---
title: Claims and risk register
tags: [risk, claims-ledger]
---

# Claims and risk register

| Claim | Evidence | Status | Main risk |
|---|---|---|---|
| $\det JF=-2$ | Hand proof; SymPy; Sage; Magma | Proved | Formula transcription |
| Announced collision | Exact substitution in three systems | Proved | None after formula freeze |
| Fiber is exactly three reduced points | Ideal equality and radicality | Proved | Coordinate-order mistakes in reuse |
| Normalized $H$ has determinant $1$ | Linear conjugation and CAS | Proved | Quoting an older normalization |
| Generic degree is $3$ | Marked simple-root bijection | Proved | Saying every fiber has size three |
| Set-theoretic image omits exactly triple-root curve | Complete projective-root classification | Proved over $\mathbb C$ | Scheme-theoretic image is still all target space |
| Nonproperness set is the discriminant | Explicit escape plus bounded inverse branches off discriminant | Proved over $\mathbb C$ | Definition of nonproperness over other fields |
| First public occurrence | Exact-phrase search; timestamped post | Provisional | Unindexed or private prior work |
| Community acceptance | Same-day online checks only | Not yet established | No peer review as of cutoff |
| Dimension two remains open | Current refereed literature | Current as of 2026-07-20 | Future developments |

## Frozen notation

- Source: $(x,y,z)$.
- Output functions: $(A,B,C)=(F_1,F_2,F_3)$.
- Fixed target: $(a,b,c)$.
- Binary cubic: $Q_{a,b,c}(U,V)$.
- Affine root: $w=U/V=y+1/x$.
- Discriminant factor: $\Delta$, with
  $\operatorname{Disc}(p)=4\Delta$.

Any later edit should preserve these conventions or state the change
prominently.