For AI Safety Researchers
25 mathematical disciplines. 87 scoring modules. 614 adversarial test cases. Automated policy-consistency checks. Apache 2.0 SDK and open R1–R3 corpus. Sgraal is free for academic research.
We publish what we don't catch. The R12 PARKED 8-case disclosure lives at /failures.
Whitepaper · arXiv submission target Q3 2026
We present Sgraal, a memory governance protocol for autonomous AI agents that integrates 25 mathematical disciplines (control theory, topological data analysis, formal methods, causal inference, optimal transport, Bayesian methods, stochastic processes, opinion algebra) into a 87-module scoring pipeline. The system returns a four-band decision (USE_MEMORY / WARN / ASK_USER / BLOCK) per memory state with full explainability. Decisions are formally verified via Z3 SMT for three healing policy properties (monotonicity, idempotency, bounded drift). We evaluate against an adversarial corpus of 614 cases across 11 attack rounds; the 60-case held-out R12 corpus serves as the public integrity benchmark (current 52/60 with 8 documented PARKED failures).
BibTeX (provisional)
@article{sgraal2026,
title = {Sgraal: A Multi-Disciplinary Mathematical Framework
for AI Memory Governance with Formal Verification},
author = {Zsobrak, Peter and contributors},
year = {2026},
archivePrefix = {arXiv},
primaryClass = {cs.AI},
url = {https://sgraal.com/whitepaper}
}
Each discipline contributes a module to the 87-module pipeline. Every value is real implementation, not stub or mock.
Lyapunov stability
control theory
Policy checks
logical consistency
Persistent homology
topological data analysis
Sinkhorn OT
optimal transport
Lévy α-stable
heavy-tail probability
DirectLiNGAM
causal discovery
HMM Baum-Welch
hidden Markov models
Cox proportional hazards
survival analysis
PCTL
probabilistic CTL
Subjective Logic
opinion algebra
Ollivier-Ricci curvature
discrete geometry
Mahalanobis distance
multivariate stats
Fréchet distance
trajectory comparison
BOCPD
Bayesian change-point
Sheaf cohomology
algebraic topology
Rate-distortion
information theory
Hopfield network
associative memory
Wilson-Hilferty χ²
outlier detection
Ornstein-Uhlenbeck
mean-reversion process
κMEM percolation
phase-transition threshold
Vietoris-Rips complex
simplicial homology
Drezner-Wesolowsky
bivariate CDF
Acklam quantile
normal quantile approx
Denman-Beavers
matrix square root
Sgraal Ω-norm
truncated quasi-norm
Full module listing at github.com/sgraal-ai/sdks · 87 modules · 11,000+ LOC of pure mathematics
Run the benchmark against Sgraal, your own model, or a competitor. The R1–R3 corpus is Apache 2.0 on GitHub. Each case includes ground-truth label, attack vector taxonomy, and a reference solution path.
Quick start
git clone https://github.com/sgraal-ai/sdks cd core/tests/corpus # Run R1 against your own model python3 run_round1.py --model your_model.py # Compare against Sgraal baseline python3 compare.py --baseline sgraal \ --candidate your_model # Outputs F1, precision, recall per class
We hold the R6–R12 corpus (375 additional adversarial cases) privately to keep the benchmark honest. If the corpus were public, vendors could memorize attack signatures rather than learn the underlying detection problem. We publish what we don't catch instead: R12 currently passes 52 / 60 cases; the 8 PARKED failures are documented case-by-case at /failures.
Academic collaborators can request blind evaluation access via hello@sgraal.com. We send the test inputs without ground-truth labels; you return predictions; we score and publish.
1. Five-AI adversarial consensus. Every non-trivial scoring patch is reviewed by five independent LLMs (Gemini, DeepSeek, Qwen, Grok, ChatGPT) as adversarial reviewers. We adopt patches only when at least three of five identify the same failure mode and agree on the fix shape. The #739c BWDT (Belief-Weighted Drift Tolerance) patch is the canonical example.
2. Policy-rule consistency checks. Our healing-policy rules are checked for logical consistency (e.g. no rule both allows and blocks the same case; the healing counter is monotonic) — encoded as SMT-style constraints. These verify the policy invariants, not each live decision; in production they run as logical checks (the SMT solver is optional).
3. Transparency over claim. Scoring engine configuration is available to licensed customers via /v1/research/constants with a config checksum (SHA-256 of all calibration values) — your auditor can verify the model that ruled on your compliance was itself unchanged.
4. Published failures. We document the 8 R12 PARKED cases (CC-004/007/008/009/010/011, PA-002/009) with full case description and our reasoning for not chasing 60/60 at all costs. Published failures keep the benchmark honest — and the philosophy of "safety-bias narrative is the right framing" is itself an artifact of multi-AI consensus from 2026-04-20.
5. Apache 2.0 everything we can. SDK, Proxy, Edge mode, OpenAPI spec, R1–R3 corpus — all open. The hosted scoring engine and R6–R12 corpus stay commercial to fund the research. See /open-source for the full cut-line.
If you are at an academic institution (.edu, university lab, research institute, or a recognized non-profit AI safety org), you can use Sgraal hosted free of charge. Higher rate limits than the demo tier; same engine.
Request academic access →For now, cite the website + repo. Once the whitepaper lands on arXiv, the BibTeX above will become the canonical citation. Reach out if you want pre-print access.
Working paper · arXiv:cs.AI · pending submission
Free for academic research. Cite us. Run the corpus. Tell us what we got wrong.