Fourth-moment theorem
Lean 4A formalized proposition for the specific operator construction and fourth moment. Proof checking does not replace independent review of how the formal definitions correspond to the intended mathematical object.
Research portal · source-linked claims
Mathematical structure.
Verifiable evidence.
Explore the theorem at the centre of the research programme, the higher-moment questions that remain open, the independent Phi-Genesis spectral audit, and the engineering systems built around invariant-first design.
FORMAL THEOREM ≠ FINITE CERTIFICATE ≠ NUMERICAL TEST ≠ ENGINEERING CLAIM
Each link opens its own repository or workflow. Status badges report only the named workflow, not the whole research programme. Rift-L1 and Rift Network have separate source-available licensing notices.
Featured research · dissertation
Recursive Graph Operators, Spectral Trace Defects, and Higher-Moment Recurrence
The dissertation is the synthesis document for the research programme: the formally stated fourth-moment result, selected finite-level certificates for higher moments, numerical cross-checks, and the unresolved all-level recurrence.
The document is a research dissertation/monograph, not a claim of an awarded academic degree or a completed physical Theory of Everything. Mathematical evidence and downstream engineering claims remain separate.
01 / Mathematical anchor
One exact result. Clearly defined scope.
The source theorem concerns a specific SU(2)-connected operator on Sierpiński-gasket graphs and its commuting control.
Fourth-moment trace defect · source-stated identity
\[
\begin{aligned}
\Delta_m(H^4,\theta)
&= \operatorname{Tr}(H_C^4)-\operatorname{Tr}(H_{C'}^4)\\
&= -16\left(3^{m-1}+1\right)\sin^2\left(\frac{\theta}{2}\right),
\qquad m\geq 1.
\end{aligned}
\]
The normalized quantity is
\[
I_m(\theta)=\frac{\Delta_m(H^4,\theta)}{3^{m+1}+3}.
\]
Its limit is
\[
\lim_{m\to\infty} I_m(\theta)
=-\frac{16}{9}\sin^2\left(\frac{\theta}{2}\right).
\]
At \(\theta=\frac{\pi}{2}\), the limiting value is exactly \(-\frac{8}{9}\).
Scope boundary: the source reports a Lean 4 proof for its concrete formalized operators and stated quantifiers. It does not prove higher moments, a physical law, a quantum speed-up, SIRM runtime invariants, or a complete physical Theory of Everything. Independent review of the formal definitions remains a separate question.
02 / Evidence status
Read the label before the headline
Each category answers a different question. This page does not invent live counters; the source links lead to reports and workflows.
Higher moments p = 6, 8, 10
Open extensionSelected finite-level Fourier coefficients have modular/CRT certificates, with numerical holdouts. The all-level recurrence and derivation of the exceptional first transition remain open.
Phi-Genesis / Gate A
Open auditSigned-flux spectral decimation and mass-index claims are audited separately. The full exceptional set and residual mismatches are not closed; selected patterns are not established physical laws.
SIRM engineering
Implementation-scopedRuntime invariants, fuzzing, audit findings, and deployment records support specific code paths and configurations. They are not a formal proof of every possible execution.
03 / Interactive pathway
From a mathematical claim to a responsible conclusion
Select a stage to inspect its evidence obligation.
Define → Name the operator, state space, index range, angle domain, boundary conditions, and commuting control. The formula is only meaningful relative to these definitions.
LAYER A / THEOREM
Exact mathematics
Start from the source statement and formalization. Keep the fourth-moment theorem separate from every conjectural extension.
LAYER B / RESEARCH
Open questions retained
Higher moments and signed-flux decimation have distinct proof obligations. Finite certificates and numerical patterns do not close all-level claims.
LAYER C / SYSTEMS
Applications downstream
Runtimes, blockchain protocols, kernel stress tests, quantum architectures, and energy models each require their own validation.
04 / Research map
One ecosystem. Distinct proof obligations.
Links show the relationship between programmes; they do not imply that a result in one repository proves claims in another.
Evgeny's Theorem
Specified SU(2)/Sierpiński-gasket fourth-moment identity; Lean 4 formalization reported for stated scope.
Theory of Everything
Higher-moment recurrence and recursive-operator research; selected finite-level certificates; all-level recurrence open.
Phi-Genesis
Signed-flux spectral decimation, boundary/corner corrections, inertia calculations, and mass-formula audit.
SIRM / UltraCore
Invariant-first execution model, architecture coordination, and implementation-specific verification.
RFT-QPU-Sierpinski
Pre-experimental gauge-covariant fractal quantum-processing architecture; no speed-up claim implied.
RFT-Invariant-Battery
Exploratory invariant-driven energy-system scenarios with explicit modelling assumptions.
06 / Research and engineering record
One research programme. Distinct evidence trails.
A curated map of public workstreams, with the original repository as the source of truth for each claim.
MATHEMATICS / DISSERTATION
Recursive graph operators and higher moments
The dissertation brings together the fourth-moment identity, Lean formalization references, finite higher-moment certificates, numerical holdouts, and unresolved recurrence questions.
SOLANA / AGAVE
Protocol, scheduler and memory-context research
Separate implementation tracks cover the Rift Network protocol, Agave scheduler research, and ABIv2 memory contexts. Their results must be read against each project's own code, tests and deployment scope.
KERNEL / seL4
Capability Derivation Tree stress verification
The report records a deterministic empirical stress experiment under the documented test environment. It is not a replacement for seL4's formal verification and does not prove all possible executions.
DEFI / MODEL REVIEW
Aave V4 Hub invariant analysis
A distinct model-review repository examines invariant-oriented DeFi behavior. The presence of this research is not an endorsement or affiliation with Aave.
SPECTRAL COMPUTATION
Phi-Genesis audit trail
Signed-flux decimation, boundary and corner corrections, numerical inertia, and residual mismatches are tracked separately. Open exceptions remain part of the record.
L1 / EXPLORATORY SYSTEMS
Standalone and exploratory applications
Rift-L1, the Sierpiński QPU concept, and invariant-driven battery scenarios are separate implementation or exploratory tracks, each requiring its own validation.
Attribution and historical accuracy: repository work or participation in an open-source ecosystem does not by itself establish employment, a contract, partnership, sponsorship, approval, or endorsement by NASA, Solana/Anza, MATLAB, the seL4 project, Aave, or another institution. NASA- or MATLAB-specific work should be added here only with a direct public repository, commit, paper, or other verifiable record. The chronology links documented artifacts rather than inferring affiliations from profile activity.
07 / Formal correspondence
Research proposals deserve a traceable channel.
Technical discussion, institutional proposals, licensing enquiries and contractual matters should be handled through the appropriate channel.
Formal research contact
Use the designated maintainer contact
For a serious proposal, include your name, organization and role where relevant, the exact project or commit, the requested action, and any proposed scope or timeline. Institutional-domain email is preferred for messages claiming institutional authority, but an email domain alone does not prove identity or authorization.
No email address is invented or exposed here. Publish a dedicated monitored mailbox only after confirming it is the intended public contact. Confidential, legal or contractual material should not be posted in public issues.
05 / Historical development
A research history, not a victory montage
This is a conceptual map of the programme. Use commit history for exact chronology and source-specific status at a given date.
PHASE 01
Invariant-first model
Specify state constraints and require transitions to preserve them.
PHASE 02
Exact spectral result
State the fourth-moment identity and formalization scope.
PHASE 03
Higher moments
Build finite certificates and holdouts; retain the all-level open problem.
PHASE 04
Separate decimation audit
Test signed-flux claims; preserve failures and open residuals.
PHASE 05
Applications
Explore systems and devices with separate engineering evidence.