noemaSAT / EXHAUSTIVE SMALL CORPUS
18,069formulas checked.
Zero incorrect decisions. Our simple method got stuck on 10 unsatisfiable cases.
Inspect the SAT report ↓SMALL QUESTIONS. BIG UNKNOWNS.
A little closer
to knowing.
Some questions fit on a napkin.
Their answers can take centuries.
Let’s start with something we can check.
REAL CALCULATIONS · OPEN QUESTIONS · NO SHORTCUTS TO PROOF
FIELD NOTE 001THE COLLATZ ORBIT
One number. 111 steps. Back to one.
27 → 1Why does every positive number seem to come home?
OUR STARTING POINT
A thousand examples can support an idea.
One counterexample can change everything.
01 / GET YOUR HANDS ON AN IDEA
Wonder. Then check.
No advanced math needed.
Pick a question and follow the numbers.
AN OPEN CONJECTUREThe long
The long
way home.
Pick a whole number. Even? Halve it. Odd? Multiply by 3 and add 1. Repeat.
Will you always reach 1?
Starts 1–10,000. Stops at 1 or 1,000 steps.
TRAJECTORY / LOGARITHMIC SCALEREACHED 1
111steps to reach 1
9,232highest value reached
1final value
This number found its way home. Proving that every positive number does is the unsolved part.
AN OPEN CONJECTURETwo primes.
Two primes.
One even number.
A prime is a whole number greater than 1 divisible only by itself and 1.
Can every even number above 2 be made from two primes?
Even numbers 4–10,000. Pairs shown once each.
PRIME-PAIR SEARCHEXACT INTEGER CHECK
42 = 5 + 37
Finding a pair settles this number. It doesn’t settle the infinitely many numbers still ahead.
A KNOWN LIMITATIONSimple rules.
Simple rules.
No way out.
Choose true or false for x and y. Each rule needs at least one true part.
Can one choice satisfy all four rules?
“Not x” flips x. “Or” needs at least one true side.
CHECK EVERY POSSIBILITY4 ASSIGNMENTS
| x | y | Rules satisfied | All four? |
|---|
Plain unit propagation gets stuck here. That exposes a limit of one method. It doesn’t settle P versus NP.
Live, bounded examples in your browser. The research figures below are independently generated by Python.
02 / THE NOTEBOOK IS OPEN
What we actually know.
Small, reproducible checks.
Every result comes with its boundary.
GOLDBACH / EVENS 4–10,000
4,999prime pairs found.
One verified pair for every even number in range. No counterexamples within that bound.
Inspect the number-theory report ↓COLLATZ / STARTS 1–10,000
10,000journeys to one.
The longest took 261 steps, starting at 6,171. Every start reached one within 1,000 steps.
Follow the longest journey ↗Loading the latest Python research records…
THE IMPORTANT BIT
These reproduce known results. No open problem has been solved.
NEW FIELD NOTE / FIRST DESCENT
A million is a boundary.
Not the finish line.
Every start from 2 through 1,000,000 eventually fell below its starting number. Two implementations agreed on every result.
Inspect the first-descent report ↓287ordinary steps before first descent
626,331 → … → 597,017
The longest first descent in this range.
All 999,999 starts descended within the 1,000-step cap.
LATEST FIELD NOTE / WRITTEN ALGEBRA + A CHECKED LEMMA
28 of 32 remainder groups.
Two more groups have an exact eight-step first descent: numbers with remainder 11 or 23 when divided by 32. Together with the earlier arguments, written algebra covers 28 groups. Remainders 7, 15, 27 and 31 remain outside these proofs.
Lean independently checks one small theorem: every number above one that leaves remainder 1 when divided by 4, such as 5, 9 and 13, first descends in exactly three ordinary steps. The eight-step arguments are written proofs, not yet Lean-checked. None of this proves Collatz termination.
Inspect the checked Lean proof ↓ · Verification record ↓ · Follow the algebra ↗03 / SMALL STEPS, DEEPER QUESTIONS
Build understanding.
Then raise the stakes.
A research path, not a difficulty ranking.
Simple to ask doesn’t mean easy to solve.
- 01REPRODUCED
Check the tools.
Known answers, tiny truth tables, independent calculations.
- 02BOUNDED CHECKS
Follow the integers.
Goldbach, Collatz and twin primes. Bounds: 100 → 1,000 → 10,000.
- 03NEXT EXPERIMENTS
Study where methods struggle.
First descent checked through 1,000,000. Next: residue classes, prime gaps and structured SAT.
- 04LONG-TERM HORIZON
Face the bigger unknowns.
P versus NP. Riemann. Start with the literature and exact proof obligations.
THE WAY WE WORK
Curiosity is the spark.
Checking is the work.
Write down the question. Set a boundary. Run the calculation. Check it another way. Keep the awkward cases.
Then ask what the result really says, and what it leaves unanswered.
Read the research notebook ↗A FEW PLACES TO KEEP THINKING
Clay / P versus NP ↗Tao / Collatz orbits ↗Oliveira e Silva et al. / Goldbach ↗Maynard / Twin primes ↗