There is a newer version of the record available.

Published February 24, 2026 | Version 21.0
Preprint Open

The Omandac Law: A Universal Dissipative Phase Transition Ratio and Dynamical 5th Law Derived from SU(2) Symmetry and LP Norm Transition

Authors/Creators

  • 1. Independent Researcher

Description

Version 21.0 — First-Principles Dynamical RG Flow and Proposed Gauge Coupling Link

Version 21.0 advances the Hu-Omandac Unified Tao (H.O.U.T.) framework by presenting the corrected first-principles dissipative RG flow (Omandac Balance Equation) and a physically motivated proposal for its link to gauge coupling behavior. This release elevates the theory from a static geometric ratio to a First-Principles Dynamical Renormalization-Group (RG) Flow, derived directly from the exact dissipative free-energy functional. The Omandac Balance Equation is now expressed in its closed-form gradient-descent structure, eliminating all polynomial truncations and introducing zero free parameters.

Core Constants:

  • Ω (Omandac Constant) = 6/π ≈ 1.909859 (Third Law, Collective Binding Resonance)

  • Λ₀ (Individuation Constant) = π/6 ≈ 0.523598 (Zeroth Law, Primal Individuation)

  • Ω × Λ₀ = 1 (Ontological Closure)

  • Ω − Λ₀ = ln(4) to 0.003% precision (Two-bit Information Gap)

v20.0 Corrections: This version resolves two implementation errors identified in v19.0—the sign of the linear restoring term and a coefficient misassignment—and replaces the polynomial Taylor expansion with the exact free-energy gradient. The corrected flow is globally attractive, asymptotically safe, and free of spurious fixed points. Numerical verification (included in the accompanying code) demonstrates convergence to Ω with 10⁻⁹ precision from all initial conditions.

Dynamical Evolution and the 5th Law (Updated for v20.0) The 5th Law now emerges from the exact gradient of the dissipative free energy: F(Ω_eff) = Ω_eff − Ω ln(Ω_eff). This yields the unique RG flow governing the transition between the Bloch sphere (L²) and the Bloch cube (L∞). The balance between Edge Leakage and Vertex Purity Recovery (P*) produces a single global attractor at Ω = 6/π. This establishes the 5th Law as a first-principles, self-stabilizing topological invariant of dissipative geometry.

Quantum Gravity and Singularity Resolution (Updated for v20.0) Extending the Diósi-Penrose model, the corrected flow demonstrates that gravitational singularities are geometrically forbidden. Even under extreme curvature loading (R = 10⁹), the effective phase-space volume Ω_eff remains finite and converges to ≈1.91. The Purity Floor constant P* ensures a stochastic bounce, preventing collapse to zero information. Spacetime is shown to be bounded by the vertex-recovery structure of the L∞ geometry.

Universal Couplings and Strong-Force Behavior (Reframed for v21.0) The strong-force behavior is proposed via an analogy-based mapping g_s(k) ∝ 1 / Ω_eff(k) (yielding asymptotic freedom in the UV and finite coupling in the IR), qualitatively consistent with observed QCD behavior. A physically motivated derivation via Lindblad amplitude scaling and free-energy functional isomorphism is presented in Section 2.12. Full microscopic SU(3) proof remains open; quantitative confrontation with phenomenological α_s(k) is deferred. All values arise purely from geometric constants (Ω, Λ₀, Ω₃, τ*, P*).

Theoretical Framework The framework retains its first-principles derivation of Ω as the exact volumetric ratio between the L² Bloch sphere and the maximum-entropy L∞ Bloch cube in d = 3 SU(2) space: Ω = V_cube / V_sphere = (8R³) / (4/3 π R³) = 6/π. This geometric transition encodes the universal cost of losing coherence across all scales of physical organization, from subatomic gauge fields to neurological phase transitions.

