Ollivier-Ricci Curvature for Complex Networks
Published — 3 papers on ORC theory, semantic networks, and biomedical applications
FOR RESEARCHERS · PHARMACOLOGY · NEUROSCIENCE · CLIMATE · QUANTUM
YourCalculationsHideUncertainty
When you compute a drug dose, an fMRI threshold, or a climate projection, the answer is a number. But how confident is that number? Where did the input data come from? What happens when the measurement error matters? Sounio is a programming language that tracks all of this automatically.
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Try It: Live Uncertainty Propagation
Change the measurements below and watch how uncertainty flows through the calculation. This is what Sounio does automatically with every computation.
Measurements
\u00B1
\u00B1
Lenient (0.50)Strict (0.99)
What Sounio Computes
BMI = 22.73 \u00B1 0.53
\u03B5 = 0.9767
prov: clinical_scale_001 \u00D7 stadiometer_001
GATE PASSED: \u03B5 ≥ 0.95
Confidence is high enough to proceed with this result.
Try increasing the uncertainty on either measurement and watch the confidence (\u03B5) drop. When it falls below your threshold, the system refuses to approve the result. This is GUM-compliant uncertainty propagation, enforced automatically.
Numbers Without Context Are
Dangerous.
Your Python script says the dose is 500 mg. But was the patient’s kidney function measured today or last week? How much did the scale drift? These questions have answers — your current tools just don’t track them.
What If the Computer Tracked It For You?
Imagine every measurement carrying its confidence level, its source instrument, and its date. When you multiply two uncertain values, the uncertainty propagates automatically. No manual error bars. No spreadsheet formulas.
Decisions You Can Defend.
When confidence is high enough, approve the dose. When it’s not, the system itself requests remeasurement. Every decision traces back to the evidence that supports it.
// Confidence-gated vancomycin dosing
let dose: Knowledge<f64> = Knowledge(
500.0,
ε=0.92,
prov="ASHP_2020_RCT"
)
if dose.ε >= 0.82 {
approve_dose(dose)
} else {
request_remeasurement(dose)
}See the System Protect Itself
Watch what happens in a real drug dosing scenario when uncertainty crosses safe thresholds.
Pharmacometrics: PK/PD Confidence Bounds
Adjust the patient data noise to see how Sounio evaluates the expanding uncertainty envelope against the rigid toxicity threshold in real-time.
Simulate higher uncertainty in patient sensor data or population variability.
Toxicity Threshold (60 mg/L)
95% Confidence Envelope
Predicted Concentration
Sounio WASM Runtime
From Chaos to
Rigorous Bounds.
Scroll to observe the epistemic state transition. Entropy collapses as formal proofs establish absolute mathematical certainty.
Peer-Reviewed Research
Trusted by standards and science. GUM-compliant. Peer-reviewed. ISO-aligned.
Published Papers
The 168 Theorem: Nonzero Octonion Basis Associators
Advances in Applied Clifford Algebras — 2026
168 = |PSL(2,7)| nonzero basis associators. Binary 2 norm property. Fano plane classification.
Epistemic PBPK: GUM-Through-ODE for Drug Dosing
Master’s Dissertation — Biomaterials & Regenerative Medicine
GUM vs Monte Carlo validated: σ ratio 0.97, 94% coverage on rapamycin 3-compartment PBPK.
Verified Artifacts
2,300+
Commits
gen2=gen3
Self-hosting fixed point
736
Stdlib modules
1,003+
E-graph rewrite rules
Epistemic ML
Transformer MHA + FFN + LayerNorm + GUM — 2,096 params
O-SSM Octonion State Space Model — 86K-param LM, backprop
E-KAN Epistemic Kolmogorov-Arnold Network — per-edge GUM
Classifier MLP 4→16→8→1 — file I/O, 100% accuracy
All native x86-64 ELF. No Python. No PyTorch. Full backpropagation with GUM uncertainty.
Standards
GUM (JCGM 100:2008)
ISO 17025
CONSORT
OWL 2
GUM Validated
PBPK ODE σ ratio 0.97
PBPK coverage 94%
E-KAN NN 1.5x conservative
E-KAN coverage 99.8%
GUM vs Monte Carlo (N=200–500). Finite-difference Jacobian through RK4 and neural network.
