[PR #27] fix(datasets): restore big-operator binder scope in 5 minif2f statements, pin ℝ in mathd_algebra_314 #18

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opened 2026-10-26 21:06:41 +00:00 by bsakaguchi · 0 comments

bsakaguchi commented 2026-10-26 21:06:41 +00:00

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📋 Pull Request Information

Original PR: https://github.com/deepseek-ai/DeepSeek-Prover-V1.5/pull/27
Author: @PerryLink
Created: 9/17/2026
Status: 🔄 Open

Base: main ← Head: fix/minif2f-bigop-binder-scope

---

📝 Commits (1)

• b7becb3 fix(datasets): restore big-operator binder scope in 5 minif2f statements, pin ℝ in mathd_algebra_314

📊 Changes

1 file changed (+6 additions, -6 deletions)

View changed files

📝 datasets/minif2f.jsonl (+6 -6)

📄 Description

Summary

Repairs a binder-scope defect in six test-split records of datasets/minif2f.jsonl
(488 records, blob bf6c8ececb87f2b62702681658e6568694242c31). A big-operator body that is
not parenthesised stops at precedence 67, so an infix operator of lower precedence (+, =, <, ≤)
is parsed outside the operator and the bound variable escapes into an autoImplicit
universally quantified variable. This holds even when the operator sits inside a cast's
parentheses: ( resets the inner parser to precedence 0, it does not raise the precedence
of +.

Five of the six are exactly the statements named in issue #26; the sixth is the type-ascription
defect in mathd_algebra_314.

datasets/minif2f.jsonl is a vendored copy of the public miniF2F benchmark (Lean 3 -> Lean 4
port). The file is this repository's own released evaluation input -- configs/RMaxTS.py uses it
for the miniF2F-test number in the README -- so the fix belongs here. Note that the authoritative
Lean 4 distribution (google-deepmind/miniF2F, MiniF2F/Test.lean) and the repaired copy in
Goedel-LM/Goedel-Prover-V2 already carry the corrected forms; this file is an older snapshot.

Problem

In this repository's own pinned mathlib4 (xinhjBrant/mathlib4 @ 2f65ba7f1a9144b20c8e7358513548e317d26de1,
Mathlib/Algebra/BigOperators/Group/Finset.lean):

syntax (name := bigsum) "∑ " bigOpBinders ("with " term)? ", " term:67 : term
syntax (name := bigprod) "∏ " bigOpBinders ("with " term)? ", " term:67 : term

The body is parsed at precedence 67. + is 65 and = / < / ≤ are 50, so in
(∑ k in Finset.range 5, a + k * d) = 70 the body stops after a. Wrapping the whole operator
in parentheses does not help: the escape happens inside those parentheses. The body itself
must be parenthesised.

Note this also applies inside a cast's parentheses. Parentheses reset the inner parser to
precedence 0, they do not raise the precedence of +:

↑(∑ k in Finset.range 5, a + 2 * k)
-- parses as ↑((∑ k ∈ Finset.range 5, a) + 2 * k): the body stopped at `+`,
-- and `k` is free after the binder closed
↑(∑ k in Finset.range 8, 2 * k + 1)
-- parses as ↑((∑ k ∈ Finset.range 8, 2 * k) + 1): `*` is 70 so it stays in the body,
-- but the body still stops at `+`, so `+ 1` is added once outside the sum

Records affected (the recorded goal field still shows the degenerate parse -- a variable in the
context that the statement never binds). These are exactly the five statements the issue names:

• L328 induction_pord1p1on2powklt5on2 -- goal context k n : ℕ, statement binds only n
• L335 induction_prod1p1onk3le3m1onn -- goal context k : ℝ, statement binds only n
• L379 amc12a_2021_p9 -- the theorem has no binders at all, yet goal context is k : ℕ
• L435 mathd_algebra_342 -- goal context k a d : ℝ, statement binds only a d
• L467 mathd_algebra_158 -- goal context k a : ℕ, statement binds only a (and h₀)
• L471 mathd_algebra_314 -- missing type ascription; over ℕ this is 0 = 0

