non-hermitian-conscious-preconscious-subliminal

name	non-hermitian-conscious-preconscious-subliminal
description	Non-Hermitian Potential Well Formalism for Conscious-Preconscious-Subliminal Processing methodology. Models the Global Neuronal Workspace (GNW) as a complex-valued landscape where sensory encoding and conscious access are unified. Activation: non-Hermitian consciousness, GNW landscape, conscious preconscious subliminal, potential well consciousness, complex-valued GNW, non-Hermitian Hamiltonian consciousness.
version	1.0.0
author	Hermes Agent
license	MIT
metadata	{"hermes":{"tags":["neuroscience","consciousness","GNW","non-Hermitian","quantum-analogy"],"trigger_words":["non-Hermitian consciousness","GNW landscape","conscious preconscious subliminal","potential well consciousness","complex-valued GNW","non-Hermitian Hamiltonian consciousness"]},"source":"arXiv:2607.08302"}

Non-Hermitian Conscious-Preconscious-Subliminal Processing

Description

Phenomenological model of the Global Neuronal Workspace (GNW) using a non-Hermitian, non-normal Hamiltonian framework with complex-valued potential landscape dynamics. Provides a unified dynamical description linking sensory processing, attention, and conscious access.

Source: arXiv:2607.08302 (Lubashevskiy & Lubashevsky, 2026-07-09)

Activation Keywords

• non-Hermitian consciousness
• GNW landscape
• conscious preconscious subliminal
• potential well consciousness
• complex-valued GNW
• non-Hermitian Hamiltonian consciousness
• 非厄米特意识模型
• 全局神经元工作空间势阱

Core Framework

1. Complex-Valued GNW Landscape

The model defines a complex-valued effective potential landscape over a perceptual state space:

• State space: Hilbert space over perceptual states
• Cloud function: Encodes high-level stimulus representations, combining holistic mental image structure with neural implementation
• Landscape: Generated by early sensory processing, governing dynamics of representations

2. Governing Dynamics

The dynamics is governed by a nonlinear Schrödinger-type equation in imaginary time:

iℏ ∂ψ/∂t = H ψ + nonlinear terms

Where the Hamiltonian H is non-Hermitian and non-normal, decomposed into:

• Hermitian part (H† = H): Recognition via dissipative localization at landscape minima
• Anti-Hermitian part (H† = -H): Information broadcasting via spatial spreading across state space

The nonlinear Lotka-Volterra-type term preserves norm and enables spatially nonlocal interactions.

3. Subliminal → Preconscious → Conscious Hierarchy

The model naturally reproduces the three-tier processing hierarchy:

Level	Dynamics	Condition
Subliminal	Weakly localized, dissipative	Below both thresholds
Preconscious	Intermediate localization	One threshold exceeded
Conscious	Bound state emergence	Both landscape depth AND top-down attention exceed thresholds

4. Conscious Access as Bound State

Key insight: Conscious access corresponds to the emergence of a bound state in the complex potential well. This requires:

1. GNW landscape depth ≥ threshold (bottom-up signal strength)
2. Top-down attention ≥ threshold (attentional amplification)

Both must be satisfied simultaneously — explaining why weak stimuli require attention to reach consciousness.

5. Complementary Processes

The Hermitian and anti-Hermitian parts generate complementary processes:

• Recognition (Hermitian): Dissipative localization → pattern identification
• Broadcasting (anti-Hermitian): Spatial spreading → global availability (GNW "ignition")

Mathematical Structure

Hilbert Space Formulation

• Perceptual state space → Hilbert space structure
• Cloud function ψ(x,t) encodes mental representations
• Non-Hermitian Hamiltonian H = H_hermitian + H_antihermitian

Nonlinear Schrödinger Equation

∂ψ/∂t = -(i/ℏ)Hψ + NL(ψ)

Where NL(ψ) is the Lotka-Volterra nonlinear term preserving ||ψ||².

Bound State Criterion

Conscious access occurs when:

• Landscape depth V₀ > V_critical
• Attention parameter A > A_critical
• Both conditions satisfied simultaneously → bound state emerges

Novelty & Contributions

1. First unified GNW dynamics: Links sensory encoding and conscious access in single framework
2. Complex-valued landscape: Novel effective potential formalism for consciousness
3. Non-Hermitian quantum analogy: Uses non-normal Hamiltonian structure for complementary recognition/broadcasting
4. Tractable dynamics: Provides mathematically tractable description of consciousness transitions
5. Threshold mechanism: Explains conscious access as bound state emergence

Applications

• Modeling conscious access transitions
• Studying attention-consciousness interactions
• Understanding subliminal vs supraliminal processing
• Building computational models of GNW
• Analyzing disorders of consciousness

Related Work

• Global Neuronal Workspace (GNW) theory (Dehaene et al.)
• Non-Hermitian quantum mechanics
• Neural field theories
• Consciousness theories (IIT, HOT, etc.)
• Schrödinger-type neural models

Limitations

• Phenomenological model — not derived from first principles
• Requires empirical validation of landscape parameters
• Complex-valued formalism may be mathematically challenging to simulate
• Bound state criterion needs experimental testing

References

• arXiv:2607.08302 — "A Non-Hermitian Potential Well Formalism for Conscious--Preconscious--Subliminal Processing"
• Authors: Vasily Lubashevskiy, Ihor Lubashevsky
• Categories: q-bio.NC, nlin.AO
• Submitted: 2026-07-09

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Last updated: 2026-07-12