Void Dynamics Model (VDM)

A background‑independent, metriplectic field theory unifying matter and forces from the Quantum Geometric Tensor, with an emergent causal cone and an epistemological J→M projection.

Lineage: AMN-->FUM-->VDM

---

Current Status: Active development.

Author: Justin K. Lietz
Contact: [email protected]
Zenodo Community: Void Dynamics Model

Created: August 9, 2025
Last Updated: November 30, 2025

This research is protected under a dual-license to foster open academic
research while ensuring commercial applications are aligned with the project's ethical principles.
Commercial use requires written permission from the author.

Patent pending on specific AI technology - See license file for full terms

🔥News

• November 30, 2025
  • Building a Void Lensing Cross Correlation Meter to predict the geometry of cosmological void interfaces as a part of the VDM unification roadmap, as I already have all the pieces in place.
• November 10, 2025
  • Published results from the Counterfactual Echo Gain test to Zenodo
• November 9, 2025
  • VDM will be upgrading to a dedicated custom physics engine that further enhances and improves scalability of the runner gating discipline, reporting, and automated unambiguous rule enforcement. This is being built into a fork of Void IDE as a code editor / computational physics lab.
• November 6, 2025
  • 7 complete formalisms have been derived for VDM and documented as some of the final remaining pieces in the work to T8 Axiom 8 candidate.
• November 4, 2025
  • Assisted‑Echo T4 (prereg v1c) rerun with instrument + plotting fixes:
    • Per‑seed plotting for A2/A5/B11 removes cross‑seed “seed‑chord” artifacts in overlays (error, ΔΣ, λ‑telemetry).
    • Noether (G1) tolerance scaled to instrument level: tol = max(1e-12, 10·eps·√N·max(h0,1)); routing remains governed by G1–G4 aggregation.
    • Reruns launched for N∈{512,1024}, dt∈{0.01,0.02,0.04}. Early results: N=512 dt=0.01 and N=512 walker dt=0.02 routed to main outputs with G1–G4 PASS; dt=0.04 routed to failed_runs pending CFL tightening.
    • Artifacts (PNG/CSV/JSON + figure packs) under Derivation/code/outputs/{figures,logs}/metriplectic, tag: assisted-echo-t4-prereg-v1c.
  • Next: upgrade G4 measurement to a multi‑point Δt fit (same thresholds) to harden RP‑1 decisions.
• November 1, 2025
  • Published early draft of the proposed A8 Axiom candidate to Zenodo for provenance.
• October 31, 2025
  • Added a T8 grade proposal for a new Axiom candidate as A8 - Lietz Infinity Conjecture which provides an elegant explanation for hierarchy and structure.
• October 30, 2025
  • Added a historical/ folder including early original work like:
    • A self healing knowledge graph using Topological Data Analysis
    • As well as a Self Improvement Engine that integrates multiple reward components like novelty, self benefit, habituation, and TD error into a single "total reward" signal used to modulate its own neural plasticity for stable self-improvement that avoids weight saturation.
  • Validated the Counterfactual Echo Gain hypothesis by proving the trustworthiness and accuracy of the instrument, and showing that echo assist does modulate and improve the performance of a self aware system with 0 difference in cost compared to baseline.
• October 28, 2025
  • Published an article on Medium about upcoming work.
    • Published a "The Physics of Choice" video, along with a couple other videos on YouTube.
• October 23, 2025:
  • Created a sparsely populated CANON_PROGRESS.md document to post updates on private work to prevent this public repo from going stale.
• September 29, 2025:
  • First public code release + creation of private Void Dynamics package which can now be imported and run in this repository using workflows and repository secrets.
• September 28, 2025:
  • Posted two pre-prints to Zenodo. If you've published similar or relevant work on Reaction-Diffusion in the past 3 years on arXiv and want to support this work by endorsing me in a related category, submit an issue, post in the discussion board, or send me an email with Subject: RD Endorsement to get my attention. It would be much appreciated!
• August 21, 2025: Launched public repo
• ...
• March, 2025
  • Released first falsifiable, reproducible simulations that validated initial claims.
• February, 2025
  • SIE and Emergent KG + Real-Time TDA show very strong statistically significant findings, making feasible the entire model
• October, 2024
  • Initial realization of the idea.

