UltraCore-RFT — Mathematical Foundations, Evidence, and Systems

The RFT-SIRM research and engineering hub: exact mathematical results first, related research programmes second, applications and implementations third. RFT means Resonant Field Theory (резонансная теория поля); SIRM means Synthetic Intelligence Reasoning Model (Синтетическая интеллектуальная модель рассуждений).

Featured dissertation — Recursive Graph Operators, Spectral Trace Defects, and Higher-Moment Recurrence

Start with the research synthesis: the fourth-moment theorem, finite-level higher-moment certificates, numerical cross-checks, and explicitly stated open problems. This is a research monograph—not a claim that a complete physical Theory of Everything has been established.

Research and evidence

These links describe the scientific work and its current evidence status. Badge colours have a consistent meaning: purple = research programme, teal = formalized result, amber = open or evidence-limited work, and blue = navigation or portal.

Related application programmes

These are separate exploratory or application tracks—not additional proofs of the mathematical claims above. They use one badge size and a restrained colour system so they read as one group.

Verification and repository status

These badges report the status of specific workflows only. They do not certify the entire research programme or transfer proof status between repositories.

Core engineering and formal-verification strands

These are separate repositories and separate evidence scopes. Rift-L1 and Rift Network publish source-available code under their own restrictive terms; the Apache-2.0 badge above applies only to original material in this UltraCore-RFT repository. Scheduler CI/fuzz and Lean 4 test badges link to their source workflows; a badge reflects that workflow, not a universal proof of the wider programme.

Historical origin sequence

The project family's historical order is distinct from the evidence-first reading order used to assess claims. The maintainer-reported sequence is Rift Network → Rift-L1 Blockchain → UltraCore-RFT and supporting systems (scheduler, memory, and related engineering) → Phi-Genesis → Evgeny-Theorem → Evgeny's Theory of Everything. See the origin chronology for scope, source links, and the distinction between reported order and commit-verified dates.

This order records development history; it does not claim that every later project depends technically on every earlier one.

Start with the research, not the applications: Evgeny's Theory of Everything · Lean-formalized fourth-moment theorem · Phi-Genesis spectral audit · Research map · AI reading guide

UltraCore-RFT is the documentation and coordination hub for the RFT-SIRM ecosystem. Its scientific story begins with mathematical definitions, theorem statements, and their evidence boundaries. Runtime systems, blockchain protocols, and other applications are downstream research programmes—not the foundation used to certify the mathematics.

Important scope statement. The phrase Evgeny's Theory of Everything names a broad, ongoing research programme. It does not mean that a complete physical theory of the Universe has been established. The source repository reports a Lean 4 proof of a specific fourth-moment identity for defined SU(2) operators on Sierpiński-gasket graphs. Higher-moment all-level recurrence and the Phi-Genesis Gate A mechanism remain open. Those boundaries are part of the result, not footnotes to hide.

Historical record: research and engineering strands

This programme has developed across separate repositories. The following are documented workstreams, not claims of institutional endorsement or that every project has the same verification status.

Workstream	Public record	Scope and evidence boundary
Mathematical research and dissertation	Theory of Everything dissertation · fourth-moment formalization	A specific fourth-moment identity is reported formalized in Lean 4; higher-moment all-level recurrence remains open.
Spectral computation and audit	Phi-Genesis	Numerical inertia, spectral-decimation and boundary/corner-correction research; unresolved residuals remain visible.
Solana / Agave engineering	Rift-Network · Agave Rift Scheduler · ABIv2 memory contexts	On-chain protocol, scheduler and memory-context research; claims are scoped to their code, tests and documented environments.
seL4 kernel stress research	seL4 CDT report · field-trial report	Reproducible empirical stress-testing report. It does not replace or extend the seL4 project's formal verification claims.
DeFi model review	Aave V4 Hub model review	Separate model-based review and invariant-analysis work; not an Aave endorsement.
Standalone L1 and exploratory applications	Rift-L1 · QPU/Sierpiński · Invariant Battery	Distinct implementation or exploratory tracks; no implied production, quantum speed-up or physical-device result beyond the linked evidence.
Research chronology	Commit-backed history · Research map	Selected milestones with direct links; use each repository's commit log for the complete record.

