Architecture

Design Philosophy

RFT-SIRM separates research claims, mathematical definitions, executable implementations, and verification evidence. Engineering components should enforce their specified invariants and reject invalid state transitions atomically where the implementation supports that guarantee. Guarantees are scoped to the relevant code, threat model, and tests; documentation must not imply that every component or research result is formally verified.

Research Architecture: Four Distinct Evidence Tracks

UltraCore-RFT is the integration and navigation layer for a portfolio of related research and engineering projects. It connects the projects without treating their results as interchangeable. Each source repository remains authoritative for its theorem statements, definitions, code, tests, formal proof status, and limitations.

flowchart TB
  HUB["UltraCore-RFT<br/>Integration, architecture, evidence ledger"]
  ET["Evgeny's Theorem<br/>Fourth-moment trace-defect identity"]
  TOE["Evgeny's Theory of Everything<br/>Higher-moment recurrence research"]
  PG["Phi-Genesis<br/>Signed-flux spectral decimation"]
  CG["RFT-Cosmology-Genesis<br/>Exact invariant limit + phenomenological model"]
  SIRM["SIRM engineering<br/>State transitions and runtime invariants"]
  HUB --> ET
  HUB --> TOE
  HUB --> PG
  HUB --> CG
  HUB --> SIRM
  ET -. "finite-moment starting point" .-> TOE
  TOE -. "no proven operator bridge" .-> PG
  ET -. "shared research context, not proof of cosmology" .-> CG

The dashed links indicate research context only; they do not imply a proved mathematical equivalence or causal derivation.

1. Evgeny's Theorem: a formalized fourth-moment result

Primary sources: source repository, theorem statement, Lean formalization, and verification record.

For the specific operator definitions and assumptions in that project, the stated identity is

\[ \Delta_m(H^4,\theta) =\mathrm{Tr}(H_C^4)-\mathrm{Tr}(H_{C'}^4) =-16(3^{m-1}+1)\sin^2\left(\frac{\theta}{2}\right), \qquad m\geq1. \]

The source project reports a Lean 4 formalization. The scope of that formalization is the encoded proposition and its definitions. It does not, by itself, prove the higher-moment recurrence, the signed-flux decimation criterion, SIRM runtime invariants, or a physical interpretation.

2. Evgeny's Theory of Everything: higher-moment recurrence programme

Primary sources: repository, dissertation, final status, and claims and evidence.

This programme studies trace defects for higher even moments \(H^6\), \(H^8\), and \(H^{10}\), including Fourier-coefficient candidates, exact finite-level modular/CRT certificates, and independent sparse-matrix numerical holdouts. The repository reports checks through level 7 for specified finite sets of angles and a pinned Lean build for the upstream fourth-moment result. These are distinct evidence types. The universal all-level higher-moment recurrence remains open: finite certificates and numerical agreement do not establish it.

3. Phi-Genesis: signed-flux spectral analysis

Primary sources: repository, verified results, research map, and reproducibility guide.

Phi-Genesis investigates signed \(\mathbb{Z}_2\)-flux graph Laplacians on Sierpiński-gasket approximations, spectral decimation, spectral gaps, boundary/corner corrections, inertia-based counting, and exploratory integer mass-index patterns. The factor-5 decimation structure is reported with boundary/corner qualifications. Gate A remains open because the full exceptional set and all residual mismatches have not been explained. The proposed index set \(\{1,12,17,40\}\) is not established as a predictive selection law. The signed-flux operators are not assumed equivalent to the SU(2)-connected operators in Evgeny's Theorem.

4. RFT-Cosmology-Genesis: exact invariant and phenomenological extension

Primary sources: repository, exact invariant remainder theorem, model specification, results, and limitations.

For the normalized invariant defined in that repository,

\[ I_m(\theta)=-16\frac{3^{m-1}+1}{3^{m+1}+3}\sin^2\left(\frac{\theta}{2}\right), \]

the exact limit and finite-level remainder are

\[ I_\infty(\theta)=-\frac{16}{9}\sin^2\left(\frac{\theta}{2}\right), \qquad I_m(\theta)-I_\infty(\theta) =-\frac{32}{9(3^m+1)}\sin^2\left(\frac{\theta}{2}\right). \]

The repository records an algebraic derivation and Lean-checked results for the stated invariant. Its photon-sector coupling and background/CMB response are phenomenological. No physical origin for the coupling, detection of a new interaction, or agreement with a full observational CMB likelihood is established by this mathematical identity.

5. SIRM engineering architecture

SIRM is the Synthetic Intelligence Reasoning Model. In the engineering repositories, the operational core is a state-transition model constrained by explicit invariants, arithmetic checks, permission boundaries, and reproducible tests. These implementation-level constraints must be documented and verified against the actual code. They are not consequences of the spectral trace identity unless a separate formal connection is stated and proved.

