Research Lab → Operator-grade System

Symbolic AI for the Edge of Mathematics

Production-grade proof engines, verification pipelines, and live dashboards — engineered to push frontiers, not pixels. If a path exists, we’ll find it. If not, we’ll build the path and replay it deterministically.

200k+ Lines across ProofX & ProjectX
Multi-Prover SMT + Finite Model Checking
Realtime Dashboards & Entropy Analytics
Benchmarks: Goodstein Paris–Harrington GUE Conformity

Trusted where rigor matters

Designed for labs, verifiers, and number-theory explorers.

Where ProofX Compounds

Industrial verification, research automation, number-theory exploration.

Formal Verification

Safety

Prove or falsify properties of mission-critical systems. SMT + FOL pipelines surface counterexamples with full traces and model witnesses.

  • Invariant discovery & regression guardrails
  • Model construction on failure paths
  • Deterministic replay across solver portfolios

Research Copilot

Throughput

Automate conjecture generation, lemma mining, dataset construction, and ablation study planning with entropy-aware search.

  • Curriculum schedulers & bandit exploration
  • Trace compression & replay seeds for comparisons
  • Evaluation walls: instant side-by-side diffs

Quant Dashboards

Realtime

Live telemetry over symbolic runs: anomaly detection, decay maps, and operator consoles so researchers steer runs instead of babysitting them.

  • Roll-ups with anomaly flags & outlier surfacing
  • Entropy/decay overlays & time-to-signal estimates
  • APIs for custom viewers & wall displays

Systems

Orchestrated, observable, and built for frontier proofs.

ProofX Core

Orchestrator

The control plane. Multi-prover orchestration with deterministic pipelines for SMT + finite model testing, theorem synthesis, and entropy-guided scheduling. Every attempt emits structured traces for audit-grade replay.

  • Curriculum runs & priority queues
  • Counterexample harvesting
  • Evaluation walls & trace compression

CollatzX

Distributed

A distributed numeric/symbolic explorer for chaotic regimes. Streams telemetry in real time, flags anomalies, and maps symbolic decay—so researchers can steer runs instead of babysitting them.

  • Shardable search with backpressure
  • Realtime anomaly detection & rollups
  • Dashboards with entropy/decay overlays

RiemannX

Spectral

Analytic-number-theory engine for the critical line. Spectral methods for zeta/L-functions, zero-finding, spacing statistics, and prime-gap probes—wired into ProofX telemetry for reproducible experiments.

  • High-precision zero locators (GPU/CPU hybrid)
  • GUE conformity & pair-correlation stats
  • Experimental APIs for prime-gap heuristics

Visual Proofs in Motion

Live outputs from engines — interpretable, rigorous, and replayable.

Collatz sequence length distribution (log scale x-axis)
Collatz sequence lengths (up to 106) — hot spots tracked by anomaly flags. The dashboard overlays decay and entropy, making structure legible to the eye.
Riemann zeros spectral view placeholder
RiemannX spectral panel — pair-correlation windows, heatmaps, and spacing statistics.
Evaluation wall comparative panel placeholder
Evaluation wall — side-by-side diffs across runs; think operator cockpit for math.
Counterexample trace and witness placeholder
Counterexample witness — failure paths with model construction for immediate action.

ProofX Overview

Executive brief — positioning, applications, and philosophy.

ProofX unites formal theorem verification with symbolic AI experimentation. Its modular architecture blends GPU-accelerated numeric pipelines with custom first-order logic engines, orchestrated for deterministic, reproducible results.

  • Mathematics: conjecture verification & proof discovery
  • Verification: safety properties, SMT portfolios, finite model witnesses
  • Dashboards: run diffs, anomaly flags, entropy/decay overlays

Every proof attempt is transparent: visual proof-path tracers and symbolic heatmaps illuminate key steps, ensuring results are verifiable, reproducible, and scalable.

Core Engines

The primitives that make ProofX feel inevitable.

Logic Engine

FOL

First-order logic with quantifier handling, skolemization, evaluation traces, and counterexample generation.

  • Unification & substitution stacks
  • Traceable inference steps with IDs
  • Model witnesses on failure

Verification Kernel

SMT/FMC

Deterministic pipelines for SMT + finite model checking, SAT bridges, and property proving.

  • Assumption sets & proof obligations
  • Solver portfolios & routing
  • Deterministic replay

Entropy Engine

Search

Entropy-guided scheduling, decay maps, and anomaly detection across proof runs.

  • Curriculum & bandit schedulers
  • Entropy/decay overlays
  • Outlier surfacing

Dashboard Runtime

Realtime

Operator-grade telemetry: streaming traces, evaluation walls, and drill-down for fast iteration.

  • Live rollups & timelines
  • Run diffs & compare
  • APIs for external viewers

Architecture

ProofX stacks deterministic solvers with symbolic search and telemetry. Observability is first-class: every proof attempt is a data point.

  • Solvers: SMT, FOL, finite model testing, SAT bridges
  • Search: entropy-aware scheduling, curriculum runs, counterexample harvesting
  • Telemetry: traces, dashboards, anomaly flags, decay maps
Rreplay seed Ddiff runs Wevaluation wall

Design target: truth-aligned latency — the fastest path from idea to verified evidence.

