Live distributed proof system

Turning spare machines into verified OEIS terms.

This site tracks a proof engine for A276661, then becomes the control surface for the next sequence. Every claimed witness is checked against all subset sums before it can move a bound.

current proof

Testing a(11) <= 593

run #29 · 23.2% of branches · <=92.2% of est. compute

last settled term

a(10) = 309

10 known terms

throughput

0.4/hr

@..........@............ · 10 today

workers

across 1 machines

Current Run

RIGOROUS v29 unified max<=593 (a1 from 1, free-max leaf). a(11)>=594 iff no DSS found.

Coverage

branches ######.................. 23.2%

branches covered39,447 / 170,236 pairs

est. compute done0.03% – 92.2% · hardest branches ahead

frontiera1 (set's smallest element) ≈ 329 · sweeping 583 → 1

claim under test461 < a(11) <= 594 · this run tests 593

snapshot statelive

covered jobs39,447 / 170,236

reserved now5

pending130,784

failed0

split pairs0

triple jobs0

cpu time recorded19.9mo

recent p50/p952.0h / 44.0h

Work In Flight

one row per worker · longest-held first

workerclaim under testbranches held (a1,a2)held for

ntindle-prod/w0a(11) <= 593(329,433) … (329,437) · 5 held12.4h

Machines

grouped by host

hostprocessestotal

ntindle-prod|...............1 workers

Result Feed

live workers and bulk imports share the same verifier

machineresultsnodes searchedcompute timelast result

ntindle-prod10 results138,138,829,864 nodes10.4h cpu · 20.8h wall12.4h ago

What A276661 Solves, Concretely

Choose reference weights so every combination has a unique total: read one number off the scale and you know exactly which weights are on it. That decode-from-a-sum property is the engine of coin-weighing puzzles, single-measurement component identification, and the knapsack encodings behind early public-key cryptosystems. A276661 asks: how small can the largest weight be?

Sequence Ledger

proof state by term

knownA276661a(1) = 1 trivial (singleton sets are always DSS){1}

knownA276661a(2) = 2 trivial (any 2-element set with max=2 is DSS){1, 2}

proven_hereA276661a(3) = 4 proven by this distributed search{2, 3, 4}

proven_hereA276661a(4) = 7 proven by this distributed search{3, 5, 6, 7}

proven_hereA276661a(5) = 13 proven by this distributed search{6, 9, 11, 12, 13}

proven_hereA276661a(6) = 24 proven by this distributed search{11, 17, 20, 22, 23, 24}

proven_hereA276661a(7) = 44 proven by this distributed search{20, 31, 37, 40, 42, 43, 44}

proven_hereA276661a(8) = 84 proven by this distributed search{40, 60, 71, 77, 80, 82, 83, 84}

proven_hereA276661a(9) = 161 proven by this distributed search{77, 117, 137, 148, 154, 157, 159, 160, 161}

knownA276661a(10) = 309 Conway-Guy 1969 + exhaustive search confirmed a(10)=309{148, 225, 265, 285, 296, 302, 305, 307, 308, 309}

searchingA276661461 < a(11) <= 594 in progress · lower: Dubroff-Fox-Xu 2021, upper: Conway-Guy

frontierA276661a(12) <= 1164 queued by upper bound

Proof Map

green settled, teal live, indigo queued

a10

a11

a12