Author
Why Sounio
The value proposition is still the same, but the current public contract is narrower than the older marketing copy.
Epistemic Core
Confidence-aware types such as Knowledge<T> are exercised through canonical check fixtures, including compile-time refusal cases.
Check-First Workflow
The most trustworthy repo path today is souc check over canonical fixtures and gate-backed stdlib lanes, with runtime claims scoped by artifact evidence.
Self-Hosted Stack
The repository includes a self-hosted compiler tree, SOIR serialization, and the Poseidon bootstrap VM used to track the rustless cutover.
Gate-Tracked Stdlib
Repo artifacts track which stdlib lanes are callable today, which remain stub surfaces, and which are still disabled.
How Sounio Protects Your Conclusions
Three capabilities that change how you work with scientific data.
Numbers Without Context Are Dangerous
Traditional tools lose where your data came from and how reliable it really is.
Sounio automatically tracks provenance and uncertainty for every measurement. When confidence drops too low, it warns you — before you draw the wrong conclusion.
What this means for your research
- \u2192 Automatic GUM-compliant error propagation
- \u2192 Full audit trail of every data source
- \u2192 Safety gates that prevent overconfident results
- \u2192 Reproducible and defensible findings
Fully implemented
Correlation Is Not Causation
Most code cannot tell the difference between association and real cause.
Sounio lets you build causal models and apply interventions that remove confounding. You get the true effect size — not just statistical correlation.
What this means for your research
- \u2192 True treatment effect quantification
- \u2192 Automatic confounder removal
- \u2192 Stronger causal claims in papers
- \u2192 Better clinical and policy decisions
Stdlib — actively maturing
Knowledge With Guardrails
Scientific data always carries uncertainty that normal code silently ignores.
Sounio wraps your data in Knowledge<T> and enforces confidence thresholds. It refuses to let unsafe or unreliable results proceed.
What this means for your research
- \u2192 Prevents dangerous overconfidence
- \u2192 Enforces your lab’s risk standards
- \u2192 Clear compliance and audit trail
- \u2192 Built-in protection for patients and conclusions
Fully implemented
See the Difference
Your current tools compute the number. Sounio computes what you can trust about that number.
example.py
# Python: bare floats, no uncertainty
mass = 75.3 # kg... probably?
height = 1.82 # meters... maybe?
bmi = mass / (height ** 2)
# bmi = 22.74
# No idea how confident we are
# No idea where the data came from
if bmi < 25:
print("Normal weight")
# What if the scale was off by 2kg?example.sio
// Sounio: epistemic computing
// ε is the confidence level (0.0 to 1.0)
let mass: Knowledge<f64> = Knowledge(
75.3,
ε=0.98,
prov="clinical_scale_001"
)
let height: Knowledge<f64> = Knowledge(
1.82,
ε=0.99,
prov="stadiometer_001"
)
// GUM Uncertainty propagates automatically:
// ε(a/b) = ε(a) × ε(b)
let bmi: Knowledge<f64> = mass / (height * height)
// bmi.value = 22.74, bmi.ε = 0.96
if bmi.ε >= 0.95 {
println("Confidence sufficient for diagnosis")
} else {
println("Request remeasurement")
}In plain language: What this means: Every measurement carries its confidence level (ε) and where it came from (prov). When you compute BMI from weight and height, the system automatically calculates how confident the result is. If confidence is high enough, you can proceed. If not, it tells you to remeasure.
The Sounio Difference
The current repository focus is explicit uncertainty, auditable semantics, and evidence that lives next to the code.
Numbers Without Context Are Dangerous
Traditional tools lose where your data came from and how reliable it really is.
Sounio automatically tracks provenance and uncertainty for every measurement. When confidence drops too low, it warns you — before you draw the wrong conclusion.
