+command, permutation policy, or seed used to create its rating column. This
+release therefore preserves `official_rating` as an upstream measurement rather
+than claiming to reproduce it.
+
+For a fully controlled future rating, pin a Tdoku commit and configuration,
+record the branch count for the exact stored puzzle, and optionally measure its
+mean and variance over Sudoku-preserving isomorphic transformations.

metadata/audit.json

@@ -1,5 +1,5 @@
 {
-  "dataset_version": "1.0.1",
+  "dataset_version": "1.0.2",
   "pairwise_overlap": {
     "test__vs__test_ood_confirm": {
       "digit_normalized_id": 0,

metadata/manifest.json

@@ -1,15 +1,15 @@
 {
   "audit_file": "metadata/audit.json",
   "dataset_id": "stwistzz/Sudoku_DLM_Reasoning",
-  "dataset_version": "1.0.1",
+  "dataset_version": "1.0.2",
   "files": {
     "RAW_DATA_LICENSES.md": {
       "bytes": 1252,
       "sha256": "4749d8f59f442d90f1241e37ee2a6de27e0de0bc9b2712ec8a44a5a64e4a0c95"
     },
     "README.md": {
-      "bytes": 5349,
-      "sha256": "812dc60c7543bd923a04eac5ef12391996063137966b1d717c9344cf0f309e6f"
+      "bytes": 6164,
+      "sha256": "350518f69a660d092b34a73a0b47f500ec7407ce814e6c07af39af9db7a37bde"
     },
     "data/test.parquet": {
       "bytes": 742254,
@@ -33,11 +33,15 @@
     },
     "docs/BUILDING.md": {
       "bytes": 1228,
-      "sha256": "5c4d605f33bfc700afba5a37ce8049ea48a24e64e0e6eb9b3cce2c18d103fa87"
+      "sha256": "360e3e44a58cefcdb883d89ab05ecc49efdba1b46e3453648ef6f7f782f29a64"
+    },
+    "docs/DIFFICULTY.md": {
+      "bytes": 7685,
+      "sha256": "5fcbc6349b289af7dc013b4b0ebc00b49d3a5d09ec74c3105f928f2bf2005fd5"
     },
     "metadata/audit.json": {
       "bytes": 5465,
-      "sha256": "970bd16c1120344e1eb04a5325b0ba45d592b79b4360317b35da9a099b0b030d"
+      "sha256": "716a623debed5e9e699de4092619585e1822651fb1857b72344c451ca721b345"
     },
     "metadata/raw_manifest.json": {
       "bytes": 2592,
@@ -45,11 +49,11 @@
     },
     "metadata/split_spec.json": {
       "bytes": 849,
-      "sha256": "18e4e6ffe8dbd843a9882ad78164da7152532a214ef7d9dcd4460a59c6f775e1"
+      "sha256": "e080a20ae0e8dd90c71c3bc5be5a2cdaac36d42f27328702e2133a137548cdeb"
     },
     "raw/README.md": {
       "bytes": 1187,
-      "sha256": "101942ebbc7a1550e9a304d89e29dcd771e036d377eb73cfe94f5decd92c1be5"
+      "sha256": "dfc414593ecec884d4719f438d74e62ed1735d2909d444f2576d038a893ff3ca"
     },
     "raw/processed/sudoku_extreme_test_r0.csv": {
       "bytes": 13913402,
@@ -95,15 +99,15 @@
       "sha256": "1842dad6fc80950a344e79b6831aeacf39f51f9949742de90114bccb350a26a9"
     },
     "scripts/build_dataset.py": {
-      "bytes": 44856,
-      "sha256": "1133254160b1496d6bc017753247c98acf8dc06d5ab494db15a98f19bfd75090"
+      "bytes": 53351,
+      "sha256": "b4b921f6380b18e618a920f8b2ec102ef6033dc596d9081472d937745082960b"
     },
     "scripts/verify_dataset.py": {
       "bytes": 10838,
       "sha256": "1cc3a341225c6aa700ec6d675e675d75982ee6325682d643112000010e6571bd"
     }
   },
-  "generated_at_utc": "2026-08-15T17:06:43.211264+00:00",
+  "generated_at_utc": "2026-08-15T19:57:19.021875+00:00",
   "raw_snapshot_file": "metadata/raw_manifest.json",
   "schema": [
     {

