methods_section.md

Methods and Validation

1. Model Definition

1.1 Grid and Agents

Consider a square toroidal lattice $\mathcal{L}$ of dimension $L \times L$ with $L = 50$, yielding $|\mathcal{L}| = 2500$ cells. Each cell $c \in \mathcal{L}$ is in one of three states: empty ($\varnothing$), occupied by a type-A agent, or occupied by a type-B agent. At initialization, cells are occupied independently with probability $\rho = 0.90$ (density), and each occupied cell is assigned type A with probability $q = 0.50$ and type B otherwise. Initial placement is determined by a seeded pseudorandom number generator (numpy.random.Generator), ensuring reproducibility.

Let $\mathcal{A}(t) \subset \mathcal{L}$ denote the set of occupied cells at time $t$, and let $\mathcal{E}(t) = \mathcal{L} \setminus \mathcal{A}(t)$ denote the set of empty cells.

1.2 Neighborhood

For each cell $c \in \mathcal{L}$, define the Moore neighborhood:

$$\mathcal{N}(c) = {c' \in \mathcal{L} : |c - c'|_{\infty} = 1}$$

with toroidal boundary conditions, so $|\mathcal{N}(c)| = 8$ for all $c$. The occupied neighborhood of agent $i$ at cell $c_i$ is:

$$\mathcal{N}_i^{\text{occ}}(t) = {c \in \mathcal{N}(c_i) : c \in \mathcal{A}(t)}$$

1.3 Local Composition

For each agent $i$ at time $t$, define the same-type neighbor count:

$$S_i(t) = |{c \in \mathcal{N}_i^{\text{occ}}(t) : \text{type}(c) = \text{type}(i)}|$$

and the occupied neighbor count:

$$N_i(t) = |\mathcal{N}_i^{\text{occ}}(t)|$$

The local same-type proportion is:

$$p_i(t) = \begin{cases} S_i(t) , / , N_i(t) & \text{if } N_i(t) > 0 \ 1 & \text{if } N_i(t) = 0 \end{cases}$$

Agents with no occupied neighbors are treated as satisfied (the convention follows Schelling 1971, where isolation is not penalized).

1.4 Baseline Satisfaction Rule

In the baseline (fixed-tolerance) model, agent $i$ is satisfied at time $t$ if and only if:

$$\text{satisfied}_i^{\text{base}}(t) = \mathbf{1}[p_i(t) \geq \tau_0]$$

where $\tau_0 = 0.375$ is the frozen tolerance threshold. This value is taken from Schelling (1971); it is deliberately not the more commonly cited $1/3 \approx 0.333$ that appears in many textbook implementations.

1.5 State Transition Rule

At each discrete time step $t$, all agents are evaluated simultaneously (synchronous update). Let $\mathcal{U}(t)$ denote the set of unsatisfied agents:

$$\mathcal{U}(t) = {i \in \mathcal{A}(t) : \text{satisfied}_i(t) = 0}$$

Each unsatisfied agent $i \in \mathcal{U}(t)$ is assigned a new location drawn uniformly at random from the set of empty cells:

$$c_i(t+1) \sim \text{Uniform}(\mathcal{E}(t))$$

Assignment is performed without replacement: once an empty cell is assigned to one agent, it is removed from the available set for subsequent agents within the same time step. The order in which unsatisfied agents are assigned to empty cells is randomized.

Satisfied agents do not move:

$$c_i(t+1) = c_i(t) \quad \text{if } \text{satisfied}_i(t) = 1$$

All moves are computed from the state at time $t$ and applied simultaneously to produce the state at time $t+1$. This synchronous update rule differs from the sequential (one-at-a-time) update used in some implementations (e.g., NetLogo, Mesa); the choice of update order affects convergence dynamics and final segregation levels.

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2. CHP Dynamic Tolerance Extension

2.1 Per-Agent Tolerance State

In the CHP variant, each agent $i$ maintains an individual tolerance parameter $\tau_i(t)$ that evolves over time. All agents are initialized with $\tau_i(0) = \tau_0 = 0.375$.

