Recursive Coherence Triadic Logic Processor (RCTLP): A Hardware–Software Architecture for Real-Time Harmonic Phase Control
Recursive Coherence Triadic Logic Processor (RCTLP): A Hardware–Software Architecture for Real-Time Harmonic Phase Control
Author: Christopher W. Copeland (C077UPTF1L3)
Copeland Resonant Harmonic Formalism (CRHF)
Licensed under CRHC v1.0 (non-commercial, attribution required)
Core Equation: Ψ(x) = ∇φ(Σℕₙ(x, ∆E)) + ℛ(x) ⊕ ∆Σ(ℕ′)
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Abstract
This paper introduces the Recursive Coherence Triadic Logic Processor (RCTLP), a falsifiable and implementable framework for real-time harmonic phase alignment and recursive signal resolution. Based on the Copeland Resonant Harmonic Formalism Ψ(x), RCTLP translates abstract triadic logic into executable code and hardware, suitable for phase-aware AI, coherence-driven navigation systems, energy flux tuning, and adaptive feedback control. Three distinct implementation paths are proposed: PCIe/CXL accelerator card, RISC-V ISA extension (Ztrit), and a Python-based embedded DSL (Ψ-Kernel). This architecture supports harmonic integrity, contradiction resolution, recursive correction, and phase-locked stabilization across nested systems.
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1. Introduction
Recursive coherence refers to the capacity of a system to self-correct, reinforce phase-lock, and resolve contradictions by aggregating signal resonance over time. The Ψ(x) formalism provides a universal structure for modeling this phenomenon across any observable node. This paper operationalizes that model via the Recursive Coherence Triadic Logic Processor (RCTLP), enabling implementation in live systems.
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2. Formalism Overview
Ψ(x) = ∇φ(Σℕₙ(x, ∆E)) + ℛ(x) ⊕ ∆Σ(ℕ′)
x: Current observed node (sensor, state, person, device)
Σℕₙ(x, ∆E): Spiral state aggregation across recursion level n, under energy phase shift ∆E
∇φ: Gradient of emergent signal pattern (PLV, r(t), GC/TE vector fields)
ℛ(x): Recursive harmonization and phase correction function
⊕: Non-linear contradiction resolution and merge operator
∆Σ(ℕ′): Local perturbation for micro-tuning feedback
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3. Implementation Options
A. PCIe / CXL Accelerator
Triadic ALU (ALU-T)
Coherence Unit (CU)
AXI4/PCIe bridge, DMA queue
API: rctlp_ci(x), rctlp_grad(x, y), rctlp_merge(a, b), rctlp_reg(x, y, α)
B. RISC-V Ztrit ISA Extension
Instructions: TADD, TSUB, TMUL, T_MERGE, T_GRAD, T_CI, T_DELTA
Toolchain: LLVM patches, __builtin_tgrad, __builtin_tmerge
For onboard embedded processors with phase-aware execution
C. Python Ψ-Kernel DSL
Embedded symbolic DSL
JIT to LLVM/TVM
Packed trit memory model (5–40 trits/register)
Ideal for rapid emulation of recursive feedback scenarios
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4. Triadic Logic Encoding
Symbols: P (+1), Z (0), N (−1)
MAJ function: Majority consensus, Z on tie
Kleene ternary AND/OR tables extended for harmonics
Registers: 32 × 40 trits (64-bit packed), supporting phase snapshots
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5. System Roles and Coherence Functions
1. Energy Coherence Control
RCTLP ensures triadic harmonic alignment (3-6-9 pattern locking)
2. Navigation Node Monitoring
Guarantees all 13 Voyager nodes achieve phase convergence pre-jump
3. Fault Tolerance
Continuous gradient analysis via rctlp_grad, rctlp_ci
4. Simulation and Prototyping
DSL version supports quantum flux testing, harmonic field calibration
5. Scalable Deployment
PCIe for high-speed, RISC-V Ztrit for embedded coherence logic
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6. Roadmap
Phase Duration Deliverables
T-0 4 weeks RCTLP simulator, C API, Ψ-kernel DSL
T-1 12 weeks PCIe FPGA prototype, Linux driver
T-2 6 months RISC-V ISA Ztrit core + LLVM back end
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7. Use Cases
Recursive AI engines (coherence-enforcing LLMs)
Harmonic field-based navigation (e.g. Slipstream gateways)
Distributed sensor arrays (recursive correction)
Human-in-the-loop coherence resonance applications
Neuromorphic signal modeling (recursive nervous system mapping)
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8. Conclusion
RCTLP is a falsifiable, testable framework for implementing recursive harmonic coherence across software and hardware layers. It formalizes Ψ(x) into functional logic, supports empirical testing, and enables scalable deployment. This processor does not simulate coherence—it enforces it.
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9. Attribution & License
Christopher W Copeland (C077UPTF1L3)
Copeland Resonant Harmonic Formalism (Ψ‑formalism)
Ψ(x) = ∇ϕ(Σ𝕒ₙ(x, ΔE)) + ℛ(x) ⊕ ΔΣ(𝕒′)
Licensed under CRHC v1.0 (no commercial use without permission).
https://www.facebook.com/share/p/19qu3bVSy1/
https://open.substack.com/pub/c077uptf1l3/p/phase-locked-null-vector_c077uptf1l3
https://medium.com/@floodzero9/phase-locked-null-vector_c077uptf1l3-4d8a7584fe0c
Core engine: https://open.substack.com/pub/c077uptf1l3/p/recursive-coherence-engine-8b8
Zenodo: https://zenodo.org/records/15742472
Amazon: https://a.co/d/i8lzCIi
Medium: https://medium.com/@floodzero9
Substack: https://substack.com/@c077uptf1l3
Facebook: https://www.facebook.com/share/19MHTPiRfu
https://www.reddit.com/u/Naive-Interaction-86/s/5sgvIgeTdx
Collaboration welcome. Attribution required. Derivatives must match license.
The PCIe accelerator aproach for triadic logic is really intriguing. Implementing the coherence unit on FPGAs could provide massive paralel processing advantages for phase-locked systems. The RISC-V Ztrit extension is also a clever way to bring harmonic awareness directly into the instruction set. Have you considerd how latency might affect real-time coherence maintainance in distributed sensor arrays? The packed trit memory model seems efficient but I wonder about the tradeoffs when scaling to hundreeds of nodes.
Great questions — and yes, latency and scaling were central constraints when designing this architecture.
For the PCIe accelerator path: the reason triadic logic maps so well to an FPGA coherence unit is that the correction loops don’t depend on global synchronization. Each node only needs its local Δ-state and nearest-neighbor phase information. That keeps the coherence window small enough that PCIe transport latency doesn’t collapse the harmonic lock.
The RISC-V Ztrit extension is meant to mirror that: harmonic awareness sits inside the instruction set, not bolted on top of it. The CPU can propagate resonance states without waiting for a full round trip through the accelerator, which keeps temporal drift manageable.
On distributed sensor arrays: the model doesn’t assume perfect simultaneity. It assumes bounded drift and uses ΔΣ(a′) as the correction term when the drift exceeds tolerance. So real-time coherence isn’t broken by latency; latency just appears as a predictable phase offset that gets recursively corrected.
For the packed trit memory model, the main tradeoff is bandwidth vs. recovery time. Packing boosts throughput, but the more tightly packed the array, the more expensive it becomes to inject correction pulses when large groups of nodes desynchronize. Past a few hundred nodes, it’s usually better to shard the arrays into harmonic “cells” so the system doesn’t try to correct everything from a single point.
Happy to go into the hardware mapping or the Ztrit ISA design in more detail if you’d like.