Experience Binding — PPM Framework Demonstration¶

A phenomenal moment is the joint extraction of content from a synchronized population of τ-firing sites cast in a common measurement frame (Ontology Ch. 20, §The Unity of a Phenomenal Moment). Within a single τ-event, unity is intrinsic: the V₄ partition delivers all four fact types — Kähler doublet {A spectral, B spatial} and gauge doublet {C chiral, D intensity} — co-extracted in one projection, with no binding step required.

Unity across events is where the binding question lives. A spatially-connected population of τ-firings falling within one integration window fuses into a single collective actualization only if the population is cast in a common projective frame. The measurement torus T² = [0, π/2]² parameterizes that frame: θ = (θ_AB, θ_CD) selects the viewing angle through V₄ at which the population reads out content. Sub-streams that converge on the same θ extract jointly; sub-streams that pick different θ extract independently and produce no shared content.

The demonstration. N sub-stream agents search T² for the θ that resolves a hidden signal mixed into the four V₄ channels. Each agent sees an independently-noisy copy. One group is bound — coupled through shared environment via a consensus pull on θ that mimics the synchronizing couplings of an integrated boundary. The other group is severed — identical agents, identical noise, no coupling. The bound population converges to a common θ and reads the signal jointly; the severed population scatters and doesn't.

The signal-resolution gap is the adaptive advantage of binding: populations that share a measurement frame extract content that no individual sub-stream has the signal-to-noise ratio to track alone. Biology exploits the mechanism rather than constructing it.

Adjust the parameters and run the simulation.

What the dynamics look like¶

Recorded animation: N = 4 witnesses, coupling α = 0.6, noise σ = 1.2. Bound agents lock onto a shared θ together while severed agents drift independently. The slider defaults below match this run — adjust to explore other regimes.

Parameters¶

Set the conditions and run the simulation.

• Witnesses (N) — sub-streams per group.
• Coupling α — strength of the consensus pull on θ for the bound group. α = 0 reproduces the severed group; α = 1 is maximally coupled.
• Per-witness noise σ — channel noise on each sub-stream's observations. Higher noise widens the resolution gap binding closes.
• Late-stage learning floor (η_floor) — minimum descent rate after the annealing schedule. Higher reaches θ* faster but jitters at the endpoint.
• Duration — number of time steps.
• Show severed group — uncheck to render only the bound population.

What to watch¶

• θ search on T² (top center). Blue (bound) agents should converge together toward the gold star at θ*. Orange (severed) agents scatter and don't reach it. The V₄ corners label the Kähler/gauge cell pairings available at the edges of the torus.
• Per-agent |θ − θ*| (top right). Bound traces fall together; severed traces stay higher and stay spread. The gap between the bold means is the signal-resolution advantage of binding.
• Projected view (bottom left). The bold blue line is the joint extraction through the bound population's shared θ — it tracks the dashed hidden signal. The faint orange lines are severed agents each reading the channels through a private θ; their views fragment.
• Cluster tightness (bottom center, dashed). The maximum θ-spread across the population. For the bound group it collapses toward zero as the population locks onto a common frame; for the severed group it stays high.

Knobs worth turning¶

• Set α = 0 and the bound group reduces to the severed group — no consensus pull, no shared frame, both populations fail.
• Increase noise σ. Severed performance degrades fast; the bound population degrades slowly because the shared frame pools the channel information across sub-streams.
• Raise η_floor to reach θ* faster at the cost of endpoint jitter; lower it to see the slow trickle a stricter annealing schedule produces.