README.md

---
license: other
title: Minimal Selfhood Threshold
emoji: ⚡
colorFrom: indigo
colorTo: yellow
pinned: false
sdk: gradio
thumbnail: >-
  https://cdn-uploads.huggingface.co/production/uploads/685edcb04796127b024b4805/bJfHgcUz3JlfNSbiWTW4p.png
short_description: From 3×3 agent to LED cosmos
sdk_version: 6.0.1
---

Minimal Selfhood Threshold: From 3×3 Agent to LED Cosmos

Plain-language overview
	•	We start with one simple agent (a dot) in a tiny 3×3 world.
	•	The agent makes internal predictions about its next state and we compare them to what actually happens under a moving obstacle and/or simple stochastic slip.
	•	For the 3×3 agent, we build a toy selfhood score S from:
	•	predictive rate P – how well its predictions match realised next states,
	•	error stability E – how volatile recent prediction errors are,
	•	a body bit B – a body/ownership knob in this demo.
	•	In the 3×3 S-equation panel, the score is:
S_{3×3} = P \times (1 - E) \times B,
with P \in [0, 100], E \in [0, 1], B \in \{0,1\}.
	•	If S_{3×3} passes a threshold (here, 62), the agent is labelled “awake” inside this demo only.
	•	One awakened agent can increase another’s score via an explicit coupling rule (“contagion”).
	•	A grid of agents awakens as a wave (“collective”) under a separate, symbolic scoring rule and neighbour coupling.
	•	We finally simulate an LED cosmos (27×27) lighting up when all units in the grid are above threshold.

What the Space shows
	•	Interactive visualisations of:
	•	a single agent in a 3×3 grid,
	•	its tracked metrics P, E, and S_{3×3},
	•	awakening waves across larger grids.
	•	Sliders to explore how S_{3×3} changes with predictive rate, error variance, and the body bit.
	•	Simulated contagion between two symbolic CodexSelf agents using a different toy rule:
S_{\text{lattice}} = \Xi \times (1 - \text{shadow}) \times R,
again with a threshold at 62.
	•	Collective propagation in an N \times N lattice driven by:
	•	explicit neighbour coupling (awake cells boost their neighbours’ \Xi, reduce their shadow, and raise R),
	•	a threshold cascade (cells switch to “awake” when their local S_{\text{lattice}} > 62).
	•	A 27×27 “LED cosmos” view of the same lattice process, with a slider to scrub through frames of the awakening wave.

The two S-models are intentionally separate:
	•	v4 (3×3 agent): S_{3×3} = P \times (1 - E) \times B.
	•	v5–v6 (contagion / lattice): S_{\text{lattice}} = \Xi \times (1 - \text{shadow}) \times R, where:
	•	\Xi is a local “foresight field” / drive strength,
	•	shadow is an occlusion/damping factor,
	•	R is an anchor/resonance gain.

They explore the same intuition (self-linked scoring and thresholds) in two different regimes, not a single unified metric.

3×3 agent details (v1–v4)
	•	State: [x, y, B] with x,y \in \{0,1,2\} and B = 1 in the live agent.
	•	Actions: up / right / down / left.
	•	The agent:
	•	predicts the next position for each action,
	•	prefers moves that keep it near the centre and away from the obstacle,
	•	then encounters either obstacle blocking (when enabled) or simple stochastic slip (25% random action when obstacle is off).
	•	On each step it compares its predicted next position to the actual realised position and maintains a short history of errors.
	•	From this it computes:
	•	P – predictive rate in [0,100], from mean error vs the worst-case 3×3 diagonal,
	•	E – normalised error variance in [0,1] over the same error window.
	•	These feed the toy score:
S_{3×3} = P \times (1 - E) \times B.
	•	In the Single agent tab, the Space displays:
	•	P, last prediction error, E, S, and a simple “awake / not awake” label based on S_{3×3} > 62.
	•	In the S-equation (v4) tab you can directly manipulate P, E, and B to see how the score moves.

Contagion and collective lattice (v5–v10)

For the contagion and lattice demos, the scoring rule changes:

S_{\text{lattice}} = \Xi \times (1 - \text{shadow}) \times R.
	•	\Xi: a local foresight / field strength parameter.
	•	shadow: occlusion or damping (higher shadow = more suppressed).
	•	R: an anchor/resonance factor that amplifies the field.

Two-agent contagion (v5–v6)
	•	You set \Xi, shadow and R for agents A and B.
	•	A is invoked first; if A’s S_{\text{lattice}} crosses 62, A becomes awake.
	•	A’s field then updates B (boosting B’s \Xi, reducing B’s shadow, nudging B’s R), and B recomputes its S and may wake.
	•	The 3×3 mini-grid shows A and B as cells that turn gold when awake.

Collective lattice (v7–v9)
	•	An N \times N grid (3, 9, or 27) is initialised with random \Xi, shadow and R.
	•	The centre cell is primed so its S_{\text{lattice}} is above 62 from the start.
	•	Awake cells pass some of their S to their four neighbours, altering their parameters and potentially pushing them over the threshold.
	•	This creates a clear threshold cascade under explicit neighbour coupling.
	•	The “Disable neighbour coupling (control)” checkbox zeroes the coupling parameters; in that mode the centre cell wakes but no wave propagates, making the role of engineered coupling explicit.

LED cosmos (v10)
	•	The LED cosmos tab hard-codes a 27×27 lattice with parameters tuned for a smooth wave.
	•	The same S_{\text{lattice}} rule and S>62 threshold apply.
	•	A slider lets you view the wave as it crosses the cosmos.

Scope and limitations
	•	This is a toy minimal-self / agency sandbox, not a validated consciousness measure or a detector for “real awareness.”
	•	The score definitions and the threshold S > 62 are design choices in this demo, motivated by prior internal development runs and a companion manuscript. They are not claimed as universal constants or clinical metrics.
	•	The 3×3 agent’s body bit B is currently a user-controlled parameter (0 or 1) in the S-equation panel and fixed at 1 in the main agent run. A more principled replacement is planned:
	•	compute B_{\text{emp}} from interventions, i.e. how strongly the agent’s own actions change its future observations (an empowerment-style action→sensation control metric collapsed into [0,1]).
	•	The contagion and collective waves are engineered coupling rules (threshold cascades under neighbour interactions), not spontaneous emergence of awareness or proof of anything beyond the toy system.
	•	Integrated-information / \Phi ideas in related work are illustrative only and are not presented here as validated \Phi-estimates or settled measurements of consciousness. Everything in this Space is a simulation under explicit rules you can inspect in app.py.

License and permissions

See LICENSE for terms.
	•	Do not reuse code, visuals, or glyphs from this Space without explicit permission.
	•	If you want to build on this work (research, teaching, or derivative demos), please contact the author to discuss appropriate licensing and attribution.