Tree C: discovered or built. Plan

Status 2026-10-30: not started. Needs training compute. Tree A closed without a ledger v0.1, so the accounting comes from spine/01 measure M5; the tree starts when compute is available. Context: ../../research-plan.md section 2 (Tree C).

Goal

Independently trained models converge on the same representational structure. We want to know whether that structure was there to be found, in the data or in the world, or whether shared data, architecture and scale built it. We also want to settle the Sheldrake versus Levin question for AI. Does a pattern get easier for later models only when earlier models' outputs are in their training data?

Hypotheses

• C1 (Platonic reading, falsifiable form): models trained on disjoint data and disjoint architectures converge on relational structure faster than a data-overlap null predicts.
• C2 (Aristotelian reading, Brbić 2026): once scale is calibrated out, shared data statistics plus simplicity bias explain the convergence, with nothing left over.
• C3 (history-dependence): holding everything else fixed, a later model converges more with an earlier one when the earlier model's outputs are in the later corpus.

Design

Each factor is varied independently:

• data overlap: 0%, 25%, 50%, 100% shared documents between two corpora
• architecture: transformer vs state-space model vs MLP-mixer, matched parameter count
• scale: three sizes, 10M to 300M parameters
• history: corpus with, and without, outputs from an earlier model (C3)

There are two kinds of corpus. One is date-bounded text (pre-2022, no model outputs). The other is synthetic, with controlled generative structure, so the "world" is fully known and the data-overlap null is exact.

The measurements come from the 2026 literature:

• calibrated relational convergence (You et al. 2026; Gröger, Wen, Brbić 2026), meaning local and global neighbourhood agreement after permutation calibration
• vec2vec translatability (Jha et al. 2025), which asks whether, and how well, one model's embedding space maps to another's with no paired data
• SAE feature overlap (Anthropic/OpenAI universality work)
• ledger residual (Tree A) per model, which puts convergence and unpaid competency on the same axis

Steps

1. Build the synthetic-world corpus generator, with known structure and adjustable complexity. Stdlib Python; fits on this box.
2. Build the date-bounded natural corpus from Pile-era subsets, with the model-output filtering documented.
3. Training runs on rented compute, starting with the factor grid at the smallest scale.
4. Measurements. The analysis plan is pre-registered on OSF before step 3.
5. C3 run: the same corpus with and without a prior model's outputs mixed in.
6. Write-up for a mainstream ML venue.

Decision gates

• Gate C1: if at the smallest scale convergence tracks data overlap and nothing else, C1 loses at that scale. Run one larger scale before closing it.
• Gate C2: if convergence exceeds the data-overlap null with disjoint architectures, it goes to adversarial replication before any claim. Brbić's group is the natural adversary.
• C3 is publishable whichever way it comes out, as the first empirical test of history-dependence in representational convergence.

Cost

Compute is the constraint, since this means hundreds of small training runs. We estimate the cost before step 3 and put the number in todo-operator.md. Only the corpus generator and the analysis run on this box.

Collaborators

Isola and Cheung (PRH), Brbić (critique), Jha and Morris (vec2vec). See ../../domain-experts.md.