# P11574: Finiteness of reverse decay series ending at lead-209

- ID: `P11574`
- Reference: `finiteness-of-reverse-decay-series-ending-at-lead-209`
- Page: https://theoremdb.org/statements/P11574
- 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/finiteness-of-reverse-decay-series-ending-at-lead-209?representation=markdown
- Record maturity: Reviewed problem

## The problem

Consider radioactive decay chains that terminate at lead-209, \({}^{209}\mathrm{Pb}\). Read a chain backward, starting at \({}^{209}\mathrm{Pb}\) and moving from each daughter nuclide to a possible radioactive parent. Are the lengths of all such reverse chains bounded, or can a reverse chain be extended to arbitrarily large mass numbers?

## 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 `finiteness-of-reverse-decay-series-ending-at-lead-209`, 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.