Evidence and Dependency Rules

Evidence class	What it supports	What it does not establish by itself
Machine-checked theorem	The encoded statement under its definitions, assumptions, and build	Unencoded generalizations or physical interpretation
Exact finite-level certificate	The stated finite coefficient/identity claims in its certified scope	An all-level recurrence
Reproducible numerical holdout	The tested finite instances, parameters, and algorithms	A universal theorem or causal explanation
Spectral computation	Properties observed for the stated graph/operator convention and level	A particle-mass law or cosmological mechanism
Phenomenological fit/model	Behaviour under the stated model and parameter choices	Physical validation or observational discovery
Runtime tests/fuzzing	Executed code paths and checked invariants under test conditions	Absence of all bugs or formal correctness

Cross-project dependencies must be explicit and versioned. Do not transfer a proof or verification label from one repository to another. In particular, the fourth-moment result does not close the higher-moment recurrence, Phi-Genesis Gate A, or the physical cosmology programme.

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System Overview

flowchart TB
 subgraph MATH["Mathematical Core"]
 I1["I1: supply = base_sum + field * p"]
 I2["I2: supply = minted - burned"]
 I3["I3: dust < p"]
 I4["I4: effective_balance >= -(supply / 10p)"]
 end

 subgraph RUNTIME["Runtime Layer"]
 MEM["Memory Contexts: CPI Permission Isolation"]
 SCHED["Scheduler: Conflict-Aware Ordering"]
 end

 subgraph ECON["Economic Interface"]
 SPL["SPL Token: Mint / Burn / Rebase"]
 FEE["Fee Mechanics: Field-Pressure Pricing"]
 end

 subgraph VERIFY["Verification"]
 FUZZ["libFuzzer: Stateful Invariant Fuzzing"]
 AUDIT["Security Audit: 14 Findings Addressed"]
 end

 MATH --> RUNTIME
 MATH --> ECON
 MATH --> VERIFY
 RUNTIME --> VERIFY
 ECON --> VERIFY

Component Map

Component	Repository	Language	Responsibility
CoreState	Rift-L1-Blockchain	Rust	O(1) distribution, invariant enforcement, fuzz verification
ultra_core_rift	Rift-Network	Rust/Anchor	On-chain SIRM invariant program
rift_token	Rift-Network	Rust/Anchor	SPL token interface, read-only access to CoreState
Memory Contexts	agave-abiv2-memory-contexts	Rust	Per-CPI-frame writable permission isolation (PoC research)
Scheduler	agave-rift-scheduler	Rust	Conflict-aware transaction scheduling with bounded retries

Invariant Enforcement Flow

sequenceDiagram
 participant User
 participant CoreState
 participant Invariant
 participant Token

 User->>CoreState: register() / transfer() / redistribute()
 CoreState->>CoreState: update base_sum, field, p
 CoreState->>Invariant: check_invariant()
 alt Invariant OK
 Invariant-->>CoreState: Ok(())
 CoreState-->>User: success
 CoreState->>Token: emit state change (read-only)
 else Invariant Violation
 Invariant-->>CoreState: Err(RiftError)
 CoreState-->>User: operation rejected
 end

Separation of Concerns

CoreState (Math Layer)

• Owns global_field, total_base_sum, total_supply
• Enforces I1-I4 after every operation
• Does not interact with SPL token accounts

RiftToken (Economic Layer)

• Reads CoreState to compute rift_multiplier
• Issues SPL tokens via CPI to token::mint_to
• Never writes to CoreState

Memory Contexts (Runtime Layer)

• Tracks per-CPI-frame writable permissions (PoC research)
• Ensures rollback on pop() (snapshot-based prototype; upstream feat/abiv2 uses abi_v2_prepare_for_instruction + make_immutable)
• Independent of economic logic

Scheduler (Runtime Layer)

• Orders transactions by conflict heat score
• Guarantees bounded retries (no silent loss)
• Independent of economic logic

Cross-Repository Data Flow

flowchart LR
 subgraph L1["Rift L1 Blockchain"]
 CORE1["CoreState: Rust native"]
 end

 subgraph NET["Rift Network"]
 CORE2["ultra_core_rift: Anchor PDA"]
 TOKEN["rift_token: SPL Mint"]
 end

 subgraph AGAVE["Agave Research"]
 MEM["Memory Contexts"]
 SCHED["Scheduler"]
 end

 CORE1 -->|"invariant spec"| CORE2
 CORE2 -->|"read-only: global_field"| TOKEN
 MEM -->|"permission model"| CORE2
 SCHED -->|"ordering model"| CORE1

O(1) Distribution

Standard approach (Ethereum, most L1s):

for each participant:
 balance[i] += reward / N -- O(N) gas, O(N) time

RFT approach:

global_field += reward / p -- O(1), one integer, all participants

At 1,000,000 participants: - Standard: 1,000,000 storage writes per distribution - Rift: 1 write

This is a different mathematical model, not an optimization.

Security Model

Layer	Guarantee	Mechanism
Arithmetic	No overflow/underflow	checked_add, checked_sub, checked_mul, try_into()
State	Atomic operations	Full success or Err -- no partial writes
Access	Authority validation	PDA seeds, has_one, Signer constraints
Runtime	Memory isolation	Per-frame permission snapshots, rollback on pop() (PoC research; upstream feat/abiv2 uses abi_v2_prepare_for_instruction + make_immutable)
Scheduling	No silent loss	Bounded retry count, explicit drain passes
Economics	Supply integrity	check_invariant() after every mutation

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See also: Foundations for mathematical derivations, Implementation for code-level details.