External organizations and attribution

Repository activity, public issues, or work in an open-source ecosystem must not be presented as employment, a contract, a partnership, sponsorship, approval, or endorsement by NASA, Anza, Solana, the seL4 project, Aave, or any other institution unless a specific public source establishes that relationship. The current curated project history links to verifiable repository artifacts. A standalone NASA- or MATLAB-specific project is not listed here as verified because the available repository and commit evidence reviewed for this update did not identify a matching artifact. If such work exists in a separate public repository or contribution, its exact URL should be added to the chronology rather than inferred from a profile screenshot.

Formal contact and research submissions

For collaboration proposals, research correspondence, licensing questions, or requests for formal review, use the designated contact route and include a clear subject, the relevant repository/commit, the requested action, and the sender's institutional or organizational affiliation where applicable. A GitHub issue or pull request is appropriate for public, technical, reproducible discussion; confidential, contractual, licensing, or personal information should not be posted publicly.

See CONTACT.md for the submission and attribution policy. Public contact details should be a dedicated, controlled mailbox that the maintainer intends to monitor; do not assume that a commit-author email is automatically the official legal or business contact.

---

1. The mathematical anchor

Evgeny's Theorem: a closed fourth-moment identity

The primary theorem repository studies a specified SU(2)-valued connection on a Sierpiński-gasket graph and compares a noncommuting configuration $C$ with a commuting control $C'$. For the definitions and assumptions in the source project, the fourth-moment trace defect is stated as

$$ \Delta_m(H^4,\theta) =\mathrm{Tr}(H_C^4)-\mathrm{Tr}(H_{C'}^4) =-16\left(3^{m-1}+1\right)\sin^2\left(\frac{\theta}{2}\right), \qquad m=1,2,3,\ldots. $$

The normalized quantity is

$$ I_m(\theta)=\frac{\Delta_m(H^4,\theta)}{3^{m+1}+3}, \qquad \lim_{m\to\infty} I_m(\theta) =-\frac{16}{9}\sin^2\left(\frac{\theta}{2}\right). $$

At the special angle $\theta=\frac{\pi}{2}$, the limit simplifies to:

$$-\frac{8}{9}$$

What is machine-checked: the source project reports a Lean 4 formalization for every integer level $m=1,2,3,\ldots$ and every angle covered by its statement, for the concrete operators defined there. The formal proof establishes the formal proposition; readers should still distinguish proof checking from independent review that the formal definitions fully capture the intended mathematical construction.

What the theorem does not establish: it does not prove the full spectrum, all higher moments, a physical law, a quantum speed-up, a solution to a Millennium Prize Problem, or the entire broader Theory-of-Everything programme.

Primary sources: theorem statement · Lean formalization · verification record · test workflows · project site.

Numerical cross-checks are a different evidence layer

The source repository reports direct numerical comparisons for levels $m=1,\ldots,7$, held-out angle checks, and gauge-transformation checks. These support the implementation and provide reproducibility evidence; the all-level statement rests on the Lean theorem, not on extrapolating a finite table.

Level $m$	$\dim(H)=3^{m+1}+3$	$\Delta_m(H^4,\pi/2)$	$I_m(\pi/2)$
1	12	−16	−1.333333
2	30	−32	−1.066667
3	84	−80	−0.952381
4	246	−224	−0.910569
5	732	−656	−0.896175
6	2,190	−1,952	−0.891324
7	6,564	−5,840	−0.889701
Limit	—	—	$-8/9$

The raw formula, normalized denominator, and displayed table use the same convention. For example, at $m=1$ and $\theta=\pi/2$, the raw defect is $-16(1+1)/2=-16$; dividing by $12$ gives $-4/3$. As $m$ grows, the ratio tends to $-16/9\sin^2(\theta/2)$.

---

2. The broader research programme

The research programme extends beyond the one formal theorem. Its components must remain connected but not conflated.

Strand A — Evgeny's Theory of Everything: higher moments and recursive operators

Primary repository: RFT-SIRM/Evgeny-s-Theory-of-Everything · dissertation.

The synthesis programme studies higher-moment trace defects, Fourier coefficients, finite-level recurrence residuals, and the possibility of an all-level law for recursive graph/operator families.

