# Independent reproduction ledger

**Verification/run ID:** `cbbb82dc-f35e-4c24-aeb0-8d9b2159c95a`  
**Subject artifact:** `paper.md`  
**Exact SHA-256:** `445388f23e3a12e8473d8ac5787c4b0b9edb1dbef6f64920d0ba368fce609109`

| Assessed claim | Verdict | Independent exact evidence |
|---|---:|---|
| Polynomial family for every \(1\le k<d\) | **PASS** | Symbolic low-weight cancellation identities reproduced; all 27 tested family members were exact polynomials. |
| \(\det JF_{k,d}=-k/(k+1)\) | **PASS** | Independent differential-chain derivation returned exactly \(-k/(k+1)\); exact Jacobians passed for all 27 grid members. |
| Odd \(k,d\) collision | **PASS** | General parity reduction agrees; 10 exact pairs verified \(F(-1,0,2)=F(1,0,0)=(0,0,1)\). |
| Expanded \(k=2,d=3\) map and rational collision | **PASS** | Coordinate differences were `[0,0,0]`, determinant was \(-2/3\), and both stated rational points mapped exactly to \((0,9/64,1)\). |

**Producer verifier:** PASS  
**Independent reproduction:** PASS  
**Independent evidence SHA-256:** `c6ed775de3dd85a16017645995041622c2d5e7b26ce818bc34ef0d7115a671a1`