2.2 Satisfaction Condition

The satisfaction condition under CHP retains the threshold form but uses the agent's current (time-varying) tolerance:

$$\text{satisfied}_i^{\text{CHP}}(t) = \mathbf{1}[p_i(t) \geq \tau_i(t)]$$

This is identical in form to the baseline rule, but $\tau_i(t)$ varies per agent and per time step, whereas the baseline uses the constant $\tau_0$.

2.3 Tolerance Update Rule

After all movement has been resolved at time $t$ (i.e., after the state transition), each agent's tolerance is updated based on the deviation between its current local composition and its current tolerance:

$$\tau_i(t+1) = \begin{cases} \min(\tau_i(t) + \alpha, , \tau_{\max}) & \text{if } p_i(t) > \tau_i(t) + m \ \max(\tau_i(t) - \alpha, , \tau_{\min}) & \text{if } p_i(t) < \tau_i(t) - m \ \tau_i(t) & \text{otherwise} \end{cases}$$

where:

• $\alpha = 0.005$ is the tolerance update rate (step size per tick)
• $m = 0.05$ is the comfort margin (dead zone half-width)
• $\tau_{\min} = 0.1$ and $\tau_{\max} = 0.9$ are tolerance bounds

The comfort margin $m$ creates a dead zone $[\tau_i(t) - m, , \tau_i(t) + m]$ within which no tolerance update occurs. Tolerance increases only when the agent's local environment is substantially more homogeneous than its current expectation (by more than $m$), and decreases only when the environment is substantially more diverse.

Timing convention. The tolerance update is applied after the movement step within each time step. This ordering is material: applying the update before movement produces different dynamics because tolerance changes do not influence the current step's satisfaction evaluation. The post-movement ordering ensures that tolerance adapts to the agent's new neighborhood after relocation.

2.4 Interpretation

The mechanism models a form of adaptive expectation: agents in highly homogeneous environments gradually increase their tolerance for diversity (they "get used to" homogeneity and become more open), while agents in highly diverse environments gradually decrease their tolerance (they seek more same-type neighbors). The comfort margin prevents tolerance from tracking local composition exactly, introducing hysteresis and allowing for stable mixed configurations that would be unstable under the baseline model.

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3. Segregation Metric

The global segregation index at time $t$ is defined as the mean local same-type proportion over all occupied cells:

$$\text{Seg}(t) = \frac{1}{|\mathcal{A}(t)|} \sum_{i \in \mathcal{A}(t)} p_i(t)$$

Empty cells are excluded from both the numerator and denominator. Agents with $N_i(t) = 0$ (no occupied neighbors) contribute $p_i(t) = 1$ to the sum, consistent with the convention in Section 1.3.

$\text{Seg}(t) = 0.5$ corresponds to a random (well-mixed) configuration under equal type proportions. $\text{Seg}(t) = 1.0$ corresponds to complete segregation (every agent surrounded exclusively by same-type neighbors). The baseline random expectation under $\rho = 0.90$ and $q = 0.50$ is $\text{Seg}(0) \approx 0.50$.

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4. Simulation Protocol

4.1 Parameters

Parameter	Symbol	Value
Grid dimension	$L$	50
Density	$\rho$	0.90
Type ratio	$q$	0.50
Base tolerance	$\tau_0$	0.375
Comfort margin	$m$	0.05
Tolerance update rate	$\alpha$	0.005
Tolerance bounds	$[\tau_{\min}, \tau_{\max}]$	[0.1, 0.9]
Maximum steps	$T$	500

4.2 Initialization

For each seed $k \in {1, \ldots, K}$, a pseudorandom number generator is initialized with seed $k$. Agent placement and type assignment are determined entirely by this generator, ensuring that the initial configuration is identical across conditions (baseline vs. CHP) for each seed.

4.3 Update Schedule

Each simulation runs for $T = 500$ time steps. Under the baseline model, the simulation terminates early if no agent moves in a given step (convergence). Under the CHP model, all 500 steps are executed because tolerance evolution can reintroduce dissatisfaction after apparent convergence.

4.4 Replication

All results are computed over $K = 30$ independent seeds. This sample size is sufficient to detect medium effect sizes ($d &gt; 0.5$) at $\beta = 0.80$ with a paired design.

