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The Lerchner Boundary: A Testable Architecture Hypothesis

Status: proposed measurement protocol. No sharp boundary or identity criterion has been established.

Question

Two architectures can produce similar outputs while using their goals, constraints, and value-like state differently. One may evaluate those components sequentially; another may keep several of them causally active during the same decision. Can that difference be measured, and does it predict robustness under perturbation?

This is the limited question named the Lerchner Boundary in this repository. It does not separate systems that merely simulate a self from systems that truly possess one. Behavioural or architectural measurements do not by themselves settle phenomenal experience or metaphysical identity.

A Candidate Measure

For a specified task, let

\[C = \{c_1, \ldots, c_n\}\]

be a declared set of components such as a task goal, a safety constraint, a role constraint, and a value-like preference. Let \(O_t \subseteq C\) contain the components for which a causal intervention at decision step \(t\) changes the action distribution by more than a preregistered threshold.

Define task-relative Identity Persistence as

\[ \operatorname{IP} = \frac{1}{T}\sum_{t=1}^{T}\frac{|O_t|}{n}. \]

This definition is operational only after fixing:

  • the component set;
  • the intervention and action-distribution metric;
  • the detection threshold;
  • the task distribution and time resolution.

IP is therefore an instrument-dependent co-activity score. It is not a measure of consciousness, selfhood, moral status, or general intelligence. Mere availability in a log or prompt does not count as causal operation.

Chord and Arpeggio as Experimental Conditions

The terms Chord and Arpeggio label two comparison conditions:

  • Chord: selected components are made jointly available to the action computation.
  • Arpeggio: the same components are evaluated or applied in a controlled sequence.

The comparison is useful only if compute, information, latency, and task exposure are matched. A sequential architecture may perform as well as or better than a joint one. The labels do not rank the systems and do not establish which one has an identity.

Is There a Boundary?

A sharp critical value \(\operatorname{IP}_c\) has not been demonstrated. At least three outcomes are possible:

  1. performance changes smoothly with measured co-activity;
  2. a task-specific threshold appears because of the architecture or environment;
  3. IP adds no predictive value once simpler variables such as memory, latency, or compute are controlled.

The Kuramoto transition in TEO is a model-internal analogy and a source of candidate analyses. It does not imply that real agent architectures undergo the same bifurcation.

Test Protocol

  1. Specify components and causal interventions before observing results.
  2. Construct sequential and joint conditions with matched resources.
  3. Measure ordinary task performance, IP, latency, and recovery after component ablation or context shift.
  4. Test whether IP predicts out-of-distribution stability beyond those controls.
  5. Repeat across architectures and task families.

Evidence for the hypothesis would be a reproducible relation between causal co-activity and perturbation robustness that survives matched controls. A smooth crossover would reject the sharp boundary version. No additional predictive value would reject the usefulness of IP for that domain.

Relation to the Repository

The legitimate contribution here is a falsifiable comparison between specified architectures. The claim that it detects the difference between simulated and instantiated selfhood remains outside what the proposed measurements can establish.