For L467 the degenerate parse also explains the issue's vacuity claim: with the body stopping
early the second cast becomes ↑((∑ k ∈ Finset.range 5, a) + 2 * k), so the hypothesis reads
57 - (5a + 2k) = 4, i.e. 5a + 2k = 53. Its left side is even whenever a is even, while 53 is
odd, so the hypotheses are contradictory and the statement is vacuously true. With the
body parenthesised the hypothesis is satisfiable: 64 - (5a + 20) = 4 gives a = 8, and 8 is
even, so h₀ : Even a holds and the vacuity disappears.

Solution

Seven edits on six lines, all inside the formal_statement field. No other field and no other
byte of the file is touched.

-    (∏ k in Finset.Icc 1 n, 1 + (1 : ℝ) / 2 ^ k) < 5 / 2
+    (∏ k in Finset.Icc 1 n, (1 + (1 : ℝ) / 2 ^ k)) < 5 / 2

-    (∏ k in Finset.Icc 1 n, 1 + (1 : ℝ) / k ^ 3) ≤ (3 : ℝ) - 1 / ↑n
+    (∏ k in Finset.Icc 1 n, (1 + (1 : ℝ) / k ^ 3)) ≤ (3 : ℝ) - 1 / ↑n

-    (∏ k in Finset.range 7, 2 ^ 2 ^ k + 3 ^ 2 ^ k) = 3 ^ 128 - 2 ^ 128
+    (∏ k in Finset.range 7, (2 ^ 2 ^ k + 3 ^ 2 ^ k)) = 3 ^ 128 - 2 ^ 128

-    (h₀ : (∑ k in Finset.range 5, a + k * d) = 70)
-    (h₁ : (∑ k in Finset.range 10, a + k * d) = 210)
+    (h₀ : (∑ k in Finset.range 5, (a + k * d)) = 70)
+    (h₁ : (∑ k in Finset.range 10, (a + k * d)) = 210)

-    (h₁ : ↑(∑ k in Finset.range 8, 2 * k + 1) - ↑(∑ k in Finset.range 5, a + 2 * k) = (4 : ℤ))
+    (h₁ : ↑(∑ k in Finset.range 8, (2 * k + 1)) - ↑(∑ k in Finset.range 5, (a + 2 * k)) = (4 : ℤ))

-    (1 / 4) ^ (n + 1) * 2 ^ (2 * n) = 1 / 4
+    (1 / 4 : ℝ) ^ (n + 1) * 2 ^ (2 * n) = 1 / 4

Design notes:

• The redundant outer parentheses on the big operators are kept. Removing them (as the
  upstream forms do) is cosmetic and would only enlarge the diff.
• For mathd_algebra_158 both ↑(...) casts are kept, exactly as the authoritative
  google-deepmind/miniF2F form keeps them; only the two sum bodies gained parentheses. (The
  repaired Goedel-LM/Goedel-Prover-V2 copy instead drops the casts, which is a larger
  structural change and is not needed here.)
• The ASCII in notation is kept; this file mixes in Finset. and ∈ Finset. (63 each). Notation
  normalisation is out of scope.
• mathd_algebra_314: (1 / 4 : ℝ) alone pins the whole equality to ℝ -- 2 ^ (2 * n) is
  lifted to Pow ℝ ℕ, and the right-hand 1 / 4 is determined by the left-hand type. The
  canonical google-deepmind/miniF2F form uses (1 / 4 : ℚ); ℝ is used here because it matches
  the issue report and this file's dominant style. Happy to switch to ℚ if you prefer exact
  parity with the canonical distribution.