metadata/split_spec.json

@@ -14,7 +14,7 @@
     "train_per_bucket": 65536,
     "validation_per_bucket": 2048
   },
-  "dataset_version": "1.0.1",
+  "dataset_version": "1.0.2",
   "ood_bucket": "r5_19",
   "seed": "20260815",
   "selection": "metadata-stratified bottom-k SHA-256 rank",

raw/README.md

@@ -1,7 +1,7 @@
 # Raw source snapshot
 
 This directory is explicitly labeled **raw**. It contains unmodified copies of
-the seven upstream CSV files scanned by the `1.0.1` builder:
+the seven upstream CSV files scanned by the `1.0.2` builder:
 
 | raw path | upstream split | difficulty | rows |
 |---|---|---|---:|

scripts/build_dataset.py

@@ -32,11 +32,12 @@ import pyarrow as pa
 import pyarrow.parquet as pq
 
 
-DATASET_VERSION = "1.0.1"
+DATASET_VERSION = "1.0.2"
 DEFAULT_DATASET_ID = "stwistzz/Sudoku_DLM_Reasoning"
 DEFAULT_SEED = "20260815"
 SOURCE_REPO = "fhyfhy/diffusion-vs-ar-hard-sudoku"
 SOURCE_REVISION = "527859f62c745c16833aded130ad9f9ddddb76af"
+TDOKU_REFERENCE_REVISION = "af426180dc53aef89b82868e7b3fdfcf42165654"
 
 TRAIN_PER_BUCKET = 65_536
 VALIDATION_PER_BUCKET = 2_048
@@ -663,6 +664,175 @@ Timestamp fields may differ across rebuilds; the Parquet content hashes must not
 """
 
