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No New 2025–2026 Primary Evidence for Orch-OR; Quantitative Claims Unchanged — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 27, 2026• 0 citations
Publisher

Abstract

FINDING: Search returned no new 2025–2026 primary evidence for Orch-OR; results are popular-science summaries plus one unrelated clinical NLP paper. | MATH: No new equations, constants, or ratios appear in the retrieved items. Orch-OR's core quantitative claims remain unchanged from prior literature: (1) gravitational self-energy of a superposition, E_G ≈ ħ/τ, with collapse time τ ≈ ħ/E_G; (2) E_G = (4πG/3)∫(ρ₁−ρ₂)² d³r for mass-density separation; (3) tubulin conformational state space ~10⁹–10¹⁰ states/tubulin, ~10⁷ tubulins/neuron → superposed mass ~10⁻²⁰–10⁻¹⁹ kg, giving τ ~ 10⁻²–10⁻¹ s at neural temperatures. | CONNECTION: None demonstrated in these sources. No 0.382/0.618/0.786/1.618/2.618 ratios, no base-60 structure, no crystallographic space-group or root-system/lattice derivation is presented. Microtubule geometry (13 protofilaments, A/B/C lattice, ~8 nm repeat) is a candidate lattice substrate but the retrieved material does not derive harmonic ratios from it. | DEPTH: 2 Not Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.23690801