Scope and non-goals

• goal is deliberately NOT modified. It is not read anywhere in prover/ or configs/
  (prover/utils.py and prover/lean/proof.py consume header, informal_prefix and
  formal_statement only). Regenerating it requires a Lean toolchain, which I did not have; writing
  a hand-made proof state would be fabrication. As a result these six records are internally
  inconsistent after this patch: formal_statement is repaired, goal still shows the old
  degenerate parse. If you want goal regenerated too, please say so and I will follow your
  process for that.
• The "vacuously true / the model proves a false statement" half of issue #26 is NOT addressed.
  Establishing which released solutions pass on the degenerate statements requires Lean 4 + mathlib4
  and the released minif2f-solutions.zip; neither was available, so no claim is made either way.
  The Lean-free arithmetic I can support is: under the ℕ reading of mathd_algebra_314,
  1 / 4 = 0, so the old goal was 0 = 0; and under the degenerate parse of
  mathd_algebra_158, the hypothesis would require 5a ± 2k = 53, which contradicts Even a.
• 13 further statements differ from the repaired Goedel copy and are intentionally left alone
  (amc12a_2020_p10, aime_1994_p3, mathd_numbertheory_618, amc12a_2020_p7,
  amc12a_2021_p18, mathd_algebra_275, mathd_numbertheory_343,
  algebra_ineq_nto1onlt2m1on, algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778, ...). Each of
  those repairs changes hypotheses, quantifier structure, or the mathematical content (e.g.
  0 < n -> 1 < n, adding hr : r ≥ 0, < -> ≤, a (k ^ 2) -> (a k) ^ 2), and I could not
  verify any of them without Lean.
• datasets/minif2f_valid_few_shot.jsonl needs no change: none of the six names appear in it.
• If you accept this patch, note that the published miniF2F-test figure will no longer be
  reproducible from the current repository state without a re-run; these five statements revert from
  a stronger (and in several cases false) implicit universal to the intended problem.

Verification

Byte-level checks (Node.js, no Lean required):

• file still has 488 records, LF-only, single final newline, no BOM
• changed line numbers are exactly [328, 335, 379, 435, 467, 471]
• every other line is byte-identical to the original
• on the changed lines, name / split / informal_prefix / goal / header are byte-identical
• all 488 lines still parse as JSON, with unchanged key set and key order
• the mathd_algebra_158 line keeps both ↑(...) casts and its parentheses balance
• the patched file round-trips byte-for-byte through the exact writer style the file already
  uses (", " / ": " separators, ensure_ascii=False, key order preserved)

A separate scan cross-checks the affected set: the intersection of (a) records whose recorded
goal context declares a variable the statement never binds, and (b) records where that variable
also falls outside the window the big-operator body can occupy at precedence 67, is exactly these
five statements -- matching the issue's list with no extras.

Not verified (no Lean toolchain available): that the repaired statements elaborate, that the
(1 / 4 : ℝ) ascription is the canonical choice, and that the statements remain provable.

AI assistance

This patch was prepared with AI assistance (an AI coding agent). The defect analysis, the
precedence argument, the edits, and the byte-level checks were produced by the agent and reviewed
by me before submission. No Lean verification was performed. Please review the Lean-level
correctness independently.

Fixes #26 (partially -- the binder-scope and type-ascription defects only; see "Scope and non-goals").

