Watch nothing arrive.
Five nested counters visit each unordered placement exactly once. A queen covers its own square and every square sharing its row, column, diagonal, or anti-diagonal. The known orbit is then blocked. What remains is not small. It is empty.
live worker, direct geometryno network, no archived answer table
Preparing the complete sweep.
The counter is the certificate's domain size, computed by the loop rather than copied into the readout.
The search can succeed.
With no orbit blocked, the same search finds two labelled placements. One is the representative reported by Rostami and Bright. The other is its reflection. They are different square lists and the same geometric object.
The other labelled placement
Its mirror, found independently by the sweep.
8D4 transformations applied
?distinct labelled images
?transformations fix it
Put one in. Take it out.
A null from a detector that never fires is worthless. This control replaces only the mask-table data, then sends all 198,792,594 five-subsets through the unchanged loops and acceptance test. Five designated indices each own coverage bits that no other index has, so exactly one subset can pass.
Harness probe, not a mathematical queen placement
No result is appended and no candidate carries a precomputed verdict. The ordinary census must discover [0,1,2,3,4] through the same coverage and reporting path. This probes the loops, acceptance, counting, and display. The published placement separately probes the real geometric mask generator.
expected with probe masks = 1; expected with queen masks after blocking = 0
The normal queen-mask census is active. After the known D4 orbit is blocked, it returns exactly zero.
Nine breaks the silence.
Keep five queens and the same definitions, but move the board. At n = 10 there is still one class. At n = 9 there are 21. These buttons do not reveal stored totals. Each starts the same complete enumerator on the chosen board.
9 by 9
not swept yet
- five-subsets
- pending
- labelled
- pending
- D4 classes
- pending
10 by 10
not swept yet
- five-subsets
- pending
- labelled
- pending
- D4 classes
- pending
11 by 11
sweeping
- five-subsets
- running
- labelled
- running
- D4 classes
- running
Two labels do not make two guards.
Symmetry is computed after the geometric census, not assumed during it. The raw search uses no symmetry-breaking clauses. Only after all labelled winners are in hand does it apply the eight explicit coordinate maps and take the lexicographically smallest image as a key.
for 0 ≤ a < b < c < d < e < n²
covered := attack[a] OR attack[b]
OR attack[c] OR attack[d]
OR attack[e]
if covered = all n² bits
keep [a,b,c,d,e]
for each kept placement
make its 8 rotated or reflected images
key := smallest image
remove the known key
result := 0
- No ordering duplicates. Strictly increasing indices give one visit per unordered five-subset.
- No diagonal shortcut. Every queen mask is constructed square by square from row, column, r minus c, and r plus c equality.
- No unsafe symmetry pruning. The 198,792,594 raw candidates are all tested before quotienting.
- Orbit-stabilizer is visible. Eight maps produce two distinct images, so four maps stabilize the placement.
Is five really minimal?
The standard lower bound ceil((n - 1) / 2) = 5 already guarantees that four queens cannot dominate an 11 by 11 board. This separate complete sweep of every four-square subset corroborates that theorem-guaranteed zero. It does not discover a new emptiness.
Not run in this browser session.
What was checked, and what was chosen.
Green means recomputed from the rules in this page. Citation means a source statement. A declared choice is not evidence and is never dressed as one.
Recomputed live
The combination count, every attack mask, the raw labelled winners, the D4 orbit count, the orbit size, the stabilizer size, the post-blocking empty set, and any boundary run the reader requests.
Independently recomputed at build time
A separate Node verifier repeats the census without importing this page's code. It also checks the positive control, the mask-table harness differential, exact n = 9 and n = 10 counts, and refusal paths.
Source reported, not used as an answer table
Rostami and Bright report one non-isomorphic model at n = 11 and a checked proof certificate. Their record supplies the anchor. This page reaches the same count with a direct exhaustive geometry scan.
Free choices and uncertainties
The representative is the source's row-major model. The synthetic mask table is our chosen harness test. Browser speed depends on the device. This page does not parse the source's SAT CNF or trusted-clause DRAT proof.
Refusal boundary. The live worker accepts n = 9 through 11 with five queens, plus n = 11 with four. The harness flag is accepted only for n = 11 with five indices, and callers cannot supply masks or coverage verdicts. Other board sizes and queen budgets are refused. A refusal is a scope statement, not a zero result.
Archive correction. The build spec called for shipping and rechecking the source's n = 11 DRAT proof. We retrieved the complete Zenodo archive and verified its published MD5. Its nested n = 11 archive contains the CNF, solution files, and logs saying temporary proofs were checked, but no proof file. A log is not a certificate, so this page does not claim to have checked that proof. The direct 198,792,594-case enumeration above is the certificate used here.
Primary sources
- Taha Rostami and Curtis Bright, Queen Domination by SAT Solving, arXiv:2508.11945v2, revised 29 July 2026. The paper is CC BY 4.0.
- Taha Rostami, GammaSupp, Zenodo record 21193115, published 4 July 2026. The record is CC BY 4.0. No third-party file from it is shipped here.