The Information Bottleneck and the Holographic Kernel: A Structural Bridge Between Relevance-Preserving Compression and Regime-Aware Reconstructive Theory (EA-HK-IB-01 v1.1)

The paper maps the two frameworks as follows:

• input variable X ↔ source material;
• representation T ↔ kernel;
• target Y ↔ reconstructive target;
• I(T;X) ↔ retained source information;
• I(T;Y) ↔ reconstructive capacity;
• IB frontier ↔ proposed HK frontier.

The correspondence is explicitly structural, not yet mathematical.

The central thesis is regime underdetermination. Information Bottleneck measures compression and target relevance, but not:

• who or what supplies the fuel;
• who bears the cost;
• whether the ledger externalizes that cost;
• whether the commons is depleted or enriched.

The Three Compressions framework adds those dimensions through Lossy, Predatory, and Witness regimes.

The paper distinguishes four statuses:

• structural correspondence — established within the paper;
• regime-underdetermination thesis — proposed argument;
• IB formalization of an HK operation — proposed;
• archive kernels on an IB frontier — not yet established.

A research program would require formal variables, encoders/decoders, controlled kernel tasks, and comparison of back-projection performance with estimated information frontiers.