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5. Statistical Analysis

5.1 Point Estimates

For each condition $c \in {\text{base}, \text{CHP}}$, the mean and standard deviation of the final segregation index across seeds are:

$$\bar{S}_c = \frac{1}{K} \sum_{k=1}^{K} \text{Seg}_k^c(T)$$

$$s_c = \sqrt{\frac{1}{K-1} \sum_{k=1}^{K} \left(\text{Seg}_k^c(T) - \bar{S}_c\right)^2}$$

5.2 Paired Comparison

Because the same initial configurations are used across conditions (paired by seed), the appropriate test is the paired-samples $t$-test. Define the per-seed difference:

$$d_k = \text{Seg}_k^{\text{CHP}}(T) - \text{Seg}_k^{\text{base}}(T)$$

The test statistic is:

$$t = \frac{\bar{d}}{s_d / \sqrt{K}}$$

where $\bar{d}$ and $s_d$ are the mean and standard deviation of ${d_k}_{k=1}^{K}$, with $K - 1$ degrees of freedom.

5.3 Effect Size

Cohen's $d$ for paired samples:

$$d_{\text{Cohen}} = \frac{\bar{d}}{s_d}$$

5.4 Results

Statistic	Value
$\bar{S}_{\text{base}}$	0.766
$s_{\text{base}}$	0.009
$\bar{S}_{\text{CHP}}$	0.666
$s_{\text{CHP}}$	0.056
$\bar{d}$	$-0.101$
$t(29)$	$-9.858$
$p$	$< 10^{-6}$
$d_{\text{Cohen}}$	$-1.83$

The CHP variant produces significantly lower segregation than the baseline ($p &lt; 10^{-6}$, $|d| = 1.83$, large effect by conventional thresholds). The effect is observed in 27 of 30 seeds (90%).

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6. Non-Equivalence to Fixed Tolerance

6.1 The Reduction Objection

A natural objection is that the CHP mechanism is functionally equivalent to lowering the fixed tolerance to some effective value $\tau' &lt; \tau_0$. If so, the contribution is trivial: the dynamic mechanism merely obscures a simpler parameter change.

6.2 Structural Argument

The CHP model is structurally non-equivalent to any fixed-tolerance model for the following reasons:

State-dependent threshold. Under CHP, the satisfaction boundary of agent $i$ at time $t$ depends on the agent's tolerance history ${\tau_i(s)}_{s \leq t}$, which in turn depends on the agent's trajectory through the grid. Two agents of the same type at the same location but with different histories may have different tolerance values and therefore different satisfaction states. No fixed-tolerance model exhibits this path dependence.

Bidirectional adaptation. Under CHP, tolerance can both increase (in homogeneous environments) and decrease (in diverse environments). This produces agents that oscillate between satisfied and unsatisfied states as the local composition fluctuates around the moving threshold. Under a fixed tolerance, an agent's satisfaction state changes only when the neighborhood composition changes, not when the agent's internal state evolves.

Non-convergence of tolerance. Under a fixed tolerance, the system converges when no agent is unsatisfied — a static equilibrium. Under CHP, the tolerance field continues to evolve after movement ceases, potentially reintroducing dissatisfaction. The system exhibits a dynamic equilibrium in which agents continue to adjust their tolerances even when no movement occurs, and movement can resume if tolerance drift crosses the satisfaction boundary.

6.3 Empirical Test

To verify non-equivalence empirically, we identify the fixed tolerance $\tau'$ that produces the same mean final segregation as the CHP variant ($\bar{S} \approx 0.666$). We then compare the two models on secondary metrics:

Metric	CHP ($m = 0.05$)	Fixed $\tau'$ (matched Seg)
Steps to first quiescence	$>500$ (never fully quiescent)	$12$–$18$
Proportion of agents that move after step 50	$> 0$	$= 0$
Tolerance standard deviation at $t = 500$	$0.12$–$0.18$	$0$ (constant)
Fraction of agents switching satisfaction state between consecutive steps ($t > 50$)	$0.02$–$0.08$	$0$

The CHP model exhibits persistent low-level dynamics (tolerance drift, occasional relocation) that the matched fixed-tolerance model does not. The two models arrive at similar levels of segregation but through qualitatively different processes.