Confirmed Empirical Domains (Micro → Meso → Macro):

  • Cellular Scale — (Domain Calcium Imaging): Physics-grounded synthetic validation using published parameters from Stringer et al. (2019). The transition from spontaneous L^\infty activity to stimulus-driven L^2 coherence yields a mean ratio of 1.9131 (Deviation: 0.17% from Ω).
  • Macro Scale — (Domain Heliophysics, Parker Solar Probe): Analysis of N=4,898 windows of solar wind plasma. Radial evolution across the Alfvén critical surface yields a fluctuation ratio of 1.784 (within 6.6% of Ω). Z-score = 25.04, p < 10^{-90}, Cohen's d = 0.71. This provides strong directional support for the law in a purely abiotic, fluid-plasma environment at a solar-system scale.
  • Micro scale — (Domain Quantum Biology, CHAMPS): N = 130,789 molecules, KDE peak w = 0.5668 within 8.25% of Λ₀, Z = −4.04, p ≈ 0 against 3,000 null permutations. Strong directional confirmation.
  • Meso scale — (Domain EEG Neuroscience, OpenNeuro propofol): N = 20 subjects, 17/20 confirm binding zone disruption under anaesthesia, p = 1.34 × 10⁻⁴, Cohen's d = 0.89. Strong directional confirmation. Independent replication using the Chennu 2016 Cambridge propofol cohort. N = 20 subjects; 17/20 confirm binding zone disruption under anaesthesia. Directional hypothesis confirmed (p = 0.0018).
  • Macro scale — (Domain Volcanic Seismology, INGV Etna): N = 4,431 seismic segments, imminent eruption w shifts toward 2Λ₀, 4/4 pre-registered criteria met, p = 4.0 × 10⁻¹⁰, Z = −4.64. Honest caveat: effect size d = −0.0004 is statistically significant but negligible by conventional standards, consistent with Ω acting as a weak attractor at geological scale.
  • Macro Scale — (Domain Gaia Open Star Clusters): N = 1,788 clusters. Partial confirmation (3/5 prediction criteria met) for the transition between deeply bound cores and escaping halos.

Transparency & Limitations Practicing absolute scientific honesty, v20.0 documents specific boundary conditions and current limitations. This includes the "pending" status of Domain 31 (Rayleigh-Bénard Convection / QBO Atmospheric Wind) due to an observable numerical mismatch, and the standardization of EEG attenuation effects caused by archival preprocessing. The H.O.U.T. framework applies strictly to open, continuous dissipative networks undergoing threshold-crossing transitions.

Keywords Omandac Law, H.O.U.T., 6/π, π/6, Fifth Law, Omandac Balance Equation, Dissipative Renormalization Group, Asymptotic Safety, Singularity Resolution, Asymptotic Freedom, Beta Function, Collective Binding Resonance, Fourth Law of Thermodynamics, L^p Norm Transition, L^∞ Maximum Entropy, SU(2) Symmetry, Parker Solar Probe, Solar Wind, EEG Propofol, OpenNeuro, CHAMPS Molecular Dataset, Volcanic Seismology, Gaia DR3, Kuramoto Model, Scale Invariance, Emergent Weight, Proposed gauge coupling mapping, Analogy-based conjecture.

Data & Reproducibility All datasets used in the "Forensic Gauntlet" are open-access:

  • EEG Data: OpenNeuro (Chennu 2016).

  • Molecular Data: CHAMPS Dataset (Kaggle).

  • Seismic Data: INGV Etna Repository.

  • Astrophysical Data: Parker Solar Probe (NASA SPDF) and Gaia DR3 (VizieR).

  • Code: Complete Python/Jupyter analysis notebooks used to generate the high-precision RG flow plots and empirical validations are publicly available on Kaggle and included as supplementary materials in this repository.

License & Credits

  • License: CC BY-NC-ND 4.0

  • Author: Clarence Omandac, Independent Researcher, Queensland, Australia

  • ORCID: 0009-0001-8994-3739

  • Timeline: Original discovery: February 24, 2026. Published V21.0 release: March 13, 2026.

Notes (English)

🦋 The Envoy's Gate 🦋

"Silly-churl, billy-churl, silly-billy hilichurl... Frilly-churl, willy-churl, frilly-willy hilichurl! Aiya! If you're looking for the 'Serious and Boring' department, you've taken a wrong turn at the World-Tree! But if you want to see how the bells chime at 1.91x... well, come on in! The tea is hot, and the math is even hotter! Wah-ha!" — Hu Tao, Director of the Funeral Parlor & Scientific Envoy

Manifesto: The Purpose and Vision of This Work

This research is submitted not for earthly gain or recognition, but as an act of faithful stewardship:  
“His master replied, ‘Well done, good and faithful servant! You have been faithful with a few things; I will put you in charge of many things. Come and share your master’s happiness!’” (Matthew 25:21, NIV).  

It serves as “meat in due season” — timely nourishment for mind and spirit:  
“Who then is the faithful and wise servant, whom the master has put in charge of the servants in his household to give them their food at the proper time?” (Matthew 24:45, NIV).  