 
+def render_difficulty_guide() -> str:
+    return f"""# Difficulty definition and quantitative audit
+
+This document defines the difficulty fields used by Sudoku DLM Reasoning release
+`{DATASET_VERSION}`. Difficulty is an operational, solver-relative measurement;
+it is not a human Sudoku grade and is not defined by the number of clues.
+
+## 1. Provenance of the rating
+
+For the Sudoku Extreme rows, the upstream `rating` column is copied into
+`official_rating` and labeled `rating_type = tdoku_backtracks`. The converter
+does not recompute the rating:
+
+- Sudoku Extreme card: https://huggingface.co/datasets/sapientinc/sudoku-extreme
+- Conversion code: https://github.com/hengyuf/diffusion-vs-ar/blob/ba0445f4d0808113bf08a9a9d8c7041086bfdf10/tools/prepare_sudoku_datasets.py
+
+The upstream card describes the value as the number of backtracks required by
+Tdoku. At public Tdoku commit `{TDOKU_REFERENCE_REVISION}`, the counter is named
+`num_guesses_` and is incremented whenever the DPLL solver expands a binary
+configuration decision:
+
+- Branch implementation: https://github.com/t-dillon/tdoku/blob/{TDOKU_REFERENCE_REVISION}/src/solver_dpll_triad_simd.cc#L539-L559
+- Branch-variable selection: https://github.com/t-dillon/tdoku/blob/{TDOKU_REFERENCE_REVISION}/src/solver_dpll_triad_simd.cc#L473-L536
+
+Operationally, `official_rating` is best interpreted as the number of search
+decision nodes visited before the first solution, rather than literal failed
+undo operations.
+
+## 2. Constraint propagation and the DFS root
+
+Tdoku does not begin search from an empty board or from the first empty cell.
+For a standard 81-character puzzle it:
+
+1. loads every given digit;
+2. eliminates incompatible row, column, box, band, and stack configurations;
+3. propagates those eliminations until the initialized state is consistent; and
+4. calls depth-first search on that propagated partial state.
+
+The initialization and call path are visible in that pinned public source:
+
+- Initialization: https://github.com/t-dillon/tdoku/blob/{TDOKU_REFERENCE_REVISION}/src/solver_dpll_triad_simd.cc#L612-L634
+- Solve entry point: https://github.com/t-dillon/tdoku/blob/{TDOKU_REFERENCE_REVISION}/src/solver_dpll_triad_simd.cc#L680-L693
+
+Propagation applies only logical consequences of the current givens or branch
+assumption. It makes no new hypothesis and is not counted by the rating. It can
+end in a complete solution, a contradiction, or a fixed point that still has
+multiple configurations.
+
+This matters because two puzzles can both have rating zero while requiring very
+different amounts of propagation.
+
+## 3. What one branch means
+
+For one digit in a three-row band (or a three-column stack), there are six
+possible global placements across the three boxes. Tdoku represents these as
+band configurations. When propagation leaves multiple configurations, the
+branching heuristic selects:
+
+1. the unresolved band or stack with the fewest configurations; then
+2. the digit in that band or stack with the fewest configurations.
+
+It then creates a binary decision:
+
+- left branch: force the first remaining configuration;
+- right branch: exclude that configuration and retain the others.
+
+The counter increases once for this binary split. If the left branch fails and
+the right branch immediately solves the puzzle, the count for that decision is
+still one. A later split of the remaining configurations increases it again.
+Therefore the rating is not the recursion depth, the number of filled cells, the
+number of contradictions, or a human solving-step count.
+
+## 4. Bucket definitions
+
+The source converter applies these thresholds:
+
+| release label | operational rule | interpretation |
+|---|---:|---|
+| `original` | no Tdoku rating | separate easy collection; not numerically calibrated to Extreme |
+| `r0` | rating = 0 | propagation resolves the puzzle without a search decision |
+| `r1_4` | 1 <= rating < 5 | 1--4 visited decision nodes |
+| `r5_19` | 5 <= rating < 20 | 5--19 visited decision nodes |
+
+The upstream converter also defines `r20_49`, `r50_99`, and `r100_plus`, but
+those buckets are outside this v1 candidate pool. Thus `r5_19` is an adjacent
+held-out difficulty band, not the hardest part of the upstream corpus.
+
+## 5. Quantitative audit of the raw candidate pool
+
+The following statistics were computed over all 1,415,420 rows included under
+`raw/`. Rating and clue statistics use the full pool.
+
+| bucket | rows | rating mean / median | clue mean / median | clue range |
+|---|---:|---:|---:|---:|
+| `original` | 101,000 | not rated | 33.813 / 34 | 29--37 |
+| `r0` | 614,136 | 0 / 0 | 26.282 / 26 | 17--37 |
+| `r1_4` | 588,453 | 1.976 / 2 | 25.604 / 26 | 17--31 |
+| `r5_19` | 111,831 | 11.776 / 12 | 24.932 / 25 | 17--30 |
+
+Clue count is not a substitute for this rating. Within `r1_4`, the Pearson
+correlation between rating and clues is -0.035; within `r5_19` it is 0.002.
+
+As an independent diagnostic, standard row/column/box naked-single propagation
+was run over all 101,000 original rows and deterministic 20,000-row reservoir
+samples of each Extreme bucket. The reservoir seeds were `20260816` for `r0`,
+`20260817` for `r1_4`, and `20260818` for `r5_19`:
+
+| bucket | rows checked | solved by naked singles |
+|---|---:|---:|
+| `original` | 101,000 | 100,959 (99.959%) |
+| `r0` | 20,000 | 3,691 (18.455%) |
+| `r1_4` | 20,000 | 0 |
+| `r5_19` | 20,000 | 0 |
+
+The 41 original rows that stalled under naked singles were all solved after
+adding hidden-single propagation. This independent audit describes basic Sudoku
+logic, not Tdoku's own internal propagation, which is configuration-based and
+stronger.
+
+## 6. Released train and evaluation distributions
+
+The three training buckets are equal in size, but exact ratings inside `r1_4`
+retain the upstream proportions:
+
+| exact rating | train rows |
+|---:|---:|
+| 1 | 29,584 |
+| 2 | 16,809 |
+| 3 | 10,244 |
+| 4 | 8,899 |
+
+The main `r1_4` test allocation instead uses 250 rows at each exact rating 1,
+2, 3, and 4. The `r5_19` test allocation uses 250 rows from each of `[5,8)`,
+`[8,12)`, `[12,16)`, and `[16,20)`; `test_ood_confirm` uses 1,000 per range.
+This supports per-rating or per-range reporting rather than only a bucket-wide
+average.
+
+## 7. Source confounding
+
+Difficulty and source collection are not independent in the raw pool:
+
+- `r0`: 77.40% `puzzles1_unbiased`, 16.28% `puzzles0_kaggle`, and 6.30%
+  `puzzles2_17_clue`;
+- `r1_4`: 85.02% `puzzles1_unbiased`, 9.70%
+  `puzzles4_forum_hardest_1905`, and 3.40% `01_file1`;
+- `r5_19`: 68.19% `puzzles4_forum_hardest_1905`, 28.15% `01_file1`, and only
+  2.18% `puzzles1_unbiased`.
+
+Consequently, an `r5_19` result combines a Tdoku-rating shift, a held-out
+training-exposure shift, and a source-distribution shift. It must not be
+interpreted as a pure causal effect of search count.
+
+Recommended reporting includes exact rating or subrange, source collection, and
+clue count. A source- and clue-matched diagnostic set is appropriate when the
+goal is to isolate the rating axis.
+
+## 8. Reproducibility limitation
+
+The public Sudoku Extreme card does not pin the Tdoku commit, build flags,
+command, permutation policy, or seed used to create its rating column. This
+release therefore preserves `official_rating` as an upstream measurement rather
+than claiming to reproduce it.
+
+For a fully controlled future rating, pin a Tdoku commit and configuration,
+record the branch count for the exact stored puzzle, and optionally measure its
+mean and variance over Sudoku-preserving isomorphic transformations.
+"""
+
+
 def render_raw_license_notice() -> str:
     return """# Raw data licensing and provenance notice
 