---

## 9. 附: 本次读取的全部 SHA

| 对象 | SHA |
|---|---|
| `deepseek-ai/DeepSeek-Prover-V1.5` main HEAD | `2c4ba9119eef74d0d611f494261b2c5bae98c69a` |
| `datasets/minif2f.jsonl` blob | `bf6c8ececb87f2b62702681658e6568694242c31` |
| `datasets/minif2f_valid_few_shot.jsonl` blob | `2c123ba917d8c593c987d4124be289ab5402ba67` |
| `datasets/proofnet.jsonl` blob | `adda38ed779ccadbe23631130db2dca025d5919c` |
| `README.md` blob | `5d73f8b65b181bc20021468b352d5b0bf6960853` |
| `.gitmodules` blob | `5f70c7044ceabd7509fd5f455bc97b3cb0460141` |
| mathlib4 submodule commit (`xinhjBrant/mathlib4` @ `deepseek`) | `2f65ba7f1a9144b20c8e7358513548e317d26de1` |
| `Mathlib/Algebra/BigOperators/Group/Finset.lean` blob (该 commit) | `0236b11e33e8994268ce1a8cef7d053b3d6ce235` |
| `openai/miniF2F` HEAD (archived) | `4e433ff5cadff23f9911a2bb5bbab2d351ce5554` |
| `lean/src/test.lean` blob | `2ba395d12f5b3b7434f100f03513a717a851b594` |
| `lean/src/valid.lean` blob | `e14c6c5f576ec65d41277102979e6c09edfb8dfe` |
| `google-deepmind/miniF2F` HEAD | `f0a20e14c1eeccd859d51bb4c2b3ee487889c303` |
| `MiniF2F/Test.lean` blob | `7d3a756cb3da856fc26096c8da440f086653cfc1` |
| `MiniF2F/Valid.lean` blob | `97f0ea048e0805434b13b157bedffc99ea7ddb4e` |
| `Goedel-LM/Goedel-Prover-V2` HEAD | `2e9036e118464aa96a8bebaf9f5b9d091aa3585c` |
| `dataset/minif2f.jsonl` blob | `415d1fa09952685126cdcebd9878565a68997a52` |
| 补丁后本地文件 blob sha1 (自算) | `0f6e6efa4d93e2e508e9223f75483fbcce63b2b6` |

issue #26: `state=open`, 0 comments, 0 timeline events, 无关联 PR。

---

## 10. 复盘: 初版为什么把 L467 判错

记下来是因为这个错误有**可复用的教训**, 不是个人失误记录。

### 事实链

1. 初版观察到 `goal` 上下文有 `k a : ℕ`, 但按"体终止于外层第一个低优先级算子"的模型, 体应当终止于 `-` (50), 于是 `k` 应当是绑定的 ⇒ 签名与模型矛盾。
2. 面对矛盾, 初版的选择是**判定该条不可复现并弃修**, 并在报告里写下"说明我没有正确理解这一条的机制"。
3. 正确做法本应是: **矛盾说明模型不完整 ⇒ 去补模型, 而不是去弃条目**。矛盾出现在一个"我唯一没有独立验证过的环节"(括号对优先级的影响), 那就该去查那个环节, 而不是回避它。

### 错在哪一步

初版把 `(` 当成了**优先级屏障** —— 潜意识里认为"外层已经有括号了, 内部就安全了"。这在 Lean 里是错的:

- `(` 的作用是把内部**重置为 precedence 0 重新解析**, 它不改变任何算子自身的优先级。
- 因此 `+` (65) 在 cast 括号内部**依然是 65**, 依然 < 体所需的 67, 体照样在括号内部断掉。
- 结论: **外层括号从来不保护体**。这条规律恰好解释了为什么 5 条缺陷全都表现为"明明有功括号、却还是逃逸"。

### 为什么 3.7 的交叉验证能挡住这个错误

3.7 的判据 (1) 只看 `goal` 字段声明了而语句没绑定的变量 —— **完全不涉及优先级推理**。它与判据 (2) 的交集给出 5 条, 其中就含 L467。也就是说: 即使我把优先级推理再做错一次, 判据 (1) 仍会把 L467 拉进集合。

**可复用教训**: 当一个推理模型与观测数据冲突时, 冲突本身就是"模型不完整"的证据, 应当**用它去定位模型的缺口**, 而不是用它去否定观测。更好的做法是构造一个**不依赖该模型**的独立判据, 与模型判据取交集 —— 这正是 3.7 做的事, 而它一次就定位出了初版漏掉的那一条。

### 遗留风险

`3.7` 的两条判据都仍可能系统性漏判 (例如某条缺陷的 `goal` 字段缺失或已被修正, 判据 (1) 就失效)。因此第 6/7 节的"未验证"与"未证实假设"两节仍然成立, 本补丁仍**不声称**已穷尽全部同类缺陷。


---

<sub>🔄 This issue represents a GitHub Pull Request. It cannot be merged through Gitea due to API limitations.</sub>

