NthDS is an energy AI company. That does not mean the people who build it stop being technical when the product backlog is clear.
This month, co-founder and CEO Michael Ramirez landed a contribution on OEIS A003015 — the sequence of numbers that appear five or more times in Pascal’s triangle. The work sits in the long line of computational attacks on Singmaster’s conjecture (1971): the claim that there is some absolute bound on how often any integer can show up in that triangle.
What was actually shown
Honest version, no press-release inflation:
- Previous published exhaustive envelope (Blokhuis–Brouwer–de Weger, 2017): no unknown high-multiplicity collisions with value up to 10^60.
- New certificate: a segmented modular sieve finds no other terms below 10^62, and none with multiplicity greater than 8 in that range.
- The only high-multiplicity values in range remain the ones already known to the literature / OEIS.
- This is not a proof of Singmaster’s conjecture. It is a finite-range certificate — stronger computational evidence, still an open problem above 10^62.
Code, run logs, and the write-up are public: pair-collision certificate below 10^62.
Why it matters (and why it doesn’t)
It matters because open problems move in increments. Extending a published bound by two orders of magnitude, with a checkable certificate, is a real step on the road toward a proof — not the proof itself. Bigger searches alone will not finish Singmaster; the next work has to be theoretical. That is the point of doing the computation carefully: clear the finite range so the remaining argument has less fog.
It does not matter for buying LAS files. We are not pretending otherwise.
The technical founder angle
NthDS was founded by people who still write systems, run hard searches, and care whether a claim is proven, certified, or hoped. That habit shows up in product work as QC overlays, rejection of fake precision, and a bias toward evidence over narrative.
If you want the math: start at A003015 and the GitHub note. If you want the company: we build AI for subsurface records — and we hire for the same standard this milestone was held to.