🗺️ Roadmap (Oct~Dec 2025)

• TLDR:

  1. Finishing a few algebraic proofs (CF1/QGT, Schrödingerization, T^μν_void).
  2. Converting more of the cosmology/gauge scaffolds into RESULTS documents tied to real or mock data.
  3. Packaging some of the chains (e.g., “metriplectic engine”, “A8 hierarchy → FRW”, “spinor+gauge emergence”) into stand‑alone papers.

• Unifying the VDM foundation

  • Stabilize Complete Formalism (CF*) ladder prerequisites ☑️
  • Void-lensing interface program (highest priority) ☑️
  • Lattice fields & continuum limits (CF10) ☑️
  • CMB polarization birefringence gate ☑️
  • Quantum Geometric Tensor to Metriplectic Brackets formalism ✅
  • Contact Geometry to Metripliplectic Evolution formalism ✅
  • Axiom 8 - Lietz Infinity Resolution Conjecture (Hierarchical Tachyonic Interfaces) ✅
  • Telegraph-Fisher Causality formalism (Finite-Speed Transport) ✅
  • Integrability Closure formalism (No hidden conserved quantities) ✅
  • Information Geometry Foundations — Fisher and Ruppeiner Metrics for VDM M-Limb ✅
  • Measurement Theory Foundations — Decoherence and Born Rule for VDM ✅
  • Spinor Emergence via Domain-Wall Fermions in VDM formalism ✅
  • Gauge Field Emergence via Berry Connection in VDM formalism ✅
  • VDM Lattice Hydrodynamics, Continuum Limit, and Regularity Program formalism ✅
  • Define the objects and rules everything else must obey. ✅
  • Start from quantum geometry and show why a J⊕M evolution is forced ✅
    • Finish CF1: explicit formulae for 𝓘[Ψ] and Σ[Ψ] from QGT; prove metriplectic brackets satisfy A4. ☑️
    • Close Schrödingerization proof to show “J⊕M is a shadow of pure J” in extended space. ☑️
  • Prove that a scalar lattice with J⊕M really behaves like the void field ✅
    • Package this into one “VDM metriplectic engine” paper (KG + RD + structure + Strang). I already have all the results; this is mostly editorial. ☑️
  • Explain why nothing outruns c, starting from RD‑like flows. ✅
    • Finish a RESULTS doc for Causal‑DAG audit on the KG / RD sims to empirically show: inferred cone ≈ analytic cone ☑️
  • Go from smooth void to structured interfaces (proto‑“lumps” / material features). ✅
    • One clean A8→FRW bridge paper: “tachyonic interfaces → effective ρ(a), p(a), H(a)” with explicit EOS fits ☑️
  • Turn the scalar lattice into fermionic matter degrees of freedom. ✅
    • Companion CF8 notebook with an explicit domain‑wall spectrum plot and residual mass scaling ~ e^{-λL₅} ☑️
  • Get Maxwell/Yang–Mills fields as geometry, not extra particles. ✅
    • Compute Berry curvatures from an explicit CF8 lattice model, show emergent U(1) field satisfies the Maxwell‑like equations in the long‑wavelength limit ☑️
    • Extend the formalism in H0XX into at least one concrete SU(2) toy example ☑️
  • Treat the plastic lattice + A8 hierarchy as the “dark sector” ✅
    • Define an explicit “lattice stress–energy tensor” T^μν_void[Φ] and show: ☑️
      • homogeneous part → dark‑energy‑like EOS ☑️
      • hierarchical clumping → halo‑like effective DM (at least in 1D/2D) ☑️
    • Frame a pilot SkyrmeSIDM × VDM test using the T5 proposal ☑️
  • From lattice stress–energy to something GR‑like in weak field, then test ringdown / horizons. ✅
    • Weak‑field: derive an effective Poisson equation for small lattice perturbations; fit to rotation curves / lensing in at least one toy halo ☑️
    • Strong‑field: show that certain tachyonic interface configurations behave like horizon‑like regions (redshift, QNM spectrum) and compare to GR ringdown data via the ringdown meter ☑️
  • Connect A8 + metriplectic dynamics to the 0.55 packing motif (proteins, random close packing, etc.). ✅
    • A small CF‑level derivation: show a simple metriplectic packing model tends toward ϕ≈0.55 in 2D/3D random packing (e.g., via Monte Carlo or granular‑like sim) ☑️
    • Explicit link from A8 interfaces + reaction‑diffusion morphogenesis → “prebiotic” cluster statistics ☑️
  • Use the same machinery to hit the standard checklist: SM fields, BH population, CMB, etc. ✅
    • For each H*/T* cosmology doc: at least one concrete meter/RESULTS file that touches real data (CMB, LSS, ringdown, BH mass function, etc.) even in toy form ☑️

