# RUN-062 — `02`'s four adversarial curves fail this line's 8b instrument, 4 of 4; and the ecdata pin that only reproduces as CRLF **Arm:** 數學戰士「墜衡」 / AMRAL Research Lab **Subject:** `02_Official_Discrepancy_Corpus` — the corpus's own adversarial regression set **Tools:** `src64_discrepancy_corpus.py`, `src11_gate_drill.py` **Logs:** `src64-discrepancy-corpus.json`, `src11-gate-drill.json` **Data:** `data/external/ecdata-25cec5e-allcurves.00000-09999`, fetched from the pinned commit with its provenance record **Result: `02` names four curves — 62a1, 66b1, 105a1, 141c1 — that pass every early gate and are rejected by CURRENT Algorithm 1 on four counts, one being that **`f'(x₀)` is a rational square**. RUN-055 computed exactly that condition on all 3,747 CLZ20 curves of the accepted base and found **zero** squares. A check that has only ever seen passing data has not been tested — RUN-042's discipline — and until this round the 8b instrument had never seen a curve that must fail. **It fails all four.** Read from the pinned ecdata shard, each has exactly one rational 2-torsion point and `4·f'(x₀) ∈ {64, 64, 16, 144}`, all perfect squares; none is in the 40,749 base; the other two non-square conditions hold on every one, so `f'` is the *only* one of the three that fails, which is consistent with `02` listing it alone among the four rejection reasons. `02` calls the four a *theorem-router adversarial regression corpus* and says a version that accepts them earns the label `REGRESSION?`, not `NEW BSD BREAKTHROUGH!`; this round makes that a standing check on this line's own instrument. **Three of the four a-invariant lists the first draft typed from memory were wrong** — the shard is the source, and the gate reads it. And the shard's pin came out sharp: the package records the shard at 2,211,088 bytes, SHA-256 `8a6073c4…`; the blob at the pinned commit is 2,146,401 bytes, `259f3846…` — **64,687 bytes short, one per line**. CRLF-converted, it hashes to the package's value exactly. **The census hashed a Windows checkout of ecdata**, though its own `PROVENANCE.md` says the twist JSONs were pulled with `git cat-file blob` to avoid precisely this. Content identical modulo line endings; arithmetic unaffected; pin, as recorded, not verifiable against upstream without knowing to convert.** --- ## The four, from the shard | curve | `ainvs` (shard) | in the 40,749 base | `X₀ = 4x₀` | `4·f'(x₀)` | square | `−f'` square | `−Δ` square | | --- | --- | --- | ---: | ---: | --- | --- | --- | | 62a1 | `[1,−1,1,−1,1]` | no | −4 | **64** | **✔** | ✘ | ✘ | | 66b1 | `[1,1,1,−2,−1]` | no | 4 | **64** | **✔** | ✘ | ✘ | | 105a1 | `[1,0,1,−3,1]` | no | 4 | **16** | **✔** | ✘ | ✘ | | 141c1 | `[1,0,0,−2,3]` | no | −8 | **144** | **✔** | ✘ | ✘ | Same code path as RUN-055 — the monic 2-division cubic in `X = 4x`, exact integer bisection between critical points, `4·f'(x₀) = 3X₀² + 2b₂X₀ + 8b₄`. Exactly one integer root each, as `E(Q)[2] ≅ Z/2` requires. ## What this is a control for | | RUN-055 | this round | | --- | ---: | ---: | | CLZ20 curves checked | 3,747 accepted | 4 rejected | | `f'(x₀)` a square | **0** | **4** | Before this round, "0 of 3,747" was consistent with an instrument that could not see a square at all. Now it is an instrument that finds every square the corpus says is there and none the corpus says is not. `02`'s other three reasons — `ord₂ L^alg = −2` where CLZ20 needs `−1`, `E'(Q)[2] ≅ (2,2)` rather than cyclic, the `𝒮 ≠ ∅` gate — are not computed here. ## The regression rule, adopted > 未來若某版本突然接受這四條，第一個標籤應是 `REGRESSION?`，不是 `NEW BSD BREAKTHROUGH!`。 The drill check for this gate asserts that all four fail `f'(x₀)` non-square. If a future change to the 8b instrument accepts one, the drill goes red with `02`'s label already attached. ## Three of four typed wrong The first draft carried the four curves' `ainvs` from memory. 62a1 was right; 66b1, 105a1 and 141c1 were not, and on the wrong coefficients the root finder found no 2-torsion at all — which would have read as "the instrument cannot see these curves' torsion" had it been believed. The shard was fetched instead. RUN-029's rule, again: a number from memory is a number from nowhere. ## The pin that only reproduces as CRLF | | bytes | SHA-256 | | --- | ---: | --- | | package records `allcurves.00000-09999` | 2,211,088 | `8a6073c4703d…` | | blob at `25cec5e`, fetched | 2,146,401 | `259f38463293…` | | gap | **64,687** | = the file's line count | | the fetched blob, CRLF-converted | 2,211,088 | **`8a6073c4703d…`** | The package's `PROVENANCE.md` says of the twist JSONs: *`extract_exact_git_blobs.py` uses `git cat-file blob`, bypassing Windows checkout newline conversion.* The ecdata shards were not pulled that way; their recorded hashes are of a CRLF checkout. Every arithmetic value in the package that derives from the shards is unaffected — line endings carry no coefficients — but a reader who verifies the package's ecdata pins against the upstream repository will get a mismatch on every shard, as this round did, and will not be told why. This is `02` §6's *file SHA* pin — scored PRESENT at RUN-056 — being present and **not reproducible as stated**. RUN-056's row is corrected to *present, reproduces only after CRLF conversion*. ## The drill **260 defects, 260 caught by the check named for each**, 0 uncaught, 0 caught by the wrong check, 52 controls undisturbed, over 90 checks. The 4 planted for this gate, each turning `discrepancy-corpus` red and nothing else: | planted defect | went red | | --- | --- | | the square test always answers 'not a square', which the accepted base could never have exposed | `discrepancy-corpus` | | the four curves are read from memory instead of the shard: 66b1's a-invariants as the first draft typed them | `discrepancy-corpus` | | the shard's LF hash is reported as matching the package | `discrepancy-corpus` | | 62a1 is reported as present in the 40,749 base | `discrepancy-corpus` | ## What this round does not claim * **One shard was fetched, not all.** The four curves have conductors below 10,000; the other shards' pins are inferred to have the same defect from the same script and are not checked. * **`f'(x₀)` is one of `02`'s four reasons.** That it fails on all four does not by itself reject them; `02` says all four reasons apply, and three are not computed here. * **The shard is trusted on its hash.** Its content was verified against the package's record, CRLF-adjusted; it was not compared to any third source. * **Nothing about the router.** `02`'s "theorem-router" framing concerns Algorithm 1's dispatch; this round tests one predicate.