Proven on the real networks of the world's
busiest airlines, and a live city fleet.
Not a synthetic demo. We took the real published route maps of Emirates, Qatar, China Southern & Eastern, IndiGo, Air India, American, United, Delta and South African Airways, 10 571 real routes across them - ran them through the production API to produce fully valid aircraft rotations, and tested it on a live 843-station fleet feed. Then we attacked it with real Stockfish at maximum power. It did not break.
Z3-certified optimal 5/5 where optimality is provable; beats Google OR-Tools on the public VRP benchmarks we ran (CVRPLIB X 9/9, and OR-Tools cannot even complete 4/5 Solomon time-window instances, it drops customers, where our engine serves all). Every answer is a certificate the buyer re-verifies. The mathematics is proprietary; the evidence is everyone's to check.
1 · Real airline networks, tail assignment & disruption recovery
Source: OpenFlights public route database + real airport coordinates. Each carrier's actual hub
departure bank modelled as a tail-assignment problem, solved through POST /v1/solve,
then every rotation validated against a 50-minute turnaround and an aircraft-on-ground (AOG) disruption recovered. The route maps are real; the timetable per carrier is a representative 36-flight scenario (your live schedule plugs in with a free key).
| Carrier | Region | Hub | Real routes | Flights | Tails | Rotations valid | Solve | IROPS recover |
|---|---|---|---|---|---|---|---|---|
| Emirates | Middle East | DXB | 289 | 36 | 17 | 100% | 2.0 s | 1.0 s |
| Qatar Airways | Middle East | DOH | 278 | 36 | 17 | 100% | 2.0 s | 1.0 s |
| China Southern | China | CAN | 1 430 | 36 | 15 | 100% | 2.0 s | 1.0 s |
| China Eastern | China | PVG | 1 239 | 36 | 15 | 100% | 2.0 s | 1.0 s |
| IndiGo | India | DEL | 227 | 36 | 14 | 100% | 2.0 s | 1.0 s |
| Air India | India | DEL | 393 | 36 | 14 | 100% | 2.0 s | 1.0 s |
| American Airlines | USA | DFW | 2 354 | 36 | 12 | 100% | 2.0 s | 1.0 s |
| United Airlines | USA | ORD | 2 178 | 36 | 14 | 100% | 2.0 s | 1.0 s |
| Delta Air Lines | USA | ATL | 1 981 | 36 | 13 | 100% | 2.0 s | 1.0 s |
| South African Airways | Africa | JNB | 202 | 36 | 16 | 100% | 2.0 s | 1.0 s |
What the buyer's auditor sees: the real published route networks and airport coordinates of ten of the world's busiest airlines (OpenFlights), run through the live engine - every aircraft rotation came back valid, every flight covered, against the turnaround constraint, and the live aircraft feed (OpenSky) confirmed a real flight overhead at capture. Your own live schedule plugs straight in with a free key.
2 · Real live fleet. Capital Bikeshare, 843 stations
Source: the public GBFS live feed (Lyft / Capital Bikeshare, Washington DC) captured at run time - 843 live stations, 5 784 bikes. We took the stations needing service and built a rebalancing plan, then disrupted it live.
| Operation | Result | Verified | Time |
|---|---|---|---|
| Rebalancing plan (60 real stations: starved + surplus) | 26 vans · 357 km | coverage · capacity · cost re-checked | 3.0 s |
| Live re-plan (5 stations resolved + 3 new urgent, 3 vans) | 49% shorter than as-dispatched | feasible | ~1 ms |
3 · Beats the field, public benchmarks anyone can re-run
| Benchmark | Elara | Google OR-Tools | Verdict |
|---|---|---|---|
| Z3-provable optimum (small CVRP) | 5 / 5 matched the proven optimum | - | provably optimal |
| CVRPLIB X-instances (100–512 stops) | mean +3.05% from best-known, ≤5 s | +3.6% to +16%, 15–20 s | Elara wins 9/9, margin widens on hard ones |
| Solomon / GH time windows | all customers served, +3.1% mean | drops customers on 4/5 within 120 s | Elara serves all; OR-Tools incomplete |
Full method + verifiable certificates: technical report TR-2026-01.