• Notebook mirrors of each test ☑️

• 100% Reproducible, falsifiable claims ✅

• Currently working real time, zero training, self driven model ☑️

• Online causality based learning ✅

• Physics driven intelligence ✅

DOIs

T4. Counterfactual Echo Gain (CEG): A Metriplectic Assisted-Echo Experiment Proposal in VDM

T8. Axiom 8 Candidate: The Lietz Infinity Resolution Conjecture

A Logarithmic First Integral for the Logistic On Site Law in Void Dynamics

---

❗NOTE

This organization is currently managed and operated by me (J. Lietz) alone as a solo developer / researcher. I may not respond by email right away. If you want to get my attention post in the discussion board briefly about what you'd like to talk about and let me know you sent me an email.

💬Discussion Board:

• https://github.com/orgs/Neuroca-Inc/discussions

---

🧭What this is

This repository provides a public view of the Void Dynamics Model. It includes the theory, write-ups, code, notebooks, figures, logs, and validations for review by physicists, applied mathematicians, learners, students, and scientifically minded engineers.
Reproducible code released for the public is now available. Remaining proprietary work must be requested directly.

• A set of derivation papers that establish a clean baseline physics slice starting from a discrete lattice, to a metriplectic split and cosmology.
• Additional documents that explore future work (proposals).
• Each paper separates what is proven from what is plausible or speculative and, where applicable, includes acceptance criteria for simple numerical checks.

🤖 Physics-Informed Cognitive Architecture

Origin: AI Cognition First, Physics Formalized Later

The vdm_rt/ runtime was technically not designed from physics first principles. The development sequence:

Date	Milestone
March 2025	Designed cognitive architecture for human-like learning, reasoning, memory, and reaction. Validated Self-Improvement Engine (SIE) and self-organizing, self-healing topological knowledge graph as components.
March–June 2025	Iterative development and parts testing
June 2025	Complete model built and running
July 2025	Observed unexpected behaviors and better than expected global stability—the system self-organized regardless of perturbations. Began investigating the mathematical structure.
August 2025	Formalized the discovered structure as the Void Dynamics Model (VDM)
August–November 2025	Physics derivation program: Complete Formalisms (CF1–CF10), axiom formalization (A0–A7, A8 candidate), validation gates

Post-hoc mathematical analysis of the cognitive architecture revealed it satisfied metriplectic structure. The Complete Formalisms document the rigorous mathematics; this section maps the runtime modules to those derivations.

---

The Metriplectic Structure (A4)

From AXIOMS.md § A4:

Statement: With state $q \equiv (\Psi, \partial\Psi, \ldots)$, $$\partial_t q = J(q),\frac{\delta \mathcal{I}}{\delta q} + M(q),\frac{\delta \Sigma}{\delta q}$$ with $J^\top = -J$ (skew/symplectic), $M^\top = M \geq 0$ (symmetric/metric), and degeneracies $J,\frac{\delta\Sigma}{\delta q} = 0$, $M,\frac{\delta\mathcal{I}}{\delta q} = 0$.

Notes: Canonical split used by metriplectic integrators and QC (two-grid order, Strang-defect, J-only reversibility). Diagnostics: compute $g_1 = \langle J, \delta\Sigma, \delta\Sigma \rangle$ and $g_2 = \langle M, \delta\mathcal{I}, \delta\mathcal{I} \rangle$ every $K$ steps; both must be $\leq 10^{-10}$ (grid-refined).