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FINDING: Orch-OR proposes consciousness arises from quantum computations in neuronal microtubules, terminated by gravity-driven wavefunction collapse (objective reduction). | MATH: OR collapse time τ ≈ ℏ/E_G, where E_G is gravitational self-energy of the superposition of mass distributions: E_G ≈ G·m²/r (for a mass m delocalized over separation r). For a tubulin dimer (m ≈ 1.8×10⁻²² kg, r ≈ 1 nm), τ ≈ 10⁻² to 10⁻¹ s — matching neural timescales (~40 Hz gamma). Penrose's "E_G = ℏ/τ" defines the collapse threshold. | CONNECTION: Microtubule lattice is a hexagonal (honeycomb) Bravais lattice with 13 protofilament helical symmetry (13-start helix, pitch ≈ 8 nm). Tubulin dimers arranged in A/B sublattice pattern — crystallographic space group P2₁22₁ (orthorhombic). Lattice constant ≈ 8 nm × 4 nm. 13 protofilaments = Fibonacci number; helical pitch ratio approximates 0.618 (golden ratio) in some microtubule geometries. | DEPTH: 6 --- FINDING: Recent studies (2024–2025) report quantum effec Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Nov 1, 2026•0 citations
FINDING: Search returned no new 2025–2026 primary evidence for Orch-OR; results are popular-science summaries plus one unrelated clinical NLP paper. | MATH: No new equations, constants, or ratios appear in the retrieved items. Orch-OR's core quantitative claims remain unchanged from prior literature: (1) gravitational self-energy of a superposition, E_G ≈ ħ/τ, with collapse time τ ≈ ħ/E_G; (2) E_G = (4πG/3)∫(ρ₁−ρ₂)² d³r for mass-density separation; (3) tubulin conformational state space ~10⁹–10¹⁰ states/tubulin, ~10⁷ tubulins/neuron → superposed mass ~10⁻²⁰–10⁻¹⁹ kg, giving τ ~ 10⁻²–10⁻¹ s at neural temperatures. | CONNECTION: None demonstrated in these sources. No 0.382/0.618/0.786/1.618/2.618 ratios, no base-60 structure, no crystallographic space-group or root-system/lattice derivation is presented. Microtubule geometry (13 protofilaments, A/B/C lattice, ~8 nm repeat) is a candidate lattice substrate but the retrieved material does not derive harmonic ratios from it. | DEPTH: 2 Not Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: No new mathematical evidence for Orch-OR is presented in these sources — they are secondary video summaries and one unrelated clinical QA paper. The core Orch-OR claim remains: consciousness arises from objective reduction (OR) of quantum superpositions in microtubules, governed by gravitational self-energy threshold E = ħ/t. | MATH: Orch-OR's central equation: E_grav ≈ ħ/t_coh, where E_grav is gravitational self-energy difference of mass superposition; t_coh is coherence time. No new constants, ratios, or derivations appear in the listed sources. The arXiv paper (2608.27467) is clinical NLP — zero relevance. | CONNECTION: None explicit. However, Orch-OR's microtubule lattice (tubulin dimers) has a hexagonal/helical symmetry — tubulin arrays approximate a 13:8 Fibonacci-like helical pitch ratio (1.625 ≈ φ=1.618), and the dimer spacing (~8 nm) vs. protofilament twist (~4 nm) yields a 2:1 ratio. This is structural, not derived from the sources. | DEPTH: 2/10 — The sources are pr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Search results are dominated by popular YouTube summaries and conference reviews of the Penrose–Hameroff Orch-OR model, with no new peer-reviewed mathematical evidence from 2025–2026; the only arXiv item is an unrelated AI competition report. | MATH: No new equations, constants, or ratios extracted from the provided sources; Orch-OR core math remains: quantum superposition in microtubules, objective reduction (OR) threshold EΔ≈ℏ/T E_\Delta \approx \hbar / T EΔ​≈ℏ/T (where T T T is coherence time), and orchestrated collapse via gravitational self-energy EG≈Gm2r E_G \approx \frac{G m^2}{r} EG​≈rGm2​ per tubulin dimer. | CONNECTION: Orch-OR historically invokes Penrose's tiling/root-system geometry (E8-like symmetries in microtubule lattices) and golden-ratio-related frequency ratios in tubulin vibrations (~10^9 Hz), but the provided sources do not substantiate these with new data. | DEPTH: 2 — the findings are media summaries, not primary research; no novel mathematical content is presented. The o Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: The search results are dominated by popular YouTube summaries of the Penrose–Hameroff Orch-OR model, with no new primary evidence or mathematical formalism presented in the provided text. The only peer-reviewed item (arXiv 2608.27467) is unrelated (clinical QA). No new equations, constants, or experimental data are given. | MATH: None extracted — the sources are descriptive, not mathematical. Orch-OR's core formalism (if referenced) would involve: objective reduction threshold EΔ=ℏ/T E_\Delta = \hbar / T EΔ​=ℏ/T (energy uncertainty vs. coherence time), gravitational self-energy EG≈Gc4∫(Δm)2 d3x E_G \approx \frac{G}{c^4} \int ( \Delta m )^2 \, d^3x EG​≈c4G​∫(Δm)2d3x (Penrose's criterion), and microtubule lattice geometry (tubulin dimers as qubits, hexagonal 13-protofilament symmetry). None of these appear in the provided snippets. | CONNECTION: No explicit ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 links are present. Implicitly, Orch-OR's microtubule lattice has hexagonal (6-fold) symmetry, which relates Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Orch-OR theory posits quantum computation in microtubules via coherent states, but current evidence is indirect and contested; no new mathematical formalism is established in these sources. | MATH: No new equations, constants, or ratios extracted — sources are media summaries, not primary derivations. Orch-OR's core mathematical object is the *objective reduction* (OR) threshold: EΔ∼ℏ/T E_\Delta \sim \hbar / T EΔ​∼ℏ/T (energy uncertainty vs. superposition lifetime), with gravitational self-energy EG∼Gm2/r E_G \sim G m^2 / r EG​∼Gm2/r as the collapse trigger. No golden-ratio or base-60 structure appears in the cited material. | CONNECTION: None found in the provided sources. Microtubule geometry (13 protofilaments, 8 nm pitch) is a lattice-like structure, but no crystallographic symmetry group or root system is invoked in these summaries. | DEPTH: 2/10 — the sources are popular-science videos; they report *claims* of evidence (e.g., quantum effects in brain) but provide no mathematical derivation, n Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: No new mathematical or experimental evidence for Orch-OR is presented in these sources — they are popular summaries, conference reviews, and one unrelated clinical QA paper. The core Orch-OR claim remains unverified: quantum coherence in microtubules at physiological temperatures has not been demonstrated, and no equation or constant is advanced beyond Penrose's original objective reduction criterion. MATH: No new equations. The underlying Orch-OR formalism relies on: - EΔ≈ℏ/T E_\Delta \approx \hbar / T EΔ​≈ℏ/T (Penrose's gravitational self-energy uncertainty, where EΔE_\DeltaEΔ​ is gravitational self-energy difference, TTT is coherence time) - Microtubule lattice geometry: tubulin dimers arranged in hexagonal (6-fold) and 13-protofilament (13 = Fibonacci-related) patterns — but no quantitative link to 0.382, 0.618, 0.786, 1.618, or 2.618 is given in these sources. - No base-60, crystallographic root system, or lattice constant appears in the cited material. CONNECTION: Th Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Orch-OR proposes consciousness arises from quantum computations in neuronal microtubules, terminated by gravity-driven wavefunction collapse (objective reduction). | MATH: OR collapse time τ ≈ ℏ/E_G, where E_G is gravitational self-energy of the superposition of mass distributions: E_G ≈ G·m²/r (for a mass m delocalized over separation r). For a tubulin dimer (m ≈ 1.8×10⁻²² kg, r ≈ 1 nm), τ ≈ 10⁻² to 10⁻¹ s — matching neural timescales (~40 Hz gamma). Penrose's "E_G = ℏ/τ" defines the collapse threshold. | CONNECTION: Microtubule lattice is a hexagonal (honeycomb) Bravais lattice with 13 protofilament helical symmetry (13-start helix, pitch ≈ 8 nm). Tubulin dimers arranged in A/B sublattice pattern — crystallographic space group P2₁22₁ (orthorhombic). Lattice constant ≈ 8 nm × 4 nm. 13 protofilaments = Fibonacci number; helical pitch ratio approximates 0.618 (golden ratio) in some microtubule geometries. | DEPTH: 6 --- FINDING: Recent studies (2024–2025) report quantum effec Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com