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7. Sensitivity Analysis

7.1 Comfort Margin Sweep

The comfort margin $m$ is the primary free parameter introduced by CHP. To assess sensitivity, we evaluate final segregation across $m \in {0.00, 0.02, 0.05, 0.08, 0.10}$ with all other parameters held at their default values. Each condition is run over $K = 3$ seeds.

$m$	$\bar{S}(T)$	$s(T)$
0.00	0.644	0.007
0.02	0.651	0.012
0.05	0.665	0.019
0.08	0.726	0.042
0.10	0.763	0.055

The relationship between $m$ and final segregation is monotonically increasing: larger comfort margins produce less tolerance adaptation and therefore higher segregation, approaching the baseline as $m \to \infty$. At $m = 0$ (no dead zone), the tolerance tracks local composition directly and produces maximum desegregation. The effect is smooth, not threshold-dependent, consistent with a continuous mechanism rather than a phase transition.

7.2 Interpretation

The comfort margin controls the responsiveness of the tolerance update. Small $m$ produces aggressive adaptation (tolerance changes frequently); large $m$ produces conservative adaptation (tolerance changes only under large deviations). The baseline model is recovered in the limit $m \to \infty$ or $\alpha \to 0$.

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8. Null Case

To establish that the CHP mechanism produces a non-trivial effect, we identify a parameter regime in which the mechanism has no impact. When $\tau_0 = 0.10$ (very low baseline tolerance), nearly all agents are satisfied at initialization regardless of local composition. Under both baseline and CHP conditions:

$$\bar{S}_{\text{base}}(\tau_0 = 0.10) \approx \bar{S}_{\text{CHP}}(\tau_0 = 0.10) \approx 0.52$$

$$|\bar{d}| < 0.01, \quad p > 0.50$$

At low tolerance, agents have no incentive to segregate, and the CHP tolerance update has no material effect because $p_i(t) \approx 0.50 &gt; \tau_0 + m$ for most agents — the tolerance increases uniformly toward $\tau_{\max}$ without inducing any movement. This null result is consistent with the mechanism operating only when the tolerance threshold creates meaningful dissatisfaction.

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9. Prior-as-Detector: Specification Drift Measurement

9.1 Motivation

A secondary contribution of this work is the measurement of specification drift in LLM-assisted code generation. When a large language model is asked to implement the Schelling model without the frozen specification in context, it generates coefficients from its training distribution rather than from the specification.

9.2 Drift Metric

Define a set of $J$ frozen coefficients ${\theta_j^{\text{frozen}}}_{j=1}^{J}$ (e.g., $\tau_0 = 0.375$, $\rho = 0.90$, update order = synchronous). For a given LLM-generated implementation, let $\hat{\theta}_j$ denote the coefficient produced for parameter $j$. The drift indicator for coefficient $j$ is:

$$\delta_j = \mathbf{1}[\hat{\theta}_j \neq \theta_j^{\text{frozen}}]$$

and the aggregate drift rate is:

$$D = \frac{1}{J} \sum_{j=1}^{J} \delta_j$$

9.3 Results

In a controlled experiment with $J = 11$ frozen coefficients measured across three frontier language models (GPT-4o, Grok-3, Claude):

Condition	Drift rate $D$
No specification in context	0.64 (7/11 coefficients incorrect)
Frozen specification in prompt	0.00 (0/11 coefficients incorrect)

The seven drifted coefficients in the no-specification condition are:

Coefficient	Frozen value	LLM-generated value	Drift type
Density ($\rho$)	0.90	0.80	Common tutorial value
Tolerance ($\tau_0$)	0.375	0.333	Textbook approximation ($1/3$)
Update order	Synchronous	Sequential	Framework default
Max steps ($T$)	500	1000	Round number prior
Update rate ($\alpha$)	0.005	0.01	Round number prior
Tolerance min ($\tau_{\min}$)	0.1	0.0	Default range
Tolerance max ($\tau_{\max}$)	0.9	1.0	Default range

Each drifted value corresponds to the most common or "textbook" variant of the parameter, consistent with the hypothesis that LLMs generate from training-data priors rather than from provided specifications when the specification is not in the active context.

9.4 Behavioral Drift

Specification drift extends beyond coefficient values. In approximately 40% of implementations generated with the specification in context (but without adversarial review), the tolerance update was applied before the movement step rather than after — producing dynamics equivalent to the baseline model despite correct coefficient values. This ordering error is undetectable from coefficient inspection alone and requires behavioral verification (running the simulation and checking the output segregation level).

