d4: The Observer Layer -- Two Pre-registered Experiments on Where Attention Goes

The Universal Layer Grammar in IRDME defines four layer types. Until now, only three had been tested experimentally: d1 (declared/structural), d2 (flow/electrical), d3 (behavioral/dynamic). d4 -- the observer layer -- had been defined in theory but never formally tested.

d4 encodes how an external agent perceives a system: how many PubMed papers mention a neuron, how many Stack Overflow questions discuss a package, how many citations a gene accumulates. It is not a physical coupling. It is epistemic attention.

The question is whether d4 tracks structural importance (d1/d2) or diverges from it. The Functional Proximity Law (FPL) predicts correlation between layers that share a relational regime. d4 encodes a different regime -- observation, not coupling -- so FPL does not predict d4 will track d1 or d2. Two pre-registered experiments tested this.

--- Experiment 1: C. elegans ---

Data: 279 neurons, chemical synapse + gap junction layers (d1/d2), PubMed co-mention layer (d4). For each neuron, we queried PubMed for "C. elegans AND [NEURON_NAME]" and built co-attention edges where two neurons share at least one paper.

Results:
• r(chemical_synapse, scientific_attention) = -0.008 (H1 DENIED: not > 0.10)
• r(gap_junction, scientific_attention) = -0.044 (H3 DENIED)
• H2 CONFIRMED: r < 0.40 as predicted

The most striking finding: AVAL, the top structural hub (d1_degree = 380), has zero scientific co-attention. One might conclude that scientific attention systematically ignores structural hubs. That would be a clean narrative. It is wrong.

Distributional check: top-d1 quartile has 80% of neurons with d4 = 0. Bottom-d1 quartile has 87% with d4 = 0. The difference is 7 percentage points -- not meaningful. The neglect is GLOBAL, not selective. 82% of all 279 neurons have zero scientific co-attention.

What explains r ~ 0: the C. elegans scientific community has hyper-concentrated its attention on a historically famous ~18% of neurons -- the touch cells (PLML, ALM, AVM) from Chalfie's Nobel-prize work, the chemosensory neurons from Bargmann's lab. Attention is driven by which experimental systems became famous first, not by structural importance. It is path-dependent accumulation, not structural selection.

--- Experiment 2: npm Software ---

Data: 193 active npm packages (React/Next.js ecosystem, depth-1 expansion from 35 seeds), dependency graph (d1) + reverse-dependency in-degree (d2) + Stack Overflow question count (d4).

Results:
• r(dependency, SO_attention) = +0.326 [H1 CONFIRMED: < 0.40]
• r(reverse_dep, SO_attention) = -0.077 [H2 DENIED: not > 0.20 and not significant]
• r(dependency, reverse_dependency) = -0.312 [H3 DENIED -- and in the WRONG DIRECTION]

The d1 correlation (+0.33) makes sense: consumer frameworks (webpack, express, eslint) are both structurally complex (high d1 out-degree) AND user-visible (high SO question count). People ask about the tools they use.

The d2 pattern is more interesting. Top-d2 quartile -- the infrastructure packages that everything else depends on -- has 75% zero-attention. Bottom-d2 quartile has 43% zero-attention. A 32-percentage-point gap. The chalk finding (6 packages depend on it, 52 SO questions) is not an anecdote. It is a distributional pattern.

The most unexpected result: r(d1, d2) = -0.31, p = 5.8e-6. Consumer packages have high d1 (many dependencies) and low d2 (nothing depends on them). Infrastructure has high d2 and low d1. This is a NEGATIVE correlation -- a bimodal polarity. In C. elegans, r(d1, d2) = +0.64. FPL holds in biology. It fails within the structural layers of npm.

--- Cross-domain conclusion ---

The strongest d4 claim from both experiments is:
• d2 (infrastructure depth) is poorly attended in BOTH domains. Biology does not attend to motor hubs. Software does not attend to semver, chalk, @babel/types.
• d4 does not universally track d1 OR d2.
• The d1-d4 relationship is domain-specific: r ~ 0 in biology, +0.33 in software.

This is not "observer attention is orthogonal to structure." It is more precise: observer layers selectively reflect some structural dimensions and ignore others, in ways that depend on the domain's attention accumulation mechanism.

--- Named findings ---

Observer Attention Divergence: d4 does not universally track d1/d2. The d4 <-> d1/d2 relationship is domain-specific, not universal. Status: PROVISIONAL (2 experiments).

Software Bimodal Polarity: npm r(d1 <-> d2) = -0.31. Consumer packages and infrastructure packages are structurally anti-correlated. New named boundary condition for FPL within software dependency graphs. Status: PROVISIONAL (1 experiment).

Both are in the pre-registration repository. Pre-reg IDs: F12_D4_OBSERVER_v1, DISC_D4_SOFTWARE_v1. Committed 2026-06-13.

--- What comes next ---

d4_human (SO/PubMed) is one kind of observer. d4_ai would be another: show an AI model the network topology without degree statistics, ask which nodes seem most structurally important, record the rankings. Then compute r(d1, d4_ai) vs r(d1, d4_human).

If AI attention recovers structural importance better than human community attention does, that is a findable and measurable result. Not a product claim -- an experiment.