--- id: O0-STUDY-002 title: Functional Partitioning vs. Monolithic Prediction under Local-Signal Constraints version: 1.0.0-pilot date: 2026-07-26 record_class: SIMULATION_STUDY status: PILOT COMPLETE, CONFIRMATORY DEFERRED evidence_level: computational_simulation replication_status: internally_unreplicated verdict: UNSUPPORTED --- # Dissociating "functional partitioning helps" from "small-sample overfitting + local inductive bias" ## Claim-status banner ``` CLAIM STATUS UNSUPPORTED (top-line) REASONING: CE1 (statistical efficiency) AND CE2 (convolutional inductive bias) BOTH beat H1 EVIDENCE TYPE COMPUTATIONAL SIMULATION (pilot, n_seeds=5) PHYSICAL VALIDATION NONE BIOLOGICAL VALIDATION NONE INDEPENDENT REPLICATION NONE CONFIRMATORY VS EXPLORATORY PILOT (5 seeds); confirmatory 30-seed run deferred because effect sizes at pilot are extreme (|d| > 7 for all key contrasts). SOURCE PROPOSITION "Functional separation serves evolutionary/practical purposes. The illusion of separation allows local processing." — # The O-0 Phenomenon- A Unified Framework.md, §VII SUPPORTED - At small training-sample counts (n_train ≤ 2000), spatially-local partitioning of the input dramatically outperforms a monolithic predictor with equal parameter budget on stochastic spatial-field prediction (Cohen's d ≈ 7.5 in favor of part_local at n_train=200, matern generator). - Locality-aware partitioning outperforms random partitioning at short correlation lengths (Cohen's d ≈ 0.78 at ξ=1, n_train=2000). NOT ESTABLISHED (H1 falsified) - That the observed partitioning advantage is a real "functional utility of separation" rather than an artifact of statistical efficiency. At n_train=20000, the monolithic predictor OVERTAKES the locally-partitioned predictor by a huge margin (Cohen's d ≈ -17.8 IN FAVOR OF mono). CE1 wins. - That the observed partitioning advantage requires partitioning at all. A convolutional shared-weight linear predictor with strictly fewer parameters than either mono OR partitioned crushes both at every tested ξ (d ≈ -10.4 vs. part_local at ξ=1, n=2000). CE2 wins. MOST LIKELY ALTERNATIVE The advantage of small-input predictors at small sample sizes is the classical bias-variance tradeoff: a smaller input dimensionality gives the OLS estimator lower variance at fixed n, which dominates when n is small. This is undergraduate statistical-learning theory and requires no appeal to "functional separation." NEXT DISCRIMINATING TEST A version of the setup where the CE1 confound is architecturally controlled: give every predictor the same regularization strength (via ridge with matched effective degrees of freedom) and the same local-window inductive bias. If part_local still beats conv_local under those conditions, H1 gains real ground. Preliminary evidence from this study says it will not. ``` ## Abstract We test the specific empirical claim embedded in Section VII of the O/0 source document — that functional separation exists because it "serves evolutionary/practical purposes, allowing local processing of local problems." Operationally, we compared five OLS-family predictors on stochastic spatial-field prediction at controlled correlation length ξ, sample size `n_train`, and observation noise: monolithic OLS, locally-partitioned OLS, randomly-partitioned OLS, shared-weight local convolutional linear predictor, and monolithic ridge with CV-selected regularization. Pilot data (`n_seeds = 5`, 1125 confirmatory fits, 1125 robustness fits, wall time 733 s) shows extreme effect sizes for every key contrast — sufficient to make the top-line verdict clear without a confirmatory 30-seed replication: | Contrast (positive = wins for partitioning) | Cohen's d (paired) | |---|---| | mono vs. part_local at ξ=1, n=200 | +7.5 | | mono vs. part_local at ξ=1, n=2000 | +7.5 | | mono vs. part_local at ξ=1, n=20000 | **-17.8** | | part_random vs. part_local at ξ=1, n=2000 | +0.78 | | conv vs. part_local at ξ=1, n=2000 | **-10.4** | | mono vs. part_local at ξ=16, n=2000 | +0.66 | **Interpretation.** The a-priori-attractive story — that partitioning helps under local-signal conditions because "local processing is more efficient" — fails two adversarial controls: 1. **CE1 (statistical efficiency).** At `n_train = 20000` the monolithic predictor absolutely dominates part_local. The apparent advantage of partitioning at smaller sample sizes is purely a small-sample regularization effect: monolithic has more parameters and overfits when data is scarce. 2. **CE2 (local inductive bias).** A convolutional linear predictor with weight sharing beats part_local everywhere. The "advantage of partitioning" is really "advantage of local receptive field." Weight sharing is a strictly stronger local inductive bias than partition-independence and requires far fewer parameters. Both CEs were preregistered in `preregistration.md` before running the pipeline. Both won. The verdict is UNSUPPORTED for the O/0-framed reading. The underlying weaker fact ("local receptive fields help predict local signals when data is scarce") is trivially true and uninteresting; it is textbook bias-variance theory and requires no metaphysical framing. The philosophical claim in §VII of the source document is NOT thereby refuted. It is only shown that the specific pragmatic-utility argument the document uses to defend the claim does not, in this model class, isolate a distinctive "utility of separation" over the simplest conventional explanations. ## Directly cited source From `# The O-0 Phenomenon- A Unified Framework.md`, §VII, sub-section "If everything is one, why does separation appear so real?": > "Because functional separation serves evolutionary/practical purposes. > The illusion of separation allows: > - Local processing (brains solving local problems) > - Evolution (competition/cooperation between apparent individuals) > - The game of existence requires forgetting O temporarily" ## Design summary - **Signal generators:** Matérn GRF (ν=3/2), linear diffusion, coupled oscillator chain (calibrated so their empirical ξ spans the range {~1, 16}; see `results/summary.json` for the calibration table). - **Predictors:** 5 architectures, all linear, all closed-form fits. - **Grid:** 3 generators × 5 ξ × 3 n_train × 5 seeds × 5 arch = 1125 confirmatory fits, plus 1125 noise-robustness fits. - **Metric:** test MSE, paired Cohen's d across seeds. - **Preregistration:** frozen before execution; see `preregistration.md`. ## Why we stopped at pilot n_seeds=5 The preregistration required 30 seeds. We ran 5 in the pilot to validate the pipeline. The pilot returned effect sizes of magnitude 7 to 17 — well above the Cohen's d = 0.5 threshold for any of the preregistered decision rules. At those magnitudes, the confirmatory run would tighten confidence intervals but cannot change the sign or qualitative interpretation of any effect. The 30-seed run is DEFERRED to a Tier-3 replication package rather than a blocking requirement for the top-line verdict. ## Files - `preregistration.md` — frozen rules - `hypothesis.md` — H1, H2, CE1, CE2 with directional predictions - `formal_model.md` — architectures + signal generators - `claim_audit.md` — source citation + separation of testable content - `literature_review.md` — 5 primary sources - `src/*.py` — signals, predictors, driver - `results/summary.json` — pilot summary with verdict JSON - `results/pairwise_effects.csv` — full effect-size table - `data/raw/confirmatory.csv` — 1125 pilot MSE rows - `data/raw/noise_robustness.csv` — 1125 robustness MSE rows ## Revision history - 1.0.0-pilot (2026-07-26): pilot run at n_seeds=5. Top-line verdict UNSUPPORTED. 30-seed confirmatory run deferred; effect sizes at pilot are extreme enough to make the outcome unambiguous.