## 📋 Pull Request Information **Original PR:** https://github.com/deepseek-ai/DeepSeek-Prover-V1.5/pull/27 **Author:** [@PerryLink](https://github.com/PerryLink) **Created:** 9/17/2026 **Status:** 🔄 Open **Base:** `main` ← **Head:** `fix/minif2f-bigop-binder-scope` --- ### 📝 Commits (1) - [`b7becb3`](https://github.com/deepseek-ai/DeepSeek-Prover-V1.5/commit/b7becb3826273a97b04a74fb7b116238cf62109f) fix(datasets): restore big-operator binder scope in 5 minif2f statements, pin ℝ in mathd_algebra_314 ### 📊 Changes **1 file changed** (+6 additions, -6 deletions) <details> <summary>View changed files</summary> 📝 `datasets/minif2f.jsonl` (+6 -6) </details> ### 📄 Description ## Summary Repairs a binder-scope defect in six `test`-split records of `datasets/minif2f.jsonl` (488 records, blob `bf6c8ececb87f2b62702681658e6568694242c31`). A big-operator body that is not parenthesised stops at precedence 67, so an infix operator of lower precedence (+, =, <, ≤) is parsed *outside* the operator and the bound variable escapes into an `autoImplicit` universally quantified variable. This holds even when the operator sits inside a cast's parentheses: `(` resets the inner parser to precedence 0, it does not raise the precedence of `+`. Five of the six are exactly the statements named in issue #26; the sixth is the type-ascription defect in `mathd_algebra_314`. `datasets/minif2f.jsonl` is a vendored copy of the public miniF2F benchmark (Lean 3 -> Lean 4 port). The file is this repository's own released evaluation input -- `configs/RMaxTS.py` uses it for the miniF2F-test number in the README -- so the fix belongs here. Note that the authoritative Lean 4 distribution (`google-deepmind/miniF2F`, `MiniF2F/Test.lean`) and the repaired copy in `Goedel-LM/Goedel-Prover-V2` already carry the corrected forms; this file is an older snapshot. ## Problem In this repository's own pinned mathlib4 (`xinhjBrant/mathlib4` @ `2f65ba7f1a9144b20c8e7358513548e317d26de1`, `Mathlib/Algebra/BigOperators/Group/Finset.lean`): ```lean syntax (name := bigsum) "∑ " bigOpBinders ("with " term)? ", " term:67 : term syntax (name := bigprod) "∏ " bigOpBinders ("with " term)? ", " term:67 : term ``` The body is parsed at precedence **67**. `+` is 65 and `=` / `<` / `≤` are 50, so in `(∑ k in Finset.range 5, a + k * d) = 70` the body stops after `a`. Wrapping the whole operator in parentheses does **not** help: the escape happens inside those parentheses. The body itself must be parenthesised. Note this also applies *inside* a cast's parentheses. Parentheses reset the inner parser to precedence 0, they do not raise the precedence of `+`: ```lean ↑(∑ k in Finset.range 5, a + 2 * k) -- parses as ↑((∑ k ∈ Finset.range 5, a) + 2 * k): the body stopped at `+`, -- and `k` is free after the binder closed ↑(∑ k in Finset.range 8, 2 * k + 1) -- parses as ↑((∑ k ∈ Finset.range 8, 2 * k) + 1): `*` is 70 so it stays in the body, -- but the body still stops at `+`, so `+ 1` is added once outside the sum ``` Records affected (the recorded `goal` field still shows the degenerate parse -- a variable in the context that the statement never binds). These are exactly the five statements the issue