What this means for your research
- \u2192 Automatic GUM-compliant error propagation
- \u2192 Full audit trail of every data source
- \u2192 Safety gates that prevent overconfident results
- \u2192 Reproducible and defensible findings
Fully implemented
Correlation Is Not Causation
Most code cannot tell the difference between association and real cause.
Sounio lets you build causal models and apply interventions that remove confounding. You get the true effect size — not just statistical correlation.
What this means for your research
- \u2192 True treatment effect quantification
- \u2192 Automatic confounder removal
- \u2192 Stronger causal claims in papers
- \u2192 Better clinical and policy decisions
Stdlib — actively maturing
Knowledge With Guardrails
Scientific data always carries uncertainty that normal code silently ignores.
Sounio wraps your data in Knowledge<T> and enforces confidence thresholds. It refuses to let unsafe or unreliable results proceed.
What this means for your research
- \u2192 Prevents dangerous overconfidence
- \u2192 Enforces your lab’s risk standards
- \u2192 Clear compliance and audit trail
- \u2192 Built-in protection for patients and conclusions
Fully implemented
Scientific Domains
These are the domains with real code and artifacts in-tree, though not every lane is equally mature.
Pharmacometrics
PK/PD pipelines with confidence-aware dosing decisions.
Explore domainNeuroimaging
fMRI and signal pipelines with provenance-aware thresholds.
Explore domainQuantum
VQE and uncertainty propagation from noisy measurement loops.
Explore domainClimate Science
Ensemble projections with explicit confidence gates.
Explore domainPeer-Reviewed Research
Trusted by standards and science. GUM-compliant. Peer-reviewed. ISO-aligned.
Published Papers
Ollivier-Ricci Curvature for Complex Networks
Published — 3 papers on ORC theory, semantic networks, and biomedical applications
The 168 Theorem: Nonzero Octonion Basis Associators
Advances in Applied Clifford Algebras — 2026
168 = |PSL(2,7)| nonzero basis associators. Binary 2 norm property. Fano plane classification.
Epistemic PBPK: GUM-Through-ODE for Drug Dosing
Master’s Dissertation — Biomaterials & Regenerative Medicine
GUM vs Monte Carlo validated: σ ratio 0.97, 94% coverage on rapamycin 3-compartment PBPK.
Verified Artifacts
2,300+
Commits
gen2=gen3
Self-hosting fixed point
736
Stdlib modules
1,003+
E-graph rewrite rules
Epistemic ML
Transformer MHA + FFN + LayerNorm + GUM — 2,096 params
O-SSM Octonion State Space Model — 86K-param LM, backprop
E-KAN Epistemic Kolmogorov-Arnold Network — per-edge GUM
Classifier MLP 4→16→8→1 — file I/O, 100% accuracy
All native x86-64 ELF. No Python. No PyTorch. Full backpropagation with GUM uncertainty.
Standards
GUM (JCGM 100:2008)
ISO 17025
CONSORT
OWL 2
GUM Validated
PBPK ODE σ ratio 0.97
PBPK coverage 94%
E-KAN NN 1.5x conservative
E-KAN coverage 99.8%
GUM vs Monte Carlo (N=200–500). Finite-difference Jacobian through RK4 and neural network.
Author
Verification Layer
Official identity assets anchor the trust model across docs, platform surfaces, and release channels, so users can verify they are reading canonical Sounio materials.
Current Verified Snapshot
- 81 / 82Stdlib reliability fixtures passing
- 92Active stdlib module entrypoints
- 2Real science lanes passing today
- 7Required hyper lanes passing
Built For High-Consequence Scientific Systems
Sounio is strongest where teams need to prove what a program checked, what was only sketched, and which outputs are backed by reproducible gate artifacts.
Ready to stop guessing?
Start with the vancomycin dosing case study — a real example of how Sounio tracks confidence from raw measurement to clinical decision.
Ship scientific software that explains itself.
Start with the parts of Sounio that are already verified, then expand into the self-hosted and domain-specific lanes with the gate artifacts in hand.
export SOUC_BIN=artifacts/omega/souc-bin/souc-linux-x86_64-jit
export SOUNIO_STDLIB_PATH=$(pwd)/stdlib
$SOUC_BIN check examples/hello.sio