Meta-Topological Evolution: 6 Path Dependence and Irreversibility

After meta-cascade recomposition (Post 5), the horizon is not blank.

It bears structural memory: prior density, couplings, and constraints influence the future evolution of the topology.

This post analyses how path dependence arises and how partial irreversibility shapes horizon dynamics.

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1. Structural Memory in Horizons

Key observation:

• Horizons preserve the traces of past condensations and meta-cascades.

• Some adjacency relations, once stabilised, cannot revert without destabilising the horizon.

• Feasible trajectories are thus contingent on previous horizon configurations.

This is structural memory, not narrative memory:

• It is embedded in invariants, constraints, and meta-condensations.

• It governs future structural possibilities.

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2. Path Dependence Mechanisms

Several mechanisms generate path dependence:

1. Meta-Cascade Anchoring – Certain clusters anchor the recomposed horizon, preventing wholesale reversal.

2. Dimensional Ratcheting – Newly stabilised axes of adjacency resist contraction due to structural incompatibility.

3. Cross-Scale Reinforcement – Interdependencies propagate stability through hybrid condensations.

4. Constraint Saturation Residue – Saturated paths maintain pressure, influencing subsequent condensation.

These mechanisms bias the horizon’s evolution, not determine it absolutely.

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3. Conditional Irreversibility

Irreversibility is context-dependent:

• Some structural changes are reversible if local density decreases or meta-cascades reorganise.

• Other shifts are effectively locked in, due to path-dependent reinforcement and cross-scale stabilisation.

• The horizon is partially irreversible, producing ratcheted evolution without teleology.

This is consistent with layered continuity: local changes remain flexible, global topology is constrained.

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4. Long-Term Implications

Path dependence affects future horizon evolution:

• Structural constraints channel feasible trajectories.

• Emergent degrees of freedom from prior recompositions bias the direction of new meta-cascades.

• The horizon’s capacity to evolve is conditioned by its own history.

In other words: evolution of the horizon is lawfully constrained by its prior states.

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5. Conceptual Summary

Path dependence and irreversibility demonstrate that:

1. Horizon evolution is not memoryless.

2. Structural ratchets form naturally through accumulated density and recomposition.

3. Feasible trajectories are contingent on prior topologies.

4. Local continuity coexists with partial global irreversibility.

5. Horizon evolution remains lawful, intelligible, and non-mystical.

This allows us to link the mechanics of recomposition to long arcs of meta-topological evolution.

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6. Next Step

Next post:

Post 7 — Predicting Horizon Shifts

Here we ask:

• Are meta-topological transitions diagnosable?

• Can structural precursors forecast recomposition?

• How can we conceptually anticipate dimensional expansion or grammar reparameterisation?

This will close the series, connecting meta-topological dynamics back to Lawful Generativity.