From 886e811eaa7aef8221cfa7865f73d4fe38687166 Mon Sep 17 00:00:00 2001 From: David Roe Date: Sun, 9 Aug 2026 16:27:30 -0400 Subject: [PATCH] =?UTF-8?q?Family:=20prouhet-tarry-escott=20=E2=80=94=20Pr?= =?UTF-8?q?ouhet-Tarry-Escott=20problem?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit One family: **Prouhet-Tarry-Escott problem** (`prouhet-tarry-escott`) — P3, open. - Standard form: `sum x_i^j = sum y_i^j for j = 1..k` - Parent: `equal-sums-like-powers` Contents: the registry entry and its `docs/FAMILIES.md` section. References cited (the claim each one supports): - `BorweinIngalls1994` — survey of ideal solutions and open problems 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 --- .../data/families/prouhet-tarry-escott.yaml | 15 +++++++++++++++ docs/FAMILIES.md | 6 ++++++ 2 files changed, 21 insertions(+) create mode 100644 diophantine_classifier/data/families/prouhet-tarry-escott.yaml diff --git a/diophantine_classifier/data/families/prouhet-tarry-escott.yaml b/diophantine_classifier/data/families/prouhet-tarry-escott.yaml new file mode 100644 index 0000000..9048d62 --- /dev/null +++ b/diophantine_classifier/data/families/prouhet-tarry-escott.yaml @@ -0,0 +1,15 @@ +# Family: Prouhet-Tarry-Escott problem +# Schema: see data/families/README.md; prose documentation in docs/FAMILIES.md. +# References are keys into data/references.bib, each with a 'why' annotation. +slug: prouhet-tarry-escott +name: Prouhet-Tarry-Escott problem +priority: 3 +status: open +class: surface +form: sum x_i^j = sum y_i^j for j = 1..k +parents: +- equal-sums-like-powers +matcher: false +references: +- key: BorweinIngalls1994 + why: survey of ideal solutions and open problems diff --git a/docs/FAMILIES.md b/docs/FAMILIES.md index 86434cf..e801ea8 100644 --- a/docs/FAMILIES.md +++ b/docs/FAMILIES.md @@ -310,6 +310,12 @@ the multi-degree system version. **References.** Lander–Parkin 1966; Elkies 1988; Borwein, *Computational Excursions in Analysis and Number Theory* (PTE chapters). +### `prouhet-tarry-escott` — Prouhet–Tarry–Escott — P3, open +**Form.** Σ x_i^j = Σ y_i^j for j = 1,…,k simultaneously (ideal: size k+1). +**Status.** Ideal solutions known only in scattered sizes; existence in all sizes +open; deep links to combinatorics and analysis. +**References.** Borwein–Ingalls, "The Prouhet–Tarry–Escott problem revisited" (1994). + ---