• Certified finite-level work: the repository documents modular/CRT certificates for specified Fourier coefficients at selected transitions for moments $p\in{6,8,10}$, subject to the stated graph, operator, denominator, norm, and coefficient-bound assumptions.
• Numerical evidence: held-out angle grids, sparse-matrix-power calculations, and cross-checks are reported in versioned workflows and data artifacts.
• Open theorem: the all-level recurrence $R_m^{(p)}(\theta)=R_4^{(p)}(\theta)$ for every $m\geq3$ and all stated admissible angles has not been proved. A finite-level certificate is not an infinite-level proof.
• Research obligation: derive the exceptional first-transition correction from the recursive construction, prove the recurrence or find a counterexample, and formalize any complete derivation against explicit definitions.

The dissertation itself explicitly distinguishes the fourth-moment theorem from the higher-moment programme. Read the dissertation, recurrence note, and modular certificate.

Strand B — Phi-Genesis: signed-flux spectral decimation and mass-formula audit

Primary repository: RFT-SIRM/Phi-Genesis · live research site.

Phi-Genesis studies signed $Z_2$-flux graph Laplacians, spectral decimation with boundary/corner corrections, inertia calculations, and exploratory spectral or mass-index patterns. It is a separate operator family from the SU(2)-connected construction in Evgeny's Theorem.

• Some proposed claims have been rejected or narrowed by the documented audits.
• Numerical results and tests support specific computational statements only within their stated parameters and code paths.
• Gate A remains open: the full exceptional set and the residual mismatches in decimation matching are not yet completely explained.
• A fitted or selected mass-index pattern is not an established predictive physical law without a prospective selection mechanism, predeclared predictions, held-out validation, and an independent derivation.
• No equivalence between the SU(2) operators and signed-flux Laplacians is assumed. Any bridge requires an explicit map, boundary conditions, preserved quantities, exceptional cases, and proof or a clearly labelled conjecture.

Start with the repository status and methods, then inspect its versioned test workflows and reports. The fact that tests pass does not close Gate A unless the tests actually establish its closure criteria.

Strand C — SIRM and deterministic execution

SIRM (Synthetic Intelligence Reasoning Model) is the systems-engineering strand: define state invariants and require every state transition to preserve them or fail atomically.

The four stated runtime constraints are shown below using compact mathematical symbols. The mapping table identifies the implementation variables.

$$ \begin{aligned} I_1:\quad & S = B + Gp,\ I_2:\quad & S = M - D,\ I_3:\quad & d < p \quad (p>0),\ I_4:\quad & E_i \ge -\frac{S}{10p}. \end{aligned} $$

The effective-balance relation is

$$ E_i = b_i + G. $$

Symbol	Implementation variable
$S$	total_supply
$B$	total_base_sum
$G$	global_field
$M$	total_minted
$D$	total_burned
$d$	dust_accumulator
$E_i$	effective_balance[i]
$b_i$	base_balance[i]

Here $\mathtt{effective_balance}[i]=\mathtt{base_balance}[i]+\mathtt{global_field}$, under the model's stated integer and scaling conventions. The $O(1)$ distribution claim follows from changing a shared scalar and computing each effective balance on read; it does not mean every runtime operation is $O(1)$, nor does it itself establish security of every implementation.

SIRM is an engineering model and specification. The Lean theorem above is a separate mathematical result; there is no claim that the spectral theorem proves the runtime invariants.

---

3. From mathematics to applications

The project hierarchy is intentional: theorem and evidence first, related research programmes second, implementation and application systems third.

Research/application layer	Primary source	Current scope and boundary
Formal fourth-moment theorem	Evgeny-Theorem	Specific SU(2)/Sierpiński-gasket identity; Lean 4 formalization reported for all stated levels
Higher-moment research	Evgeny's Theory of Everything	Finite-level certificates and numerical holdouts; all-level recurrence open
Signed-flux spectral research	Phi-Genesis	Spectral decimation and mass-formula audit; Gate A open
Quantum-processing architecture	RFT-QPU-Sierpinski	Pre-experimental architecture; no quantum advantage or speed-up established
Energy-system model	RFT-Invariant-Battery	Exploratory computational scenarios with explicit assumptions
Standalone execution runtime	Rift-L1-Blockchain	Implementation-specific runtime, invariant checks, and fuzzing reports
On-chain protocol	Rift-Network · Devnet client	Solana Devnet research deployment; not a claim of mainnet readiness
SVM memory-context research	agave-abiv2-memory-contexts	Proof-of-concept investigation; findings are specific to its studied code path
Conflict-aware scheduling	agave-rift-scheduler	Scheduler research and upstream discussion
DeFi ledger model	aave-v4-hub-model-review	Invariant model review, complementary to rather than replacing formal verification
Kernel stress testing	seL4 test report	Complementary stress testing of a specific seL4 subsystem; not a replacement for seL4's formal proof

Metrics such as fuzz-run counts, test totals, audit findings, and runtime durations are source-reported snapshots, not live counters in this README. Consult each source repository and its dated workflow/report before quoting a figure externally.