@@ -756,6 +926,10 @@ diffusion language models, depth, and iterative decoding. Version {DATASET_VERSI
 trains only on `original`, `r0`, and `r1_4`; `r5_19` is held out for adjacent
 difficulty extrapolation.
 
+Version {DATASET_VERSION} is a documentation-only update relative to v1.0.1.
+The seven raw CSV files and all four released Parquet splits are byte-identical;
+only the difficulty definition, audit, and version metadata were added or updated.
+
 ## Repository layout
 
 - `raw/`: complete 1,415,420-row candidate snapshot used by this protocol
@@ -763,6 +937,7 @@ difficulty extrapolation.
 - `metadata/`: source/release hashes, split specification, and audits
 - `scripts/`: deterministic builder and independent verifier
 - `docs/BUILDING.md`: end-to-end reconstruction instructions
+- `docs/DIFFICULTY.md`: operational difficulty definition and quantitative audit
 
 Files under `raw/` are explicitly source data and are not loaded as extra splits.
 Only the four `data/*.parquet` paths declared in the card metadata form the
@@ -784,9 +959,16 @@ small number of already-selected configurations; it is not a tuning split.
 
 ## Difficulty
 
-`r0`, `r1_4`, and `r5_19` use the number of tdoku backtracks. Higher values are
-harder. `original` comes from a separate easy Sudoku collection and is not on the
-same numeric scale.
+`r0`, `r1_4`, and `r5_19` use an upstream Tdoku search measurement. In public
+Tdoku commit `{TDOKU_REFERENCE_REVISION}`, the counter increments when the
+solver expands a binary band/stack-configuration decision after constraint propagation.
+It is therefore best interpreted as visited search decision nodes, not recursion
+depth, failed undo count, clue count, or human difficulty. `original` comes from
+a separate easy collection and has no official rating on this scale.
+
+See `docs/DIFFICULTY.md` for the DFS root, propagation and branch semantics,
+bucket formulas, full raw-pool statistics, source confounding, and the upstream
+rating-provenance limitation.
 
 The evaluation sample deliberately covers subranges:
 
@@ -1072,6 +1254,9 @@ def build_dataset(
     (docs_dir / "BUILDING.md").write_text(
         render_building_guide(dataset_id, seed), encoding="utf-8"
     )
+    (docs_dir / "DIFFICULTY.md").write_text(
+        render_difficulty_guide(), encoding="utf-8"
+    )
     shutil.copy2(Path(__file__), scripts_dir / "build_dataset.py")
 
     verifier_candidates = (