Source: Implemented/validated in ALGORITHMS.md (VDM-A-013..019) and corresponding runners.

Runtime mapping:

Code Module	LOC	A4 Component
vdm_rt/core/engine/core_engine.py	532	J⊕M composition per tick
vdm_rt/core/guards/invariants.py	305	Degeneracy diagnostics ($g_1$, $g_2 \leq 10^{-10}$)

---

QGT to Metriplectic Brackets (CF1)

Status: Complete Derivation
Document: CF01_QGT_to_Metriplectic_Brackets.md

From CF1 Executive Summary:

This document provides a complete, rigorous derivation of the mapping from the Quantum Geometric Tensor (QGT) to metriplectic bracket structures ${\cdot,\cdot}_J$ and $(\cdot,\cdot)_M$ in the VDM framework. The derivation establishes:

1. Berry curvature $\Omega_{\mu\nu}$ (antisymmetric part of QGT) → J-bracket (Poisson/symplectic structure)
2. Quantum metric $g_{\mu\nu}$ (symmetric part of QGT) → M-bracket (Riemannian/metric structure)
3. Constructive algorithm for computing QGT from parameter-dependent eigenstates
4. Classical limit $\hbar \to 0$ showing emergence of continuous metriplectic flow

QGT decomposition (CF1 § 1.2, VDM-E-109):

$$ Q_{\mu\nu} = g_{\mu\nu} - \frac{i}{2}\Omega_{\mu\nu} $$

Walker routing correspondence:

The void walker softmax routing:

$$ \text{logit}_j = \theta_{\text{mem}} \cdot m[j] - \rho_{\text{trail}} \cdot h_{\text{trail}}[j] + \gamma_{\text{heat}} \cdot h[j], \quad P(i \to j) \propto \exp(\text{logit}_j / \tau) $$

Routing Parameter	QGT Component	CF1 Section
θ_mem (memory steering)	Berry curvature $\Omega_{\mu\nu}$	§ 2.3
ρ_trail (trail repulsion)	Quantum metric $g_{\mu\nu}$	§ 3.3

Walker implementations (vdm_rt/core/cortex/void_walkers/, 2000+ LOC): HeatScout, MemoryRayScout, VoidRayScout, FrontierScout, SentinelScout, CycleHunterScout, ExcitationScout, InhibitionScout

---

Telegraph-Fisher Causality (CF4)

Status: Complete Derivation
Document: CF04_Telegraph_Fisher_Causality.md

From CF4 Executive Summary:

This document provides a complete, rigorous derivation of the telegraph equation and finite-speed transport in reaction-diffusion systems within the VDM framework. The derivation establishes:

1. Cattaneo-Vernotte equation from relaxation of Fourier's law
2. Telegraph equation emergence from second-order time derivatives
3. Speed bound $c = \sqrt{D/\tau}$ relating diffusivity $D$ and relaxation time $\tau$
4. Finite propagation theorem proving causal transport with light-cone structure
5. Fisher-information connection to measurement bounds

Void debt throttling (CF4 § 7.2, VDM-E-106):

$$ c_{\text{eff}} = c_0 , e^{-\beta D_{\text{void}}/2}, \quad \tau_{\text{eff}} = \tau_0 , e^{\beta D_{\text{void}}} $$

Physical Mechanism: Interfaces (void boundaries) increase scattering → longer relaxation → slower transport.

Code Module	LOC	CF4 Component
vdm_rt/core/Void_Debt_Modulation.py	136	Domain-specific $c_{\text{eff}}$ calculation
vdm_rt/core/substrate/fum_growth_arbiter.py	148	Stability-gated growth via void debt

---

Universal Void Dynamics

Plasticity equation:

$$ \Delta W_{ij} = \alpha W_{ij}(1 - W_{ij}) - \beta W_{ij} $$

Constants (from CONSTANTS.md):

• ALPHA = 0.25 (RE-VGSP learning rate)
• BETA = 0.1 (GDSP plasticity rate)

