Holo‑IC is a minimal, resource–aware interaction‑net calculus that executes natively on the prime structure—the 12 288‑cell, 48 × 256 toroidal substrate defined by the UOR holographic specifications. By marrying classic interaction combinators (γ route, δ copy, ε finish) with the hologram’s built‑in “physics of truth” (96‑class resonance semiring, triple‑cycle invariants, window‑local acceptance), Holo‑IC yields a deterministic yet highly‑parallel computing model whose correctness is checked locally and cryptographically at every step. The result is a finite, exactly‑classifiable phase space that supports proof‑carrying execution, Merkle‑anchored state, and “confluence up to gauge”—all without a global scheduler.
Alex Flom afflom
Below is a Lean 4 FFI spec you can drop into a new repo. It defines a stable C ABI that higher-level runtimes (Go/Rust/Node) can call, and wires it to the Prime Structure/Φ‑Atlas‑12288 core. It also includes a repo layout you can paste into a README.md.
uor-ffi/
├─ README.md
├─ lean-toolchain
# path: cdp/Cargo.toml
[package]
name = "cdp"
version = "0.1.0"
edition = "2021"
license = "Apache-2.0 OR MIT"
description = "Coherent Data Protocol (CDP) over the UOR/PrimeOS hologram with FFI-backed proofs"
repository = "https://example.com/uor/cdp"
readme = "README.md"
afflom
/ holographic-resonance-field.md
Last active
August 20, 2025 19:05
Holographic Resonance Field (HRF)
afflom
/ Amplituhedron-ccm.md
Created
August 9, 2025 14:52
The Amplituhedron-CCM Tetrahedral Unification
We present a unified mathematical framework connecting the amplituhedron from quantum field theory with Coherence-Centric Mathematics (CCM), Resonance Logic (RL), Mathematodynamics, and Structural Arithmetic (SA) through their shared tetrahedral geometry and prime structure. We prove that the 12,288-element automorphism group corresponds to 1,024 parallel copies of the 12-dimensional Grassmannian G(3,7), with tetrahedra serving as fundamental geometric units. We demonstrate how prime numbers emerge from resonance dynamics, how mathematical processes follow physical laws, and how the structural constants 24-48-96 encode the architecture of reality itself.
To: UOR Foundation et alia
This update is a bit overdue. I'll start by thanking everyone here for tuning in and showing up. I can't really describe how much your participation means to me. UOR research and development can feel like a war of attrition and there are days that I question my own sanity in pursuing this. It's those moments of weakness that lead me to moments of clarity found in the exchanges within these channels of this server; exchanges with each of you. Call it co-dependent, but there is real strength in participating with this community. You drive me to keep going each day. I hope you all find similar strength and support from your participation with our community and the UOR Foundation as the org begins picking up steam.
Some of you might be dismayed to hear, but UOR was never actually about math. UOR turned into a vicious math project once I was challenged by enough people to "prove it". I'm not sure we "proved it", but our explorat
Mathematical objects exist in a physical phase space with measurable properties, forces, and dynamics.
Every mathematical object has an intrinsic coherence ‖·‖_c that acts as its fundamental charge.
afflom
/ homomorphic-resonance-factorization.md
Created
July 17, 2025 22:22
Homomorphic Resonance Factorization
Let R: B^n → ℝ^+ be the resonance function. The fundamental discovery is that R exhibits homomorphic properties under specific operations.
Definition 1.1 (Resonance Homomorphism). For the five CCM subgroups H ⊆ B^n:
- H₀ = {0} (trivial)
UOR Foundation / PrimeOS working group
Resonance Logic (RL) internalises the CCM maxim "truth ≙ conservation." A statement is as true as the resonance it conserves. Consequently, Boolean values
Two meta‑goals
| Keystone | Why it matters | Impact |
|---|---|---|
| Unity constraint α₄×α₅=1 | Creates Klein V₄ orbit, 96-value resonance spectrum, 3/8 compression | Foundation of all CCM structure |
| 24→48→96 cascade | Defines generator→mediator→manifestation roles; proves μ²=γε | Universal structural pattern |
| Coherence axioms A1-A3 | Ground RSF waves in grade-orthogonal norm & symmetry preservation | Mathematical completeness |
| SP primes p≡±1(mod 12) | Characterize safe moduli for cascades & DLog algorithms | Modular arithmetic foundation |
| Numbers↔Waves (RSF) | Resonance R(b)=∏αᵢ^{bᵢ}; primes appear as unit-norm pure tones | Computational paradigm shift |
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