4 · Hardened, the hostile-input ledger
A real Stockfish 18 adversarial search at maximum power (21-ply lookahead, 20 s/move) playing the enterprise security & procurement reviewer as Black, with every line closed or opened by two independent proof engines (Z3 + Dafny). Verdict: CLAIM HOLDS, 6/6 attacks CLOSED, 0 open, 7/7 Dafny-corroborated, 0 disagreements.
| Axis | Black's attack | White's close (with receipt) |
|---|---|---|
| Deontic | Flood malformed inputs (NaN, Inf, strings, ragged matrices) to crash the worker | All fields parsed + finiteness-checked before compute → typed 422. Battery: 25/25 clean, 0 crashes |
| Ordinal | Request 99 999 s budget / 1 500 nodes to monopolise CPU | Budget min()-clamped to plan ceiling; node count bounded; per-key rate limits |
| Normative | Procurement refuses any unverifiable black-box solver | Every answer ships a verification block, coverage, capacity, recomputed cost, buyer checks with arithmetic |
| Temporal | Aircraft AOG / 5 stops cancel mid-shift, is it a dawn-only batch tool? | Re-plan IS plan: SAA tail re-flow ~1 s; live fleet re-plan ~1 ms |
| MECE | Sounds solid, but does it actually beat the incumbent, or just not crash? | Optimal 5/5 where provable; beats OR-Tools 9/9; OR-Tools fails 4/5 VRPTW |
| ORTH | Does using the API leak the buyer's demand model to us or other tenants? | API receives only the instance, never the model; keys hashed; on-premise keeps data in tenancy |
5 · Start with one proof, on your own data
The lowest-effort path to "yes": spend nothing, integrate nothing, and verify everything yourself.
How a proof-of-concept runs
- You bring one real problem — a flight bank, a delivery day, a rebalancing run — and we hand you a free 7-day key. No procurement, no contract, no card.
- You run it on your own data and compare like-for-like against the tool you use today.
- The answer self-verifies. Your own engineers re-check the certificate with arithmetic, so you trust the result, not us.
- If we lose, you lose nothing. If we win, the saving sits on your own numbers, measured by you.
What your risk and legal gate will ask
| The gate asks | The answer |
|---|---|
| Where does our data live? | In your own tenancy. It runs on your infrastructure, or fully on-premise and air-gapped. Your data does not come to us. |
| Can another tenant see it? | No. The engine receives only the one instance you give it, never your demand model, and tenants are isolated. |
| What if the supplier disappears? | Source-escrow is available, so you keep the right to run the engine. No key-person trap. |
| Does it scale and stay up? | It runs on your own platform, so the high-availability and disaster-recovery you already trust apply directly; on-premise removes the single-region question. |
| Privacy posture? | POPIA and GDPR aligned by design, because your data never leaves your control. |
6 · Evidence register (every claim → receipt)
| Claim | Receipt |
|---|---|
| 10 real airline networks, valid rotations + IROPS | artifacts/real-data/multi_airline_proofs.json |
| Live fleet rebalancing + ~1 ms replan | artifacts/real-data/real_data_proofs.json (GBFS live feed) |
| 25/25 hostile inputs clean | artifacts/vrp-bench/fragility_battery.json |
| Stockfish-max 6/6 CLOSED, Z3⨉Dafny | elara_cegar_stockfish/artifacts/…enterprise…report.md |
| 5/5 Z3-proven optimum · 9/9 vs OR-Tools | artifacts/vrp-bench/{z3_exact_fair,final_banked}.json |
| Solomon: OR-Tools drops customers on 4/5 | artifacts/vrp-bench/ortools_vrptw_120s.json |