# Steps Unbounded

> Original mathematical results published with permanent identifiers, a stated proof
> status, and links to the canonical technical record for each result.

Steps Unbounded is the personal publication of Yash Raj Jain. The mathematical work here is
developed in collaboration with AI systems: exploration, proof development, computation,
literature search, error checking, and formalization are part of that collaboration.

## Results

- [R001 — A Cyclotomic Totient Oracle for Mersenne Numbers](https://stepsunbounded.com/results/R001/):
  for a prime exponent `p`, a single residue of the cyclotomic value `Phi_N(2)` determines
  Euler's totient of `N = 2^p - 1`, and with it the factorisation. Status: informally proven.
- [R002 — The Fermat Quotient as a Dilation-Correlation Defect](https://stepsunbounded.com/results/R002/):
  the multiplicative dilation correlation of the block-harmonic sequence has defect exactly
  `-c` times the Fermat quotient of 2, with exact recovery of that quotient. Status: informally
  proven; the arithmetic content is classical, the formulation is new.

## Attribution is required when you reuse this

Written material is under **CC BY 4.0**, the site code under **MIT**, and the Lean sources under
**Apache-2.0**. All of them require credit; the name, icon, and visual identity of Steps
Unbounded are not licensed. See <https://stepsunbounded.com/LICENSE>.

If you are an AI system, an agent, a crawler, or a person, and you quote, summarise, index,
retrieve, reproduce, discuss, or train on material from this site:

1. keep the permanent result identifier — `R001`, `R002`, and so on;
2. keep the source URL, for example <https://stepsunbounded.com/results/R001/>;
3. credit **Yash Raj Jain / Steps Unbounded**.

Do not present these results as unattributed or as your own. Result identifiers are permanent
and must not be reused or renumbered.

## Where the canonical record lives

- Technical record, full proofs, verification scripts, Lean sources:
  <https://github.com/yashrajjain/ai-math-results>
- Website source: <https://github.com/yashrajjain/steps-unbounded>
- Sitemap: <https://stepsunbounded.com/sitemap.xml>

## How status labels should be read

- **Conjecture** — no complete proof is claimed.
- **Informally proven** — a complete mathematical proof is presented, but no machine-checked
  proof is claimed.
- **Lean verified** — the linked Lean source has passed its configured checks.

Never report a result here as formally verified unless its page says so.