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Family: genus-two — Genus 2 curve - #22

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Family: genus-two — Genus 2 curve#22
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DiophantineLibrary:split/09-backbone-deepfrom
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@roed-math roed-math commented Aug 8, 2026

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One family: Genus 2 curve (genus-two) — P1, effective.

  • Standard form: y^2 = f(x), deg f in {5, 6}
  • Parent: hyperelliptic
  • Examples: y^2 = x^5 - x + 1

Contents: the registry entry, its docs/FAMILIES.md section and its rows in the classification corpus.

References cited (the claim each one supports):

  • Igusa1960 — the invariants identifying a genus-2 curve up to isomorphism (the classifier's genus-2 handle)
  • CasselsFlynn1996 — explicit arithmetic of genus-2 Jacobians

Independent of every other family PR: it needs only the registry backbone it is based on.

Part of the series that splits #1 into reviewable pieces:

  1. 01-bibliography — packaging, docs, annotated bibliography
  2. 02-parsing — equation strings to a term model
  3. 03-registry — the YAML family registry (3 seed families)
  4. 04-matchers — shape recognizers
  5. 05-classify — the classification pipeline
  6. 06-solvers — solver framework, two seed solvers, and the CLI
  7. 07..09-backbone — the 23 parent families of the DAG, by depth
  8. one PR per remaining family (38 of them, mutually independent)
  9. 99-polish — restore the full doctests and tighten the invariants

@roed-math roed-math mentioned this pull request Aug 8, 2026
@roed-math
roed-math force-pushed the split/09-backbone-deep branch from 082df89 to 35fcb63 Compare August 8, 2026 16:12
@roed-math
roed-math force-pushed the split/09-backbone-deep branch from 35fcb63 to ece9c70 Compare August 9, 2026 02:43
@roed-math
roed-math force-pushed the split/09-backbone-deep branch from ece9c70 to 6175904 Compare August 9, 2026 05:01
@roed-math
roed-math force-pushed the split/09-backbone-deep branch from 6175904 to 529528f Compare August 9, 2026 05:21
@roed-math
roed-math force-pushed the split/09-backbone-deep branch from 529528f to 8c5cfc8 Compare August 9, 2026 08:24
One family: **Genus 2 curve** (`genus-two`) — P1, effective.

- Standard form: `y^2 = f(x), deg f in {5, 6}`
- Parent: `hyperelliptic`
- Examples: `y^2 = x^5 - x + 1`

Contents: the registry entry, its `docs/FAMILIES.md` section and its rows in the classification corpus.

References cited (the claim each one supports):

- `Igusa1960` — the invariants identifying a genus-2 curve up to isomorphism (the classifier's genus-2 handle)
- `CasselsFlynn1996` — explicit arithmetic of genus-2 Jacobians

Independent of every other family PR: it needs only the registry backbone it is based on.

Part of the series that splits #1 into reviewable pieces:

1. `01-bibliography` — packaging, docs, annotated bibliography
2. `02-parsing` — equation strings to a term model
3. `03-registry` — the YAML family registry (3 seed families)
4. `04-matchers` — shape recognizers
5. `05-classify` — the classification pipeline
6. `06-solvers` — solver framework, two seed solvers, and the CLI
7. `07..09-backbone` — the 23 parent families of the DAG, by depth
8. one PR per remaining family (38 of them, mutually independent)
9. `99-polish` — restore the full doctests and tighten the invariants
@roed-math
roed-math force-pushed the split/09-backbone-deep branch from 8c5cfc8 to d767c69 Compare August 9, 2026 20:35
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2 participants