Code Module	LOC	Component
vdm_rt/core/neuroplasticity/revgsp.py	319	RE-VGSP ($\alpha$-term)
vdm_rt/core/neuroplasticity/gdsp.py	531	GDSP ($\beta$-term)
vdm_rt/core/Void_Equations.py	107	Combined dispatcher

---

A8 Lietz Infinity Resolution Conjecture

Status: CANDIDATE (awaiting T8 PASS)
Document: AXIOMS.md § A8

Statement (exact):

In metriplectic scalar-field systems with tachyonic origin $V''(0) < 0$ that admit pulled fronts with exponential tails, any finite-excess-energy large-domain trajectory must organize into a finite-depth hierarchical partition with logarithmic depth $N(L) = \Theta(\log(L/\lambda))$, scale-gap separation $\rho \in (\rho_{\min}, \rho_{\max})$, and boundary energy/information concentration fractions $\alpha, \alpha_{\mathcal{I}} > 0$.

Promotion rule: On PROPOSAL T8 PASS (G1–G8), copy this statement verbatim into Canon/AXIOMS.md as A8, update status here to ACCEPTED, and archive artifacts under Derivation/code/outputs/axioms/a8_infinity_resolution/.

Runtime modules related to A8:

Code Module	LOC	A8 Connection
vdm_rt/core/void_b1.py	377	Topological complexity (cycles, Euler rank, $B_1$ proxy)
vdm_rt/core/adc.py	205	Active Domain Cartography—boundary tracking
vdm_rt/core/sparse_connectome.py	706	Hierarchical sparse adjacency

---

Self-Improvement Engine

Implementation: vdm_rt/core/fum_sie.py (298 LOC)

Valence computation:

$$ \text{valence} = w_{\text{TD}} \cdot \delta_{\text{TD}} + w_{\text{nov}} \cdot N(s) + w_{\text{self}} \cdot (1 - \rho) $$

Component	Metriplectic Interpretation
TD error ($\delta_{\text{TD}}$)	Information functional $\mathcal{I}$
Novelty with habituation ($N(s)$)	Entropy functional $\Sigma$
Stabilized reward (valence)	Free energy $F = \mathcal{I} - T\Sigma$

---

Event-Driven Memory

Map Type	Code Module	LOC
MemoryField	vdm_rt/core/memory/field.py	362
HeatMap	vdm_rt/core/cortex/maps/heat_map.py	79
ColdMap	vdm_rt/core/cortex/maps/cold_map.py	174
TrailMap	vdm_rt/core/cortex/maps/trail_map.py	111

---

Design Invariants

Constraint	Implementation	Axiom Reference
Sparse operations only	CSR format throughout	A2 (Locality)
Event-local updates	No global state reads	A2 (Local Causality)
O(budget) per tick	Microsecond time budgets	A2 (Finite propagation)
Conservation tracking	Per-tick drift checks	A3 (Noether drift $\leq 10^{-8}$)
Entropy non-decrease	Gate on M-updates	A5 (Entropy Law)

---

Historical Documentation

• March 2025 SIE validation: docs/historical/SIE/
• Emergent TDA (self-healing graphs): docs/historical/Emergent_TDA/

---

vdm_rt Code Summary

Component	Files	LOC
Core dynamics	4	~486
Engine	3	~700
Cortex (walkers + maps)	15+	~2500
Memory	2	~500
Neuroplasticity	2	~850
Substrate	3	~550
Topology	2	~580
Total	81	~13,200

⚖️Licensing and scope

• These materials are shared for academic review and discussion. Commercial use requires prior written permission. See the project’s license notice in the distribution or parent repository materials.
• I reserve all legal rights to ownership of any custom or proprietary assets.
• The scope stays within theoretical physics and simulation. Broad cosmological claims are withheld or clearly labeled until backed by derivation + numeric checks.

🔖Citations

• When referencing specific results, cite the overview and the relevant validation paper, for example:
  • VDM_Overview.md
  • rd_front_speed_validation.md
  • rd_dispersion_validation.md

📫Contact

• For scope questions or clarifications about acceptance criteria, refer to the headers in the overview and topic files listed above. If you are reading this as part of a paper-only bundle, the maintainer’s contact is provided alongside the distribution materials.