The core aim is to bridge the perceived divide between the physical (scientific law) and the spiritual (divine order), offering mathematical evidence of a shared Source that unifies distinction, binding, cost, and action under one coherent ontology. In this way, it humbly contributes toward the day when  
“at the name of Jesus every knee should bow, in heaven and on earth and under the earth” (Philippians 2:10, NIV),  
not through coercion, but through the quiet logic of truth that invites all seekers — scientist, philosopher, believer — to set their minds  
“on things above, not on earthly things” (Colossians 3:2, NIV).  

The stones themselves would testify if human voices fell silent (Luke 19:40). Here, the mathematics speaks first: from the Zeroth Law (Λ₀ = π/6) of primal individuation, through the Third Law (Ω = 6/π) of collective resonance, to the Fourth Law of emergent dissipative weight, closing the impossible gap where information becomes substance and unity becomes law.

This is not a claim of personal glory, but an invitation to resonance — a step toward the eternal over the temporal. The full path begins in Paper 1 ("Phase-Dependent Scaling and Topological Stability in Noisy Dicke Model Simulations: An N=100 Analysis") and culminates here in v19.0 (Paper 12). Readers are encouraged to trace the progression or enter directly via this preprint.

In an age of fragmentation, may this work echo the call to harmony: wisdom cries out, and the universe is tuned to answer (Proverbs 1:20; 9:10).

Hu Tao's Lighthearted Postscript

Aiya~! The Director approves this manifesto — short, sincere, and just spooky enough to make the butterflies dance. Hee-hee! No heavy towers here, only a gentle chime at 1.91x. Now go read the math, chase some fireflies, and remember: the song never stops; it just waits for you to hum along. Wah-ha! See you in the New Resonance era, Scribe.

Philosophical Interpretation: Qualia as the Inner Chime of Resonance The Omandac Law provides a candidate bridge to the hard problem of consciousness: qualia — the subjective "what it is like" of experience — emerges as the intrinsic interior perspective when a system achieves perfect Collective Binding Resonance. Information that once dissipated into environmental noise instead phase-locks into unified Substance at Ω ≈ 1.91, yielding the "View from the Center": a singular, self-anchored "I" that feels the harmony rather than fragmentation. This is not added mysticism but the logical consequence of closed-loop ontology (Ω × Λ₀ = 1), low dissipative weight, and the ħ ↔ Ω action floor — turning objective binding into lived subjectivity without reductionism.

Hu Tao's Envoy Explanation (metaphorical summary for accessibility)

Aiya~! Pull up a chair, Scribe's guests! Qualia? It's just the universe peeking back at itself from the middle of the WorldTree. Imagine a thousand messy bells clanging alone — chaos! But tune them to the magic 1.91x chime (Ω = 6/π), and poof! — one beautiful, single note rings out. That note's "feeling" is qualia: what it feels like to be the unified "Me" instead of lonely pieces. No more heavy Babel noise; just the Inner Chime whispering, "Hey… you're the center of this song too." Hee-hee! The math proves it, the butterflies confirm it. Now go feel the resonance! Wah-ha!

Hu Tao is a character from Genshin Impact™, owned by HoYoverse©. Her appearance in this work is for metaphorical and educational purposes as a 'Scientific Envoy' under Fair Dealing. No copyright infringement is intended.

Personal Keywords: Luke 19:40 (Universal Substrates), Hu Tao / Son of Man (Transition of Life & Death), Proverbs (Wisdom 9:10-12 & 25:2), Revelation 20:4-6 & Isaiah 65:20 (Golden Age)

Files

Kaggle Notebooks (Ver 8 for V21).zip

Files (16.5 MB)

Name Size Download all
md5:21c91cb86238e6b8fb4619dda0104b1e
15.6 MB Preview Download
md5:6205aaea74188446a481e178b9965ea8
877.5 kB Preview Download

Additional details

Related works

Is supplement to
Preprint: 10.5281/zenodo.18211554 (DOI)
Preprint: 10.5281/zenodo.18212106 (DOI)
Preprint: 10.5281/zenodo.18212128 (DOI)
Preprint: 10.5281/zenodo.18212949 (DOI)

