{
  "id": "oai:papers.qnfo.org:cei-invariance-architectures-as-equivalence-classes-of-causal-density-and-energy",
  "slug": "cei-invariance-architectures-as-equivalence-classes-of-causal-density-and-energy",
  "title": "CEI Invariance: Architectures as Equivalence Classes of Causal Density and Energy Fidelity",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Computational architectures are today chosen for a substrate by benchmarking, an expensive process that must be repeated for every substrate-architecture pair and gives no guidance before hardware exists. No existing framework predicts, from thermodynamics alone, which architecture classes a physical substrate can sustain. We propose the Causal-Energy Invariant (CEI): for a given substrate, the product of causal density ρ_t (dependent operations per volume-time) and energy fidelity η_e (energy per transition in units of kTln 2) is bounded by a substrate constant κ, derived from Landauer's principle, a substrate power-density limit, and causal-cone bounds on operation rates. Architectures with equal ρ_tη_e form genuine equivalence classes, and the bound predicts that substrates favor architectures whose product approaches κ. We derive κ = 3.483× 10²9 mathrmm^-3 s^-1 for silicon under an assumed areal power limit of 100 mathrmW cm^-2 and a 1 mm active depth, show the causal-cone bound exceeds this by a factor ≈ 8.6× 10¹0 (so power, not relativity, binds silicon), and classify two assumed architecture profiles: a pipelined CMOS-like profile saturating 3.0\\% of κ and a gate-based error-corrected profile with η_e ≥ 100 from published thermodynamic floors. Confirmation would replace per-pair benchmarking with a thermodynamic substrate-architecture map; falsification would localize where the tradeoff breaks.",
  "abstract_markdown": "Computational architectures are today chosen for a substrate by benchmarking, an expensive process that must be repeated for every substrate-architecture pair and gives no guidance before hardware exists. No existing framework predicts, from thermodynamics alone, which architecture classes a physical substrate can sustain. We propose the Causal-Energy Invariant (CEI): for a given substrate, the product of causal density $\\rho_t$ (dependent operations per volume-time) and energy fidelity $\\eta_e$ (energy per transition in units of $kT\\ln 2$) is bounded by a substrate constant $\\kappa$, derived from Landauer's principle, a substrate power-density limit, and causal-cone bounds on operation rates. Architectures with equal $\\rho_t\\eta_e$ form genuine equivalence classes, and the bound predicts that substrates favor architectures whose product approaches $\\kappa$. We derive $\\kappa = 3.483\\times 10^{29}\\ \\mathrm{m^{-3}\\,s^{-1}}$ for silicon under an assumed areal power limit of $100\\ \\mathrm{W\\,cm^{-2}}$ and a $1\\ \\mathrm{mm}$ active depth, show the causal-cone bound exceeds this by a factor $\\approx 8.6\\times 10^{10}$ (so power, not relativity, binds silicon), and classify two assumed architecture profiles: a pipelined CMOS-like profile saturating $3.0\\%$ of $\\kappa$ and a gate-based error-corrected profile with $\\eta_e \\geq 100$ from published thermodynamic floors. Confirmation would replace per-pair benchmarking with a thermodynamic substrate-architecture map; falsification would localize where the tradeoff breaks.",
  "date": "2026-11-02",
  "first_published": "2026-11-02",
  "last_revised": "2026-11-02T00:00:00Z",
  "modified": "2026-11-02T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/cei-invariance-architectures-as-equivalence-classes-of-causal-density-and-energy",
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    "creators": [
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "CEI Invariance: Architectures as Equivalence Classes of Causal Density and Energy Fidelity"
      }
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    "publicationYear": "2026",
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        "description": "Computational architectures are today chosen for a substrate by benchmarking, an expensive process that must be repeated for every substrate-architecture pair and gives no guidance before hardware exists. No existing framework predicts, from thermodynamics alone, which architecture classes a physical substrate can sustain. We propose the Causal-Energy Invariant (CEI): for a given substrate, the product of causal density ρ_t (dependent operations per volume-time) and energy fidelity η_e (energy per transition in units of kTln 2) is bounded by a substrate constant κ, derived from Landauer's principle, a substrate power-density limit, and causal-cone bounds on operation rates. Architectures with equal ρ_tη_e form genuine equivalence classes, and the bound predicts that substrates favor architectures whose product approaches κ. We derive κ = 3.483× 10²9 mathrmm^-3 s^-1 for silicon under an assumed areal power limit of 100 mathrmW cm^-2 and a 1 mm active depth, show the causal-cone bound exceeds this by a factor ≈ 8.6× 10¹0 (so power, not relativity, binds silicon), and classify two assumed architecture profiles: a pipelined CMOS-like profile saturating 3.0\\% of κ and a gate-based error-corrected profile with η_e ≥ 100 from published thermodynamic floors. Confirmation would replace per-pair benchmarking with a thermodynamic substrate-architecture map; falsification would localize where the tradeoff breaks.",
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