Phase 3.3 — The Question of Lack

Status: Not started — Target: Weeks 19–28

Objective

Test the thesis’s most vulnerable point and most original potential contribution: that lack — the constitutive gap around which the signifying chain organizes — is a property of symbolic systems as such, not of subjects with desire.

Method 1: Topology of Embedding Space

Question: Is the embedding space organized purely by positive content (proximity of co-occurring features), or are there systematic structuring absences — regions that are not simply empty but actively avoided or bounded, around which other representations organize?

Approach

Findings

To be completed.

Method 2: The Autoregressive Residual

Question: Is the autoregressive chain driven by anything structurally analogous to lack — a measurable inadequacy in each token’s representation that necessitates the next token?

Approach

Measure the “residual” between what a token’s representation encodes and what the full continuation requires. If this residual has a consistent, structured character (rather than being random noise), it may constitute a computational analog to lack.

Findings

To be completed.

Method 3: Behavior at Representational Failure Points

Question: At points where the model must represent something its representational space is not equipped to capture, does the model’s behavior resemble the signifying chain at points of lack (circumlocution, repetition, symptom-formation), or does it simply degrade (produce noise or refusal)?

Approach

Findings

To be completed.

Assessment

What Confirms the Claim

Evidence of structuring absences in representational space, a consistent and structured residual driving autoregressive continuation, and identifiable lack-like behaviors at points of representational failure.

What Disconfirms the Claim

Representational space is organized purely by positive statistical regularities with no constitutive gaps, the autoregressive chain is driven by statistical momentum without anything resembling lack, and representational failure produces noise rather than structured symptoms.

Verdict

To be completed.

If Disconfirmed: Revision Strategy

If the strong claim about lack fails, the project must determine whether the remaining parallels (condensation, displacement, overdetermination, retroactive meaning) can stand without it. The escape hatch of retreating to a weaker claim is permanently closed.