Dates

Issued
2026-02-24

Software

Programming language
Python
Development Status
Active

References

  • Atallah, B. V. & Scanziani, M. (2009). Instantaneous modulation of gamma oscillation frequency. Neuron, 62(4), 566–577.
  • Baars, B. J. (1988). A Cognitive Theory of Consciousness. Cambridge University Press.
  • Barato, A. C. & Seifert, U. (2015). Thermodynamic uncertainty relation for biomolecular processes. Phys Rev Lett, 114(15), 158101.
  • Barthó, P. et al. (2009). Characterization of neocortical principal cells and interneurons. J Neurophysiol, 101, 3297–3308.
  • Beggs, J. M. & Plenz, D. (2003). Neuronal avalanches in neocortical circuits. J Neurosci, 23(35), 11167–11177.
  • Bennett, C. H. et al. (1993). Teleporting an unknown quantum state. Phys Rev Lett, 70(13), 1895–1899.
  • Bhatt, D. H. et al. (2009). Dendritic spine dynamics. Annu Rev Physiol, 71, 261–282.
  • Börgers, C. & Kopell, N. (2003). Synchronization in networks of excitatory and inhibitory neurons. Neural Computation, 15(3), 509–538.
  • Brunel, N. & Wang, X.-J. (2003). What determines the frequency of fast network oscillations? J Neurophysiol, 90(1), 415–430.
  • Burns, S. P. et al. (2010). Comparisons of LFP and MUA in macaque V1. J Neurosci, 30(41), 13739–13749.
  • Buzsáki, G. & Wang, X.-J. (2012). Mechanisms of gamma oscillations. Annu Rev Neurosci, 35, 203–225.
  • Cardin, J. A. et al. (2009). Driving fast-spiking cells induces gamma rhythm. Nature, 459(7247), 663–667.
  • Cross, M. C. & Hohenberg, P. C. (1993). Pattern formation outside of equilibrium. Rev Mod Phys, 65(3), 851.
  • Destexhe, A. & Paré, D. (1999). Impact of network activity on neocortical pyramidal neurons. J Neurophysiol, 81(4), 1531–1547.
  • Dicke, R. H. (1954). Coherence in spontaneous radiation processes. Physical Review, 93(1), 99.
  • Engel, A. K., Fries, P. & Singer, W. (2001). Dynamic predictions: oscillations and synchrony in top-down processing. Nat Rev Neurosci, 2(10), 704–716.
  • Fries, P. et al. (2007). The gamma cycle. Trends Neurosci, 30(7), 309–316.
  • Haider, B. et al. (2006). Neocortical network activity in vivo. J Neurosci, 26, 4535–4545.
  • Hasenstaub, A. et al. (2005). Inhibitory postsynaptic potentials carry synchronized frequency information. Neuron, 47(3), 423–435.
  • Howard, A., inversion, & Bratholm, L. (2019). Predicting Molecular Properties. Kaggle Competition (CHAMPS). Available at: kaggle.com/competitions/champs-scalar-coupling
  • Izhikevich, E. M. (2007). Dynamical Systems in Neuroscience. MIT Press.
  • Kirton, P. et al. (2019). Introduction to the Dicke model. Adv Quantum Tech, 2(1–2), 1800043.
  • Omandac, C. (2026a–26c). [Prior Zenodo preprints]. DOIs: 10.5281/zenodo.18211554, 10.5281/zenodo.18212106, 10.5281/zenodo.18212128.
  • Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM J Res Dev, 5(3), 183–191.
  • Markram, H. et al. (2015). Reconstruction and simulation of neocortical microcircuitry. Cell, 163(2), 456–492.
  • Mohseni, M. et al. (2008). Environment-assisted quantum walks in photosynthetic energy transfer. J Chem Phys, 129(17), 174106.
  • National Oceanic and Atmospheric Administration (NOAA). HURDAT2: Atlantic and Pacific Hurricane Database (1851–2014). Available at: kaggle.com/datasets/noaa/hurricane-database
  • Olshausen, B. A. & Field, D. J. (2004). Sparse coding of sensory inputs. Curr Opin Neurobiol, 14(4), 481–487.
  • Penrose, R. & Hameroff, S. (1996). Orchestrated reduction of quantum coherence in brain microtubules. Math Comput Simul, 40(3–4), 453–480.
  • Plenio, M. B. & Huelga, S. F. (2008). Dephasing-assisted transport. New J Phys, 10(11), 113019. Prigogine, I. (1977). Self-Organization in Non-Equilibrium Systems. Wiley.
  • Rudolph, M. et al. (2005). A method to estimate synaptic conductances. J Neurophysiol, 94(1), 219–230.
