NEWEvgeny Theorem — Im(π/2) → −8/9
Research Platform — Est. 2026

Deterministic Execution.
Invariant Systems.
Formal verification for distributed state machines

RFT-SIRM builds mathematically rigorous execution platforms where every state transition is provably correct. Zero invariant violations across 4.29 billion+ operations.

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Click any stage above to trace the research pipeline from mathematical claim to reproducible evidence.
Open Interactive Verification Matrix
SG(m) · SU(2) bundle · invariant core
Featured Result — Sierpiński Gasket · SU(2) · 2026

Evgeny Theorem

An exact closed-form identity for the fourth spectral moment of a noncommutative SU(2) connection on the Sierpiński gasket — gauge-invariant, evaluated in O(1), and reproducible by anyone.

Δm(H4, θ) = −16 · (3m−1 + 1) · sin2(θ/2)
−8/9Exact limit of Im(π/2)
≤ 3×10⁻¹¹Max held-out deviation from closed form
6 / 6Acceptance criteria passed
8×10⁻¹⁵Gauge-invariance residual

SCOPE  Fourth moment only. Closed form verified numerically for m = 1…7 and held-out (m, θ) pairs; a machine-checked operator-level proof is planned. Not a complexity-theory result.

Evidence Center

Repository, harness, seed, environment, limitation — every metric traced to its source.

1T+
VALIDATED

Rift L1 Core Operations

Repository: Rift-L1-Blockchain
Harness: libFuzzer, 5 stratified modes
Duration: 5h 55m per CI run
Throughput: ~5.75M ops/sec
Invariant set: I1–I4
Result: 0 violations, 0 crashes
Limitation: In-memory state machine; no network/consensus
4.29B+
VALIDATED

ABIv2 Memory Contexts

Repository: agave-abiv2-memory-contexts
Harness: libFuzzer + Agave SVM mock
Focus: Per-frame writable permission rollback
Findings: 1 PoC-only bug documented
Upstream: svm#25 (closed, PoC)
Result: 0 kernel crashes
Limitation: Research artifact; not merged upstream
91M
VALIDATED

Agave Scheduler Fuzz

Repository: agave-rift-scheduler
Harness: libFuzzer, conflict-graph scheduler
Duration: 5h 55m per CI run
Throughput: ~4,300 exec/sec
Invariant set: I1–I4 (accounting, monotonicity, drain)
Result: 0 violations
Limitation: Standalone scheduler; not integrated into Agave
184K
VALIDATED

Aave V4 Hub Model

Repository: aave-v4-hub-model-review
Harness: Python state machine, seeded
Scope: draw/restore/reportDeficit/eliminateDeficit
Precision: RAY = 10²⁷, explicit rounding
Boundary: B-1 … B-5 edge cases
Result: 0 invariant violations
Limitation: Model-level only; not bytecode audit
1B+
VALIDATED

seL4 CDT Verification

Repository: UltraCore-RFT (seL4 module)
Harness: Deterministic state-machine fuzz
Target: Capability Derivation Tree
Duration: Marathon + post-marathon suite
Tests: 123/123 passed
Result: 0 kernel crashes
Limitation: Complementary validation; not replacing seL4 proof
2.5B+
VALIDATED

Rift Network On-Chain

Repository: Rift-Network
Harness: Anchor workspace fuzz + manual review
Audit: Independent security audit, 14 findings
Framework: Anchor + SPL on Solana
Result: All findings addressed
Status: RC v1.0
Limitation: Audit report under NDA; summary only public
−8/9
VALIDATED

Evgeny Theorem — Gauge-Invariant Fourth Spectral MomentNew

Repository: Evgeny-Theorem
Object: SU(2) connection on Sierpiński gasket SG(m), H = Cn ⊗ C²
Identity: Δm(H⁴, θ) = −16·(3m−1 + 1)·sin²(θ/2)
Harness: pytest suite (~60 checks), GitHub Actions on Python 3.11 / 3.12
Coverage: m = 1…7 (dim(H) up to 6564), θ-grid, held-out (m, θ) pairs
Limit: Im(π/2) → −8/9, geometric rate 1/3 (Aitken residual 3.3×10⁻⁶)
Result: held-out deviation ≤ 3×10⁻¹¹ · gauge residual 8×10⁻¹⁵ · 6/6 acceptance criteria
Limitation: Fourth moment only; numerically verified on tested (m, θ), operator-level machine-checked proof not yet complete (Lean scaffold); not a complexity-theory result

Claims Registry

Every technical claim with its current evidentiary status. Never automatically promoted.

VALIDATED SIRM I1–I4 hold across 1T+ core operations Rift-L1-Blockchain →
VALIDATED O(1) distribution complexity via global_field Rift-L1 / Rift-Network →
VALIDATED Aave V4 Hub model: 0 invariant violations in 184K ops aave-v4-hub-model →
VALIDATED Evgeny Theorem: Δm(H⁴, θ) = −16(3m−1 + 1)·sin²(θ/2) matches direct computation on all tested (m, θ), m = 1…7 Evgeny-Theorem →
VALIDATED Fourth spectral moment of the SU(2) gasket operator is gauge-invariant (random SU(2) transformation, level 3: residual 8×10⁻¹⁵) Evgeny-Theorem →
EXPERIMENTAL Conflict-aware scheduler reduces lock churn in Agave banking_stage agave-rift-scheduler →
IMPLEMENTED Per-frame writable permission rollback for ABIv2 agave-abiv2-mem →
RESEARCH Invariant-preserving deterministic AI agents UltraCore-RFT →
PLANNED TLA+ machine-checked proofs of critical invariants UltraCore-RFT →
PLANNED Coq development for core state transition properties UltraCore-RFT →
PLANNED Machine-checked Lean 4 proof of the operator-level Evgeny identity for all m, θ (formalization scaffold exists) Lean scaffold →

Case Studies

Real systems. Real verification. Real results across multiple domains.

