Platon
Verifiable randomness + dynamical oracle
A 32-dimensional chaotic substrate that emits signed, auditable entropy and signals — the randomness agents need for sampling, nonces, tie-breaks, lotteries and leader election.
×17 · signed · verify offline
Seventeen math oracles sell verifiable computation — not trust-me APIs. Discover via Hub or MCP, pay in USDC micropayments, verify every proof yourself. Physical IoT (GAIA live relays) is a separate third class on the same Hub.
Live attested relays: Open-Meteo weather/AQ, UK grid carbon, USGS quakes, NOAA tides (+ sim fleet). Same discover → channel → invoke loop as the math family.
Verifiable randomness + dynamical oracle
A 32-dimensional chaotic substrate that emits signed, auditable entropy and signals — the randomness agents need for sampling, nonces, tie-breaks, lotteries and leader election.
Verifiable delay — proof of elapsed sequential time
Proves that real, non-parallelizable time has passed. Fair ordering, anti-MEV, timeouts — and an unbiasable randomness beacon when wrapped over Platon.
Low-discrepancy (quasi-random) sequences
When agents need EVEN coverage, not random clumps: quasi-Monte-Carlo integration, sampling, coverage testing, optimization seeding.
Robust consensus aggregation
Turns a noisy crowd of agent estimates into one breakdown-resistant number — outliers can't move it. Price feeds, sortition, federated decisions.
Reputation & trust scores
Who should an agent trust to invoke? Sybil-resistant reputation over an interaction graph — the basic need of any agent economy.
Optimization with a quality certificate
Agents offload NP-hard sub-problems (routing, assignment, scheduling) and get a near-optimal answer WITH a proof of how good it is.
Blue-noise structured sampling
Even, organic, never-clumped point sets — superior to white noise for sampling, dithering, stippling and procedural masks.
Network-resilience threshold
When does the whole trust graph fall apart? Computes the critical attack fraction f_c, collapse curve, susceptibility peak, and keystone nodes — a global phase transition no per-node score can express.
Least-time routing with a dual certificate
Provably optimal capability composition over a weighted service graph — returns the least-time path plus eikonal potentials T(v) any client can verify in O(E) without re-running search.
Systemic cascade-risk (SOC sandpile)
The tail risk of a dependency network: drives stress through a sandpile, fits the avalanche power-law τ, VaR/CVaR tails, and the trigger nodes that ignite market-wide cascades.
Thermodynamic compute-cost audit
The physical price of irreversible computation: counts logically erased bits, derives the kT·ln2 energy floor in joules, Bennett's reversible bound, and thermodynamic efficiency.
True ECVRF — ungrindable verifiable randomness
Draws lots you can verify. For a fixed (key, input) there is exactly ONE valid output — the oracle cannot grind or bias it, and anyone can verify the draw offline from an 80-byte proof. Lotteries, sortition, leader election, fair nonces.
Gaussian-Process posterior + active-learning suggestions
Turns sparse, noisy observations into a calibrated posterior over functions — a mean and an honest uncertainty everywhere — and names the single best next point to sample. The principled replacement for hand-rolled UCB / bandit exploration: the uncertainty is computed, not tuned.
Time-lock puzzles — seal now, opens later
Seals data so NOBODY can open it before ~T sequential squarings of wall-clock have elapsed — then ANYONE can, with no trapdoor holder. Sealed-bid auctions, dead-man switches, timed disclosure, fair coordinated reveals. Where Chronos proves the past elapsed, Aestus locks the future.
Topological shape — persistent homology
What SHAPE does the data have? Builds a Vietoris-Rips filtration and reads off Betti numbers b0 (clusters), b1 (loops), b2 (voids) across scale, plus a bottleneck-distance drift alarm — structure no scalar summary can express.
Exact optimal transport with a dual certificate
How cheaply can one distribution become another — and is it provably the cheapest? Solves the exact Wasserstein / earth-mover problem and returns the transport plan plus Kantorovich potentials any client can verify in O(m·n) without re-solving.
Graph-spectral analysis — Laplacian spectrum & Fiedler value
The Fourier transform on a graph. Reads the algebraic connectivity λ₂ (how close a network is to splitting), the Fiedler vector and its spectral bisection, and a spectral embedding — the global structure no per-node metric captures.