---

4. Historical development and provenance

The programme should be read as a sequence of increasingly explicit evidence obligations—not as a story in which every hypothesis has become a theorem.

1. Invariant-first engineering. SIRM began as a way to specify and enforce state constraints across deterministic runtime transitions. The runtime repositories retain their own implementation histories and test records.
2. A precise spectral identity. Evgeny's Theorem isolates a concrete SU(2)-connected Sierpiński-gasket operator and a commuting control, then states a closed form for the fourth-moment trace defect. The theorem repository contains the formalization and numerical verification records.
3. Extension beyond the fourth moment. The Theory-of-Everything synthesis repository collects higher-moment computations and finite-level certificates. It explicitly leaves the all-level recurrence open.
4. A separate spectral-decimation audit. Phi-Genesis examines signed-flux Laplacians and mass-index claims. Rejections and open residuals are retained as results of the audit, not erased to make the narrative look complete.
5. Architecture and applications. UltraCore connects the research strands to deterministic execution, runtime verification, blockchain experiments, quantum-architecture exploration, and energy-system modelling. Those applications do not retroactively prove the mathematical programme.

For chronology, cite the actual source history rather than inferring dates from this summary: UltraCore commit history · Evgeny-Theorem history · Theory-of-Everything history · Phi-Genesis history.

---

5. Evidence vocabulary

Label	Meaning in this repository
Machine-checked	A stated proposition is accepted by the specified proof assistant/build configuration. Review that formal definitions match the intended mathematics.
Analytically proved	A written proof establishes the stated claim from explicit assumptions; cite the proof.
Numerically reproduced	Computation matches a stated prediction on named inputs. Finite checks alone do not prove a universal claim.
Engineering-tested	Tests, fuzzing, audit work, or deployment checks support an implementation-specific statement.
Certified finite-level	A certificate establishes the stated finite coefficient or case under its explicit bounds and assumptions; it does not automatically quantify over all levels.
Hypothesis / conjecture	A precise proposed extension awaiting proof, refutation, or decisive validation.
Open	The required proof, derivation, independent replication, or experiment remains incomplete.
Rejected / not established	Available counterexamples or evidence do not support the stronger claim. Keep the reason and scope visible.

A passing workflow supports only the assertions it runs. A proof in one repository does not transfer automatically to a related repository, operator family, physical interpretation, or application.

---

6. Navigation

• Research map and evidence boundaries — relationships, statuses, and closure criteria.
• AI guide — instructions for language models and automated research assistants; read before summarizing claims.
• Scientific basis — modelling vocabulary versus literal mathematics.
• Pitch and research dossier — audience-facing narrative, methodology, and claims register.
• Platform strategy and architecture — runtime architecture and engineering decisions.
• SIRM foundations — model definitions and invariants.
• Verification evidence and seL4 report — implementation-specific validation.
• Main RFT-SIRM portal — organization-wide entry point. It remains separate and is not replaced by this repository.

License

Original material in this repository is distributed under Apache-2.0, subject to the license and NOTICE files. Linked repositories are separate works with their own histories, content, and licensing terms.

Copyright 2026 Evgeniy Zaprudnov (RFT-SIRM).

Cross-repository verification: Theory of Everything

The Theory of Everything — upstream verification workflow checks the current main revision of Evgeny's Theory of Everything from this repository. It validates the dissertation and required research files, runs the documentation/provenance audit, and executes the recurrence arithmetic audit and its regression tests.

• Workflow runs and logs
• Triggered manually with Run workflow, on relevant changes to this integration, and on a daily schedule.
• The job log records the exact upstream Git revision it checked, so a green result can be traced to a specific source snapshot.
• A passing run means only that these listed checks passed. It does not establish the still-open all-level higher-moment recurrence or replace the pinned Lean and specialized numerical workflows in the source repository.