Architecture Deep Dive

Moats

  • Data Evaluation walls & structured traces form proprietary corpora over time.
  • Ops Deterministic + probabilistic hybrid control: speed with proofs.
  • UX Live dashboards that shorten the loop, turning math into an operational practice.

Reliability

  • Seeded randomness & versioned runs
  • Artifact registry for notebooks & witnesses
  • Backpressure under heavy workloads

Research

We operate at the convergence of symbolic AI, number theory, and verification. Preprints, dashboards, and benchmarks are released on a rolling basis.

  • Goodstein / Paris–Harrington benchmarks
  • Entropy scoring & symbolic decay maps
  • GUE conformity and spacing statistics
Collaborate

Latest Notes

  • Aug ’25 Proof synthesis entropy scoring — design doc
  • Aug ’25 Multi-prover pipeline: orchestration modes
  • Jul ’25 GUE conformity checks — dashboard spec

Open Questions

  • Minimal sufficient statistics for proof-likelihood under entropy constraints
  • Counterexample distribution priors for guiding solver portfolios
  • Compression bounds for evaluation walls

Unicorn Trajectory

A research lab that scales like a systems company.

Why ProofX wins

  • Moat by evidence: every proof attempt creates assets (traces, witnesses, evaluation diffs).
  • Time-to-signal: dashboards collapse feedback cycles from weeks to hours.
  • Determinism: reproducibility converts demos into durable compounding data.
  • Portability: works on chaotic math and safety-critical verification alike.

Market Wedge

  • Start: formal verification & research teams with urgent deliverables
  • Expand: number-theory engines & analytic tooling for frontier labs
  • Platform: evaluation walls & dashboards as the operating system of truth

V1 → V2: Evaluation Wall & External Proofs

Ship public dashboards, replay seeds, and external proofs with full traces. Establish the ritual: propose → run → review → replay.

V2 → V3: Programmable Orchestration

Expose curriculum schedulers, entropy knobs, and solver portfolios as programmable modes. Users author proof strategies, not scripts.

V3 → V4: Research Copilot

Compound engines into a copilot for conjectures, lemmas, and dataset creation. Research becomes an operational discipline.

What’s the TAM/SAM/SOM narrative?

We enter where verifiable results are mandatory: verification, fintech risk, safety standards, and frontier math. The stack generalizes across these, creating a shared OS for truth.

Monetization?
  • Enterprise pilots (SaaS + managed dashboards)
  • SDK licensing for private clouds
  • Usage-linked telemetry tiers for research groups
Why now?

Compute and observability caught up with symbolic methods. Deterministic stacks + telemetry finally compress the iteration loop for verifiable work.

Defensibility?
  • Structured traces & evaluation walls become proprietary corpora
  • Operational UX & replay rituals compound switching costs
  • Hybrid deterministic/probabilistic control enables unique reliability
Risks & mitigations
  • Scope creep → strict orchestration modes & SLAs
  • Data sensitivity → private cloud + reproducible runs
  • Talent bottlenecks → platform tooling and SDK

Author

Systems, not slogans. Quiet rigor, public results.

Portrait of Alkindi

Alkindi

Founder & Architect, ProofX

I build operator-grade symbolic systems. Trained on silence, tuned by constraints. I write code like a lab notebook—every decision logged, every result replayable. ProofX is a bet that truth deserves an operating system.

“If a path exists, we find it. If not, we wire the graph and try again—deterministically.”

  • UCL Engineering — AI, mathematics, verification
  • Research at the edge: Goodstein, Paris–Harrington, GUE
  • Builder bias: dashboards over decks; traces over takes
Systems Thinking Symbolic AI Operator UX

Roadmap

Aggressive, testable, sequential.

Q3 ’25

Now

Public dashboards, evaluation wall, and first external proofs with full traces.

  • Operator cockpit v1
  • Replay seeds & artifact registry
  • External proof showcase

Q4 ’25

Next

Programmable orchestration modes; partner pilots in formal verification.

  • Curriculum schedulers as modes
  • Portfolio routing policies
  • Pilot integrations

Q1 ’26

Scale

Private beta: research copilot for conjectures, lemmas, and dataset creation.

  • Copilot loops (conjecture→lemma→dataset)
  • SDK for lab extensions
  • Usage-linked tiers

FAQ

Investor & admissions quick-read.

Why now?

Timing

Symbolic methods are compounding with modern infrastructure and data telemetry — enabling proof-at-scale and verifiable reasoning.

What’s the wedge?

Entry

Deterministic solvers + entropy-aware scheduling + live dashboards — a tighter loop than generic LLM stacks for verification and research.

How do you win?

Moat

Evaluation walls, structured traces, and operator-grade UX — turning every run into reusable, compounding intelligence.

Can you run air-gapped?

Yes. Private-cloud & on-prem via Docker. Deterministic seeds ensure reproducibility under restricted compute.

Is there a free tier?

For academics and open dashboards, yes. Enterprise pilots are paid; private betas are case-by-case.

How do I join the beta?

Send context (team, domain, timeline) to alkindi.proofx@gmail.com. We prioritize urgency + fit.

Updates

News and technical notes. RSS soon.

ProofX landing v1 live

Public launch on Vercel with domain + SSL. Subdomains for docs/dashboards next.

Partner, invest, or collaborate

We’re shipping quickly and selectively expanding pilot access.