Compute — affine copies of {0,1,3}
Aaronson’s T(S) = #{(x,y,z)∈S³ : x+2y=3z}.
Bound
verify_half.py checks T(S) ≤ ⌈n²/2⌉:
- the sum identity ∑(1+2 min(j−1,n−j)) = ⌈n²/2⌉ through n=399
- the fibre injection on exhaustive small subsets and 2360 random sets
- named witnesses (interval, {0,1,3}, n=7 sporadic, almost-interval)
Output: certs/half_bound.json.
verify_interval.py checks the interval closed form through n=79.
Search residue (does not move 1/3)
| script | what |
|---|---|
search_exact.c |
exact max T on n-subsets of {0..4n} |
search_small.py |
same in Python, smaller n |
search_periodic.py |
lifts of P ⊂ ℤ/mℤ |
search_two_ap.py |
two/three APs of difference 3 |
search_intervals.py |
two intervals, {0,1,3}-blocks |
search_local.py |
hill-climb |
energy.py |
E(S,2S) versus the interval |
Witnesses
certs/n7_triples.json— the 18 solutions in {0,3,6,8,9,12,18}plot_constants.py→../figures/constants.png
q1 (2026-08-27)
Endpoint recurrence and family search. Does not move 1/2.
Replay: q1/run_all.sh. Cert: q1/certs/q1.json.