Progress

Wording for any result on this page, per our methods policy: a completed milestone verifies every unlabelled tree on that many vertices, which together with the cited prior results extends the verified bound. It is a finite verification and not a proof for all trees — there are infinitely many.

Milestones

A milestone is one order N: every distinct tree on N vertices given a verified graceful labelling. A milestone is complete only when the coverage check passes — every residue class present, and the total number of trees matching an independently computed A000055(N) exactly. Off by one is a failure, not a rounding error.

Order	Distinct trees	Status
≤ 35	various	Reported in the literature (Fang, 2010), not by us
20	823,065	planned — operational test, not a new result
30	14,830,871,802	planned — staged beta
36	6,226,306,037,178	proposed first research target

"Planned" means exactly that: not started, not running, not partially done. Orders 20 and 30 are rehearsals for the machinery — they were settled decades ago and completing them proves nothing new about trees, only about our software.

Server state

Read live from the project database when you loaded this page.

Applications	Graceful Tree Search, GTS-36
Work units	388
Validated results	412
Volunteers	3
Computers	4

Full server status · Applications

Coverage ledger

Per-class coverage — which residue classes of which orders have been completed, and the running tree total against A000055 — is tracked in a separate ledger that is not yet built. This section will report from it once it exists. It is deliberately not being faked in the meantime.

When it is live, partial progress will be shown as "k of mod classes verified" for a given order. It will never be shown as a percentage of "the conjecture verified", because that quantity is not finite and no percentage of it is meaningful.