# P12903: Does strong jump traceability imply LR reducibility?

- ID: `P12903`
- Reference: `tianyuan-2026-sjt-implies-lr-reducibility`
- Page: https://theoremdb.org/statements/P12903
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: f295905458d7a3b058de2e38a46a52071c41c31e
- Current Markdown: https://api.theoremdb.org/v1/statements/tianyuan-2026-sjt-implies-lr-reducibility?representation=markdown
- Record maturity: Reviewed problem

## The problem

For subsets $A,B\subseteq\mathbb N$, let $A\le_{SJT}B$ mean that for every computable nondecreasing unbounded function $h:\mathbb N\to\mathbb N\setminus\{0\}$ there is a uniformly $B$-computably enumerable sequence of finite sets $(T_n)$ with $|T_n|\le h(n)$ such that $J^A(n)\downarrow$ implies $J^A(n)\in T_n$, where $J^A$ is a fixed universal partial $A$-computable jump function. Let $\mathrm{MLR}^X$ denote the Martin-Lof random reals relative to $X$. Must $A\le_{SJT}B$ imply $\mathrm{MLR}^B\subseteq\mathrm{MLR}^A$?

## Status

**Resolution status:** Open.

Research work is recorded. A complete resolution has not passed review.

## Research packet

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `tianyuan-2026-sjt-implies-lr-reducibility`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.