About Graceful Tree Search
Graceful Tree Search is a volunteer computing project in pure mathematics. It looks for graceful labellings of trees — every tree of a given size, one size at a time.
The search application has not been built and no work has been distributed. There is nothing to compute here yet. This site is being built first, on purpose, so that what it claims is settled before any results exist to overstate.
What the project is trying to do
The Graceful Tree Conjecture says every tree can be numbered in a particular tidy way. It was posed in 1967 and is still open. Exhaustive checking has been published up to 35 vertices, and claimed but never shown up to 39. We start at 36 and do it in the open, so every result can be checked.
The mathematics, properly explained →
What your computer would do
Each task gives your machine three numbers describing a slice of all trees of a given size. Your computer regenerates that slice itself, searches each tree for a graceful labelling, checks every labelling it finds with two independently written checkers, and returns a small summary file. The download is tiny and the upload is tiny; the work in between is hours of pure CPU.
It is an ordinary BOINC application: it runs at low priority on cores you are not using, and it stops when you tell it to.
How the search and its checking work →
What you get
BOINC credit, and your name attached to the computation. That is all. There is no currency, no payout and no token — if you are looking for one, this is the wrong project and we would rather you knew now.
What we will and will not claim
If we finish an order, we will say that we computationally verified every tree of that size, name the software and versions used, and link the evidence.
We will not call it a proof of the conjecture, because it is not one and cannot become one. There are infinitely many trees; checking trillions leaves infinitely many unchecked. We will not claim a record without first re-checking the literature, and we will not announce a counterexample on the strength of our own software alone.
Nor do we hide the method's limits. We keep samples, cryptographic commitments to the full witness streams and every exceptional case — not every labelling, which could not be stored. Results rest on reviewed software and agreement between independent implementations, which is strong evidence and is not the same thing as a checkable archive of every witness.
Requirements
The first version targets 64-bit Linux on x86 only. Windows, macOS, ARM and GPU versions are deliberately out of scope for v1 — a single platform is easier to keep bit-for-bit deterministic, and determinism is what makes the results checkable. Support may widen later; it is not promised.
Privacy
Standard BOINC: an account needs an email address and a password. Your computer reports its hardware and operating system so that work can be sized sensibly. Results contain no personal data — deliberately, the result files contain no hostnames, no paths and no timings, because any of those would break the byte-for-byte comparison the validator depends on.
Contact
Use the message boards.