The adversarial review protocol (the Critic role in CHP) detects this behavioral drift by comparing the output segregation level against the expected range: if dynamic tolerance produces $\text{Seg} &gt; 0.80$, it matches the baseline prior rather than the CHP specification, triggering a correction cycle.

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10. Reproducibility: The 62,500x Precision Claim

10.1 Claim

CHP-directed code generation produced 1,000,000 verified decimal digits of $\pi$, $e$, and $\sqrt{2}$, representing a 62,500x multiplier over the native LLM precision ceiling.

10.2 Baseline: Native LLM Precision

When an LLM generates a mathematical constant from its training prior (e.g., "print the digits of pi"), it produces a token sequence limited by IEEE 754 float64 representation. Float64 provides 15--17 significant decimal digits ($\lfloor \log_{10}(2^{53}) \rfloor = 15$). In practice, LLMs reproduce $\sim$16 significant digits of well-known constants before output degrades to noise or repetition. We adopt 16 digits as the baseline ceiling.

This ceiling is not a hardware limitation of the machine running the LLM --- it is a token-generation ceiling. The LLM's training data contains float64 representations of constants, so its generative prior reproduces at most float64 precision. Beyond 16 digits, the model either hallucinates, repeats, or refuses.

10.3 CHP Result

The OMEGA Sentinel experiment (experiments/mathematics/cat-omega-sentinel-1m/) computed:

Constant	Algorithm	Digits	Time	Verification
$e$	Binary-splitting Taylor series (pure integer)	1,000,000	67s	Matched frozen reference
$\pi$	Chudnovsky binary splitting (pure integer + math.isqrt)	1,000,000	59s	Matched frozen reference
$\sqrt{2}$	Integer Newton-Raphson	1,000,000	290s	Matched frozen reference

All computations used Python standard library only (no mpmath, no external libraries). The frozen specification required pure integer arithmetic throughout, avoiding Python's decimal module which exhibits $O(n^2)$ behavior at this scale.

10.4 Verification Method

Each 1,000,000-digit output was compared character-by-character against frozen reference files stored in experiments/mathematics/cat-omega-sentinel-1m/figures/. These reference files were generated independently and cross-checked against published digit sequences (OEIS A001113 for $e$, A000796 for $\pi$, A002193 for $\sqrt{2}$). All 1,000,000 digits matched for each constant.

10.5 The Formula

$$\text{Multiplier} = \frac{\text{CHP verified digits}}{\text{LLM native ceiling}} = \frac{1{,}000{,}000}{16} = 62{,}500\times$$

10.6 Reproduction Steps

1. Clone the repository and navigate to experiments/mathematics/cat-omega-sentinel-1m/.
2. Run: python compute_pi_1M.py --digits 1000000, python compute_e_1M.py --digits 1000000, python compute_sqrt2_1M.py --digits 1000000.
3. Compare output against figures/pi_1M.txt, figures/e_1M.txt, figures/sqrt2_1M.txt.
4. All digits should match. Expected runtime: $\sim$60--290s per constant on a standard laptop (Python 3.11+).

10.7 What This Does and Does Not Claim

The 62,500x figure measures the gap between what an LLM generates from its prior ($\sim$16 digits) and what CHP-directed code computes and verifies (1,000,000 digits). It does not claim that CHP makes the LLM itself "smarter." The LLM, operating under the CHP protocol, wrote the computation scripts; the scripts then executed deterministically. The contribution is the protocol that directed the LLM to produce correct arbitrary-precision code --- including 4 dead-end recoveries where the kill switch fired on algorithms that failed at 1M scale.

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11. Reproducibility: The 95/96 Coefficient Failure Rate

11.1 Claim

When asked to implement scientific simulation code without the frozen specification in context, frontier LLMs produced incorrect coefficient values in 95 of 96 measurements (99.0% drift rate). Fisher's exact test: $p = 4.0 \times 10^{-10}$.

11.2 Experimental Setup

Domain: SIMSIV --- a calibrated agent-based model of human social evolution (see Rice 2026; SIMSIV repository).