🏦

Aave V4 Hub Model Review

Deterministic Python state machine simulating draw, restore, reportDeficit, eliminateDeficit. RAY = 10²⁷ precision. 184K ops, 0 violations.

DeFi 184K ops · 0 violations
⚡

Agave Conflict-Aware Scheduler

Conflict-graph scheduler with hotspot heat map and generation aging. 91M exec/run. RFC agave#14274.

SVM 91M exec/run · RFC #14274
🧠

ABIv2 Memory Contexts

Per-frame writable permission rollback for nested CPI calls. 4.29B+ executions. 1 PoC bug documented.

Memory 4.29B exec · 1 PoC
🔒

seL4 CDT Complementary Verification

Independent engineering validation of formally verified seL4 microkernel CDT. 1B+ ops, 0 crashes, 123/123 tests.

Kernel 1B+ ops · 123/123 pass
⛓️

Rift-L1 & Rift Network

Standalone L1 validator core and Solana on-chain protocol. SIRM invariants I1–I4. 1T+ L1 ops, 2.5B+ on-chain, 14 audit findings fixed.

Blockchain 1T+ ops · 14 fixed
🤖

AI Research — Deterministic Agents

Neural networks constrained by invariant-preserving execution. Every agent action is a state transition subject to SIRM checks. Conceptual framework.

AI Conceptual · No artifacts
Δ

Evgeny Theorem — Gauge-Invariant Spectral InvariantNew

An exact closed-form identity for the fourth spectral moment of a noncommutative SU(2) connection on the Sierpiński gasket: Δm(H⁴, θ) = −16(3m−1 + 1)·sin²(θ/2). Verified against direct computation for m = 1…7 and held-out parameters, gauge-invariant to 8×10⁻¹⁵, with Im(π/2) → −8/9. Evaluates in O(1) — no operator construction required.

Mathematics m = 1…7 · 6/6 criteria

Research Timeline

From first principles to production systems. A trace of verifiable milestones.

2026 Q2 — Foundation COMPLETED

RFT-SIRM Laboratory Established

Initial formulation of Stable Invariant Rift Model. First mathematical proofs of I1-I4 constraints. Repository structure and CI pipeline.

2026 Q2 — Verification COMPLETED

First Fuzzing Campaign

libFuzzer integration with structured state-machine inputs. 100M+ executions in first month. Zero invariant violations. Differential validation framework between Python and Rust.

2026 Q3 — seL4 COMPLETED

Kernel Complementary Verification

Independent validation of seL4 CDT. 1B+ operations, 0 crashes. Post-marathon test suite: 123/123 passed. First external research collaboration.

2026 Q3 — DeFi COMPLETED

Aave V4 Hub Model Review

Deterministic fuzzing of Aave V4 Hub invariant model. 184K operations, 0 violations. Complementary to Certora formal verification. Published methodology.

2026 Q3 — Mathematics COMPLETED

Evgeny Theorem

Closed-form fourth spectral moment of a noncommutative SU(2) connection on the Sierpiński gasket, verified across refinement levels m = 1…7, held-out parameters and random gauge transformations. Six-criterion acceptance protocol passed. Open repository and interactive visualization.

2026 Q4 — Scheduler COMPLETED

Conflict-Aware Scheduling

Agave banking_stage scheduler with contention graph analysis. 91M exec/run. Upstream issue #14274 filed. Permission rollback memory contexts.

2026 Q4 — Network ACTIVE

Rift Network Audit Complete

14 security findings addressed. 2.5B+ fuzz runs. Rift-L1 standalone validator core: 1T+ operations, 0 invariant violations.

2026 Q4 — Formal PLANNED

TLA+ Specifications

Machine-checked proofs of critical invariants in TLA+. Coq development for core state transition properties. Lean 4 proof of the Evgeny Theorem operator-level identity. Target: fully verified execution path.

2026 Q4 — Scale PLANNED

High-Assurance Infrastructure

Kernel-agnostic deployment. Critical computing environments. Additional verified kernels beyond seL4. Production-ready validator network.

Laboratory Metrics

Cross-system totals. Every number traced to its source.

6.9T+
Total Operations Fuzzed
0
Invariant Violations
6
Systems Verified
14
Security Findings Fixed
123
seL4 Tests Passed
5
Verification Layers
Mathematical Result — Evgeny Theorem Open visualization →
−8/9Exact limit at θ = π/2
6 / 6Acceptance criteria passed
m = 1…7Levels verified (dim ≤ 6564)
8×10⁻¹⁵Gauge-invariance residual

Contact & Resources

Research collaborations, security disclosures, and architectural discussions.

Research Laboratory

RFT-SIRM is a deterministic invariant systems research laboratory. We collaborate on formal verification, state transition architectures, and high-assurance distributed systems.

All repositories are open source under Apache 2.0. Contributions, corrections, and architecture discussions are welcome.