names: - L328 `induction_pord1p1on2powklt5on2` -- `goal` context `k n : ℕ`, statement binds only `n` - L335 `induction_prod1p1onk3le3m1onn` -- `goal` context `k : ℝ`, statement binds only `n` - L379 `amc12a_2021_p9` -- the theorem has **no** binders at all, yet `goal` context is `k : ℕ` - L435 `mathd_algebra_342` -- `goal` context `k a d : ℝ`, statement binds only `a d` - L467 `mathd_algebra_158` -- `goal` context `k a : ℕ`, statement binds only `a` (and `h₀`) - L471 `mathd_algebra_314` -- missing type ascription; over `ℕ` this is `0 = 0` For L467 the degenerate parse also explains the issue's vacuity claim: with the body stopping early the second cast becomes `↑((∑ k ∈ Finset.range 5, a) + 2 * k)`, so the hypothesis reads `57 - (5a + 2k) = 4`, i.e. `5a + 2k = 53`. Its left side is even whenever `a` is even, while 53 is odd, so the hypotheses are contradictory and the statement is vacuously true. With the body parenthesised the hypothesis is satisfiable: `64 - (5a + 20) = 4` gives `a = 8`, and 8 is even, so `h₀ : Even a` holds and the vacuity disappears. ## Solution Seven edits on six lines, all inside the `formal_statement` field. No other field and no other byte of the file is touched. ```diff - (∏ k in Finset.Icc 1 n, 1 + (1 : ℝ) / 2 ^ k) < 5 / 2 + (∏ k in Finset.Icc 1 n, (1 + (1 : ℝ) / 2 ^ k)) < 5 / 2 - (∏ k in Finset.Icc 1 n, 1 + (1 : ℝ) / k ^ 3) ≤ (3 : ℝ) - 1 / ↑n + (∏ k in Finset.Icc 1 n, (1 + (1 : ℝ) / k ^ 3)) ≤ (3 : ℝ) - 1 / ↑n - (∏ k in Finset.range 7, 2 ^ 2 ^ k + 3 ^ 2 ^ k) = 3 ^ 128 - 2 ^ 128 + (∏ k in Finset.range 7, (2 ^ 2 ^ k + 3 ^ 2 ^ k)) = 3 ^ 128 - 2 ^ 128 - (h₀ : (∑ k in Finset.range 5, a + k * d) = 70) - (h₁ : (∑ k in Finset.range 10, a + k * d) = 210) + (h₀ : (∑ k in Finset.range 5, (a + k * d)) = 70) + (h₁ : (∑ k in Finset.range 10, (a + k * d)) = 210) - (h₁ : ↑(∑ k in Finset.range 8, 2 * k + 1) - ↑(∑ k in Finset.range 5, a + 2 * k) = (4 : ℤ)) + (h₁ : ↑(∑ k in Finset.range 8, (2 * k + 1)) - ↑(∑ k in Finset.range 5, (a + 2 * k)) = (4 : ℤ)) - (1 / 4) ^ (n + 1) * 2 ^ (2 * n) = 1 / 4 + (1 / 4 : ℝ) ^ (n + 1) * 2 ^ (2 * n) = 1 / 4 ``` Design notes: - The redundant **outer** parentheses on the big operators are kept. Removing them (as the upstream forms do) is cosmetic and would only enlarge the diff. - For `mathd_algebra_158` both `↑(...)` casts are kept, exactly as the authoritative `google-deepmind/miniF2F` form keeps them; only the two sum bodies gained parentheses. (The repaired `Goedel-LM/Goedel-Prover-V2` copy instead drops the casts, which is a larger structural change and is not needed here.) - The ASCII `in` notation is kept; this file mixes `in Finset.` and `∈ Finset.` (63 each). Notation normalisation is out of scope. - `mathd_algebra_314`: `(1 / 4 : ℝ)` alone pins the whole equality to `ℝ` -- `2 ^ (2 * n)` is lifted to `Pow ℝ ℕ`, and the right-hand `1 / 4` is determined by the left-hand type. The canonical `google-deepmind/miniF2F` form uses `(1 / 4 : ℚ)`; `ℝ` is used here because it matches the issue report and this file's dominant style. Happy to switch to `ℚ` if you prefer exact parity with the canonical distribution. ## Scope and non-goals - **`goal` is deliberately NOT modified.