The Day I Stopped Chasing the Prize

by

The Day I Stopped Chasing the Prize

Part 1 of the Room at the Bottom series

I was staring at a 10-page LaTeX proof of the Beal Conjecture.

95% rigor. 10,550 adversarial tests. Zero counterexamples. A valuation debt framework that worked.

And a $1,000,000 prize waiting.

All I had to do was claim the last 5%. Pretend the Independence Lemma was proven. Submit. Hope no one noticed the gap.

I didn’t.

This is the story of why.

The Setup

The Beal Conjecture says: If a^x + b^y = c^z with x,y,z > 2, then a,b,c must share a common factor.

Simple statement. Million-dollar prize. Unsolved for decades.

I’d spent months building a verification kernel. Testing coprime attempts. Computing p-adic valuations. Building what I called “valuation debt” – a framework showing why solutions can’t exist.

And it worked.

10,550 tests. Not one counterexample.

The framework held.

I was at 95%.

The Gap

There was one piece missing: the Independence Lemma.

I needed to prove that the valuation constraints were independent across different primes. That you couldn’t satisfy all of them simultaneously using the Chinese Remainder Theorem.

I knew it was true. The tests confirmed it. The pattern was clear.

But I couldn’t prove it rigorously.

I had two choices:

1. Claim 100%. Submit to the prize committee. Hope the gap goes unnoticed. Collect the money.

2. Stop at 95%. Document the gap honestly. Release it anyway. No prize.

The Moment

I remember the exact moment I decided.

I was looking at the kernel output. Test #10,550. Another coprime attempt rejected. The valuation debt was positive again.

The machine had done its job. It tried to break the claim. It couldn’t.

But the machine also knew where it stopped.

It flagged the Independence Lemma as “unproven.” It documented the gap. It didn’t hallucinate certainty.

The machine stopped itself when logic broke.

And I realized: if the machine can be honest about its limits, so can I.

The Decision

I chose option 2.

I documented the 5% gap in gaps_assessment.md:

Gap 1: Independence Lemma

>

The argument that valuation constraints are independent across primes needs formal proof using Chinese Remainder Theorem. Currently supported by empirical evidence (10,550 tests) but not rigorously proven.

>

Impact: Without this, the proof is at 95% rigor.

I added it to the conclusion:

Status: 95% rigor. The Independence Lemma requires formalization.

I released it anyway. No prize submission. Just honest documentation.

What I Learned

The prize wasn’t the goal.

If I’d chased the money, I would have:

  • Hidden the gap
  • Hoped no one found it
  • Lived with the lie

Instead, I have:

  • Exact knowledge of where understanding ends
  • A framework others can build on
  • Intellectual integrity intact

That’s worth more than $1,000,000.

The Real Achievement

I didn’t solve Beal.

I built a machine that knows when to stop.

That’s harder. And more valuable.

Because the next person who uses this framework might close the 5% gap. Or they might find a counterexample. Or they might hit a different boundary.

Either way, we learn.

Why This Matters

Most mathematical AI systems optimize for outcomes:

  • Generate proof
  • Hope it’s correct
  • Publish
  • Retract (maybe)

I optimized for honesty:

  • Generate claim
  • Try to break it (10k+ tests)
  • Find boundary
  • Stop and document

The difference?

I know exactly where I stopped.

And that knowledge is worth more than any prize.

The Aftermath

I released the proof as PRIME_COLLISION_PROOF.pdf. 10 pages. 95% rigor. Gaps documented.

No prize submission. No headlines. No recognition.

Just honest work, honestly documented.

And you know what?

I sleep better.

Because I didn’t lie to myself. I didn’t lie to the world. I didn’t pretend to know more than I do.

The machine stopped itself when logic broke.

And so did I.

What You Can Do

The complete Beal investigation is open source:

Repository: https://codeberg.org/ishrikantbhosale/room-at-the-bottom

Beal Proof: https://codeberg.org/ishrikantbhosale/room-at-the-bottom/src/branch/master/investigations/beal/PRIME_COLLISION_PROOF.pdf

Gaps Assessment: https://codeberg.org/ishrikantbhosale/room-at-the-bottom/src/branch/master/investigations/beal/gaps_assessment.md

Can you close the 5% gap?

Can you prove the Independence Lemma?

Can you find a counterexample?

Try.

If you succeed, we both learn.

If you fail, the proof gets stronger.

Either way, truth wins.

The Lesson

95% with honest gaps beats 100% with hidden lies.

Every time.

The prize can wait. The truth can’t.

This is Part 1 of a 15-part series documenting the 18-year journey to build “Room at the Bottom” – a thinking machine that stops itself when logic breaks.

Next: “When the AI Lied to Me (And I Caught It)” – The Goldbach logical error that validated everything.

Links:

  • Repository: https://codeberg.org/ishrikantbhosale/room-at-the-bottom
  • Landing Page: https://potatobullet.com/room-at-the-bottom/
  • Full Story: https://potatobullet.com/kernel-enforced-adversarial-exploration/