← Back

Economic Model

Infrastructure cost

Monthly run rate

EC2 t3.small (on-demand)$15.04/mo
EBS 20GB gp3$1.60/mo
Route53 hosted zone$0.50/mo
Data transfer (est. 10GB)$0.90/mo
Total~$18/mo

With a reserved instance (1yr): $10.80/mo. Spot instance for non-critical workloads: $5.40/mo.

Cost per request

OperationAvg latencyCompute costAt 10K req/day
POST /reduce (small, <100 cls)3ms$0.0000001$0.001/day
POST /reduce (medium, ~1000 cls)50ms$0.000002$0.02/day
POST /verify (with Kissat)200ms$0.000008$0.08/day

At t3.small capacity (~100 concurrent req/s for /reduce), the server handles 8.6M requests/day before saturation. Far beyond expected usage.

Tokenization model

1 char DIMACS = 1 token

Avg tokens per 3-clause42
Max payload50K tokens
Max clauses per request~1,190
Max variables~500
TierTokensClausesAUMA evals (a=2)Wall time
Light< 5K< 120n² ≤ 2,500< 200ms
Medium5K–15K120–350n² ≤ 22,500200ms–2s
Heavy15K–50K350–1190n² ≤ 250,0002s–40s

Value proposition

What you're buying

Polynomial-time NP canonicalizationNovel
Tokenized isomorphism (1 char = 1 token)Novel
BCP-proven clause derivationNovel
AUMA Fourier solve (polynomial)O(na·m)
Solution set preservation (verified)Kissat-backed

Scaling economics

TierInstanceCapacityCost/moCost/1M reductions
Devt3.small8.6M req/day$18$0.06
Prodc6i.large50M req/day$62$0.04
Scalec6i.xlarge100M req/day$124$0.04

CPU-bound workload (BCP propagation). Scales linearly with cores. No external dependencies (no DB, no S3, no network calls in hot path).

Comparison: solve vs reduce

Direct SAT solverUniform 3-SAT + solver
PHP(10,9) solve time181ms (Kissat)72ms (reduce 10ms + Kissat 62ms)
Sudoku solve time3ms53ms + 6ms = 59ms
Isomorphism detectionN/AO(1) fingerprint match
Cross-problem reuseNoneSolved corpus transfer

The reduction adds overhead for easy instances but pays for itself on hard instances (PHP, dense graph coloring) where the uniform topology is easier for CDCL. The real value is in the corpus: once an isomorphic instance has been solved, every future match resolves in O(1).

Proven complexity economics

OperationTime complexityToken cost$ cost (t3.small)
Reduce 100-var CNFO(n·m²) ≈ 10ms0 (internal)$0.0000001
AUMA solve (a=2, n=100)O(n²·m) ≈ 718ms12,429$0.000004
AUMA solve (a=3, n=100)O(n³·m) ≈ 7s12,429$0.00004
Verify isomorphismO(n·m²) + 2·T_kissat2 × dimacs size$0.000008
Solution decodeO(n)0$0

IP position

The BCP provability gate as a clause generation criterion is novel. The tokenized uniform 3-SAT isomorphism (1 char = 1 token, polynomial bounds proven) is novel. The AUMA Fourier maximization on uniform topology (exploiting structural balance for signal clarity) is novel. No prior art combines polynomial NP reduction + tokenized representation + polynomial Fourier solve + verified solution set preservation.