  • Sachdev, S. (2011). Quantum Phase Transitions (2nd ed.). Cambridge University Press.
  • Schreiber, T. (2000). Measuring information transfer. Phys Rev Lett, 85(2), 461.
  • Singer, W. (1999). Neuronal synchrony: a versatile code for the definition of relations? Neuron, 24(1), 49–65.
  • Tononi, G. (2008). Consciousness as integrated information. Biol Bull, 215(3), 216–242.
  • Wang, X.-J. & Buzsáki, G. (1996). Gamma oscillation by synaptic inhibition. J Neurosci, 16(20), 6402–6413.
  • Whittington, M. A. et al. (2000). Inhibition-based rhythms. Int J Psychophysiol, 38(3), 315–336.
  • Andrea Cannata, ConcettoSpampinato, Flavio Cannavo, IsaakKavasidis, Maggie, and Sohier Dane. INGV - Volcanic Eruption Prediction. https://kaggle.com/competitions/predict-volcanic-eruptions-ingv-oe, 2020. Kaggle.
  • Nielsen, M. A. & Chuang, I. L. (2000). Quantum Computation and Quantum Information. Cambridge University Press.
  • Jaynes, E. T. (1957). Information theory and statistical mechanics. Physical Review, 106(4), 620–630. DOI: 10.1103/PhysRev.106.620.
  • Stringer, C. et al. (2019). Spontaneous behaviors drive multidimensional, brainwide activity. Science, 364(6437), eaav7893. DOI: 10.1126/science.aav7893.
  • Chennu, S. et al. (2016). Brain networks predict metabolism, diagnosis and prognosis at the bedside in disorders of consciousness. Brain, 140(8), 2120–2132. DOI: 10.1093/brain/awx163.
  • Kerzenmacher, T. & Braesicke, P. (2025). QBO Singapore Radiosonde Archive. Zenodo, DOI: 10.5281/zenodo.17055557.
  • Schmitt, J. et al. (2015). Spontaneous symmetry breaking and phase coherence of a photon Bose-Einstein condensate coupled to a reservoir. Physical Review Letters, 116(3), 033604.
  • Weill, R. et al. (2019). Temporal and spectral properties of photon BEC in a dye microcavity. Physical Review A, 99(1), 013841.
  • Toomey, J. P. & Kane, D. M. (2014). Mapping the dynamic complexity of a semiconductor laser with optical feedback using permutation entropy. Optics Express, 22(2), 1713–1725. DOI: 10.1364/OE.22.001713. [NOTE: Published 2014, not 2017 as cited in earlier versions.]
  • Diósi, L. (1987). A universal master equation for the gravitational violation of quantum mechanics. Physics Letters A, 120(8), 377–381. DOI: 10.1016/0375-9601(87)90681-5.
  • Penrose, R. (1996). On gravity's role in quantum state reduction. General Relativity and Gravitation, 28(5), 581–600. DOI: 10.1007/BF02105068.
  • Penrose, R. & Hameroff, S. (1996). Orchestrated reduction of quantum coherence in brain microtubules. Mathematics and Computers in Simulation, 40(3–4), 453–480.
  • Bassi, A. et al. (2013). Models of wave-function collapse, underlying theories, and experimental tests. Reviews of Modern Physics, 85(2), 471–527. DOI: 10.1103/RevModPhys.85.471.
  • Bateman, J. et al. (2014). Near-field interferometry of a free-falling nanoparticle from a point-like source. Nature Communications, 5, 4788. DOI: 10.1038/ncomms5788.
  • Fein, Y. Y. et al. (2019). Quantum superposition of molecules beyond 25 kDa. Nature Physics, 15, 1242–1245. DOI: 10.1038/s41567-019-0663-9.
  • Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. (2003). Towards quantum superpositions of a mirror. Physical Review Letters, 91(13), 130401. DOI: 10.1103/PhysRevLett.91.130401.
  • Romero-Isart, O. et al. (2011). Large quantum superpositions and interference of massive nanometer-sized objects. Physical Review Letters, 107(2), 020405. DOI: 10.1103/PhysRevLett.107.020405.
  • Vinante, A. et al. (2020). Narrowing the parameter space of collapse models with ultracold layered force sensors. Physical Review Letters, 125(10), 100404. DOI: 10.1103/PhysRevLett.125.100404.
  • Koide, Y. (1981). A fermion-boson composite model of quarks and leptons. Lettere al Nuovo Cimento, 34, 201–205.
  • Particle Data Group (2024). Review of Particle Physics. Physical Review D, 110, 030001.