# Collatz Operation Translation Series — Repaired Series Index

**Package:** SSSP Repaired v1.0  
**Repair date:** 2026-08-14  
**Core series status:** 9/9 papers present  
**Follow-on research program:** Hard-Zeta / Faithful Global Quantifier Compression

## Core series

1. **Paper 01 — 考拉茲猜想既有研究的重新分類與校正** — v0.1 (content unchanged in this repair)
2. **Paper 02 — Collatz Local Affine Atlas：有限奇偶字的精確仿射化** — v0.1.1
3. **Paper 03 — Parity Word、Residue Cylinder 與局部 Identity 化** — v0.1.1
4. **Paper 04 — 雙向殘餘類轉譯：$2^k$ Cylinder 與 $3^u$ Progression** — v0.1 (content unchanged)
5. **Paper 05 — 有限字收縮邊界與二項式 Cylinder Law** — v0.1 (content unchanged)
6. **Paper 06 — Valuation Language 與 Accelerated Collatz** — v0.1 (content unchanged)
7. **Paper 07 — 廣義 $(mx+r)$ 系統與 Residue-Class Operation Translation** — v0.1.1
8. **Paper 08 — 代數判定域與結構斷裂定理** — v0.1.1
9. **Paper 09 — Finite Certificate Frontier：Collatz 有限精確覆蓋與全域鴻溝** — v0.1.1

## Follow-on research program

- **Faithful Global Quantifier Compression / Collatz Hard-Zeta Frontier** — v0.1.2

The Hard-Zeta manuscript is not Paper 10 of the closed nine-paper series. It is packaged separately under `research_program/`.

## Canonical source policy

Formal Markdown source uses only `$...$` and `$$...$$` as canonical math delimiters. The legacy `\\(...\\)` and line-delimited `\\[...\\]` forms were mechanically normalized where present, with byte-level diffs retained under `provenance/diffs/`.