Giorgio Gilestro
3b9f4f7893
One self-contained README.md per results/ figure folder (Layer 1 E1-E6 and Layer 1.5 bridge/collapse/grounding/architectures/recombination): plain-language claim, setup, a compact symbol glossary, a panel-by-panel walkthrough, and the takeaway + falsifier. Auto-renders when browsing the folder; carries the honest caveats (grounding's ruler reframing, the excluded VAE). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
32 lines
2.1 KiB
Markdown
32 lines
2.1 KiB
Markdown
# bridge — the histogram model reproduces Layer-1 E2 exactly (the HARD GATE)
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**Claim tested (a plumbing check, not science):** does the neural experiment harness, when run with a
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*trivial* model, reproduce the Layer-1 math exactly? If not, no later neural result could be trusted.
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**Setup (Layer 1.5).** Same generational loop as every neural experiment — each generation, draw the
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parent's samples, optionally mix in real data, retrain, measure — but the "model" is a **histogram**:
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it just counts which modes appeared and resamples them (no neural net, no smoothing). This reduces the
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neural setup *exactly* back to Wright–Fisher drift. `K = 200` modes, `n = 200`, 200 generations,
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60 repeats, grounding swept `g ∈ {0, …, 0.4}`.
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### Symbols
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- **mode** = one of the `K` items (Layer-1.5 word for "item"); read off each generated sequence by a zero-error oracle.
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- **`g`** grounding fraction, **`g*`** its critical value, **`H`** diversity, **`H_eq`** the exact closed-form equilibrium diversity.
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### The four panels
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1. **Trajectories.** Diversity `H` per `g`. `g = 0` collapses; `g > 0` plateaus — the E2 picture,
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now produced by the *neural runner*.
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2. **Bridge = Layer 1 (the gate).** Dots = the neural histogram runner's stationary `H` vs `g`; the
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black dashed curve = the exact `H_eq` closed form from Layer 1. The dots sit **on** the curve, and
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the recovered critical grounding is **`g* = 0.047` (CI [0.045, 0.052])** — matching Layer-1's
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0.048. This equality is what licenses every trained-model result to be read against the analytic
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core.
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3. **Tail survival.** Fraction of the rare tail retained vs `g` (item-count red, truth-mass purple) —
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rises with grounding, deep tail lags, exactly as in E2.
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4. **Per-rarity band.** Survival by rarity band vs `g`; deep bands need more grounding
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(`m·p*ᵢ ≳ 1`).
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### Takeaway
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The harness is faithful: with a memoryless model it reproduces Layer 1 to the decimal. **This is a
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gate, not a finding** — passing it is the precondition for the RNN/MLP experiments
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(`collapse`, `grounding`, `architectures`, `recombination`), where the *model* is what changes.
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