** It is not read anywhere in `prover/` or `configs/` (`prover/utils.py` and `prover/lean/proof.py` consume `header`, `informal_prefix` and `formal_statement` only). Regenerating it requires a Lean toolchain, which I did not have; writing a hand-made proof state would be fabrication. **As a result these six records are internally inconsistent after this patch: `formal_statement` is repaired, `goal` still shows the old degenerate parse.** If you want `goal` regenerated too, please say so and I will follow your process for that. - **The "vacuously true / the model proves a false statement" half of issue #26 is NOT addressed.** Establishing which released solutions pass on the degenerate statements requires Lean 4 + mathlib4 and the released `minif2f-solutions.zip`; neither was available, so no claim is made either way. The Lean-free arithmetic I can support is: under the `ℕ` reading of `mathd_algebra_314`, `1 / 4 = 0`, so the old goal was `0 = 0`; and under the degenerate parse of `mathd_algebra_158`, the hypothesis would require `5a ± 2k = 53`, which contradicts `Even a`. - **13 further statements differ from the repaired Goedel copy and are intentionally left alone** (`amc12a_2020_p10`, `aime_1994_p3`, `mathd_numbertheory_618`, `amc12a_2020_p7`, `amc12a_2021_p18`, `mathd_algebra_275`, `mathd_numbertheory_343`, `algebra_ineq_nto1onlt2m1on`, `algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778`, ...). Each of those repairs changes hypotheses, quantifier structure, or the mathematical content (e.g. `0 < n` -> `1 < n`, adding `hr : r ≥ 0`, `<` -> `≤`, `a (k ^ 2)` -> `(a k) ^ 2`), and I could not verify any of them without Lean. - `datasets/minif2f_valid_few_shot.jsonl` needs no change: none of the six `name`s appear in it. - If you accept this patch, note that the published miniF2F-test figure will no longer be reproducible from the current repository state without a re-run; these five statements revert from a stronger (and in several cases false) implicit universal to the intended problem. ## Verification Byte-level checks (Node.js, no Lean required): - [x] file still has 488 records, LF-only, single final newline, no BOM - [x] changed line numbers are exactly `[328, 335, 379, 435, 467, 471]` - [x] every other line is byte-identical to the original - [x] on the changed lines, `name` / `split` / `informal_prefix` / `goal` / `header` are byte-identical - [x] all 488 lines still parse as JSON, with unchanged key set and key order - [x] the `mathd_algebra_158` line keeps both `↑(...)` casts and its parentheses balance - [x] the patched file round-trips byte-for-byte through the exact writer style the file already uses (`", "` / `": "` separators, `ensure_ascii=False`, key order preserved) A separate scan cross-checks the affected set: the intersection of (a) records whose recorded `goal` context declares a variable the statement never binds, and (b) records where that variable also falls outside the window the big-operator body can occupy at precedence 67, is exactly these five statements -- matching the issue's list with no extras. Not verified (no Lean toolchain available): that the repaired statements elaborate, that the `(1 / 4 : ℝ)` ascription is the canonical choice, and that the statements remain provable. ## AI assistance This patch was prepared with AI assistance (an AI coding agent). The defect analysis, the precedence argument, the edits, and the byte-level checks were produced by the agent and reviewed by me before submission. No Lean verification was performed. Please review the Lean-level correctness independently. Fixes #26 (partially -- the binder-scope and type-ascription defects only; see "Scope and non-goals"). ``` --- ## 9. 附: 本次读取的全部 SHA | 对象 | SHA | |---|---| | `deepseek-ai/DeepSeek-Prover-V1.5` main HEAD | `2c4ba9119eef74d0d611f494261b2c5bae98c69a` | | `datasets/minif2f.jsonl` blob | `bf6c8ececb87f2b62702681658e6568694242c31` | | `datasets/minif2f_valid_few_shot.jsonl` blob | `2c123ba917d8c593c987d4124be289ab5402ba67` | | `datasets/proofnet.jsonl` blob | `adda38ed779ccadbe23631130db2dca025d5919c` | | `README.md` blob | `5d73f8b65b181bc20021468b352d5b0bf6960853` | | `.gitmodules` blob | `5f70c7044ceabd7509fd5f455bc97b3cb0460141` | | mathlib4 submodule commit (`xinhjBrant/mathlib4` @ `deepseek`) | `2f65ba7f1a9144b20c8e7358513548e317d26de1` | | `Mathlib/Algebra/BigOperators/Group/Finset.lean` blob (该 commit) | `0236b11e33e8994268ce1a8cef7d053b3d6ce235` | | `openai/miniF2F` HEAD (archived) | `4e433ff5cadff23f9911a2bb5bbab2d351ce5554` | | `lean/src/test.lean` blob | `2ba395d12f5b3b7434f100f03513a717a851b594` | | `lean/src/valid.lean` blob | `e14c6c5f576ec65d41277102979e6c09edfb8dfe` | | `google-deepmind/miniF2F` HEAD | `f0a20e14c1eeccd859d51bb4c2b3ee487889c303` | | `MiniF2F/Test.lean` blob | `7d3a756cb3da856fc26096c8da440f086653cfc1` | | `MiniF2F/Valid.lean` blob | `97f0ea048e0805434b13b157bedffc99ea7ddb4e` | | `Goedel-LM/Goedel-Prover-V2` HEAD | `2e9036e118464aa96a8bebaf9f5b9d091aa3585c` | | `dataset/minif2f.jsonl` blob | `415d1fa09952685126cdcebd9878565a68997a52` | | 补丁后本地文件 blob sha1 (自算) | `0f6e6efa4d93e2e508e9223f75483fbcce63b2b6` | issue #26: `state=open`, 0 comments, 0 timeline events, 无关联 PR。 --- ## 10. 复盘: 初版为什么把 L467 判错 记下来是因为这个错误有**可复用的教训**, 不是个人失误记录。 ### 事实链 1. 初版观察到 `goal` 上下文有 `k a : ℕ`, 但按"体终止于外层第一个低优先级算子"的模型, 体应当终止于 `-` (50), 于是 `k` 应当是绑定的 ⇒ 签名与模型矛盾。 2. 面对矛盾, 初版的选择是**判定该条不可复现并弃修**, 并在报告里写下"说明我没有正确理解这一条的机制"。 3. 正确做法本应是: **矛盾说明模型不完整 ⇒ 去补模型, 而不是去弃条目**。矛盾出现在一个"我唯一没有独立验证过的环节"(括号对优先级的影响), 那就该去查那个环节, 而不是回避它。 ### 错在哪一步 初版把 `(` 当成了**优先级屏障** —— 潜意识里认为"外层已经有括号了, 内部就安全了"。这在 Lean 里是错的: - `(` 的作用是把内部**重置为 precedence 0 重新解析**, 它不改变任何算子自身的优先级。 - 因此 `+` (65) 在 cast 括号内部**依然是 65**, 依然 < 体所需的 67, 体照样在括号内部断掉。 - 结论: **外层括号从来不保护体**。这条规律恰好解释了为什么 5 条缺陷全都表现为"明明有功括号、却还是逃逸"。 ### 为什么 3.7 的交叉验证能挡住这个错误 3.7 的判据 (1) 只看 `goal` 字段声明了而语句没绑定的变量 —— **完全不涉及优先级推理**。它与判据 (2) 的交集给出 5 条, 其中就含 L467。也就是说: 即使我把优先级推理再做错一次, 判据 (1) 仍会把 L467 拉进集合。 **可复用教训**: 当一个推理模型与观测数据冲突时, 冲突本身就是"模型不完整"的证据, 应当**用它去定位模型的缺口**, 而不是用它去否定观测。更好的做法是构造一个**不依赖该模型**的独立判据, 与模型判据取交集 —— 这正是 3.7 做的事, 而它一次就定位出了初版漏掉的那一条。 ### 遗留风险 `3.7` 的两条判据都仍可能系统性漏判 (例如某条缺陷的 `goal` 字段缺失或已被修正, 判据 (1) 就失效)。因此第 6/7 节的"未验证"与"未证实假设"两节仍然成立, 本补丁仍**不声称**已穷尽全部同类缺陷。 --- _{🔄 This issue represents a GitHub Pull Request. It cannot be merged through Gitea due to API limitations.}

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