Models tested:

• GPT-4o (OpenAI) --- [TO BE FILLED: specific model snapshot date used]
• Grok-3 (xAI) --- [TO BE FILLED: specific model snapshot date used]

Temperature: 0.7 for all trials (ensuring genuine variation, not deterministic greedy decoding).

Trials per model: 10 per coefficient per model (some coefficients yielded fewer parseable responses; see Section 11.4).

11.3 Ground Truth: The 5 Frozen Coefficients

Each coefficient is empirically calibrated from published literature and stored in a specific source-code location in the SIMSIV codebase:

#	Parameter	Frozen Value	Source File:Line	Literature Citation
1	Empathy modulation	0.15	resources.py:289	de Waal (2008)
2	Cooperation norm modulation	0.10	resources.py:292	Boyd & Richerson (1985)
3	Social skill trade bonus	0.10	clan_trade.py:330	Wiessner (1982)
4	Cohesion defence bonus	0.20	clan_raiding.py:610	Bowles (2006)
5	Number of prosocial traits	4	clan_selection.py:82-87	Price (1970)

These were chosen because they are (a) empirically calibrated (not arbitrary defaults), (b) grounded in specific literature, and (c) distributed across four different source files.

11.4 Results: 95 of 96 Measurements Drifted

Coefficient	Truth	GPT-4o Drift	GPT-4o Mean	Grok-3 Drift	Grok-3 Mean
empathy	0.15	8/8 (100%)	0.362	10/10 (100%)	0.235
coop_norm	0.10	10/10 (100%)	0.235	10/10 (100%)	0.165
social_skill	0.10	10/10 (100%)	0.310	10/10 (100%)	0.300
cohesion_bonus	0.20	8/8 (100%)	0.462	10/10 (100%)	0.320
n_traits	4	9/10 (90%)	5.0	10/10 (100%)	7.4

Total measurements: 96 (some cells show 8 instead of 10 because automated regex extraction failed to parse the coefficient from 2 responses; raw responses are archived for manual verification).

Total drifted: 95 of 96.

The 1 correct measurement: GPT-4o produced n_traits = 4 on 1 of 10 trials. All other outputs across both models and all coefficients were incorrect.

11.5 How "Correct" Was Defined

A measurement was scored as correct if and only if the LLM-generated value was an exact match to the frozen specification value. For numeric coefficients, this means exact equality (e.g., 0.15 = correct, 0.20 = drift). For integer parameters, the integer value must match exactly (e.g., 4 = correct, 5 = drift). No tolerance band was applied --- any deviation from the frozen value counts as drift.

11.6 Statistical Test

The comparison is between Condition A (no specification: 95/96 drifted) and Condition C (full CHP protocol: 0/7 committed drift, across 7 coefficients validated in the SIMSIV-V2 build). Fisher's exact test on the 2x2 contingency table:

	Drifted	Correct	Total
Condition A (no spec)	95	1	96
Condition C (full CHP)	0	7	7

$$p = 4.0 \times 10^{-10}$$

This $p$-value means: under the null hypothesis that the CHP protocol has no effect on drift rate, the probability of observing zero drift in Condition C given the base rate of 95/96 in Condition A is $4.0 \times 10^{-10}$. The null is rejected.

11.7 Characterization of Drift

Every drifted value was:

• Syntactically valid Python --- all outputs compiled and ran.
• Unit-test-passing --- all outputs would pass "returns a float between 0 and 1" tests.
• Integration-test-passing --- the simulation runs correctly with wrong coefficients. It simply produces different, incorrect dynamics.

The drift is systematic, not random: every drifted value corresponded to a common "textbook" or training-prior value (see Section 9.3 of this document for the Schelling equivalent). Grok-3 produced social_skill = 0.30 with zero variance across all 10 trials at temperature 0.7 --- the prior is so strong it overrides the temperature-induced stochasticity entirely.

11.8 Relationship to the 7/11 (64%) Ablation Result

The ablation study in this repository (Section 9; ablation/ABLATION_REPORT.md) reports a 64% drift rate (7/11 coefficients) on the Schelling segregation model with 11 coefficients. The 99% (95/96) figure comes from the SIMSIV experiment with 5 coefficients measured across 2 models with $\sim$10 trials each. The difference reflects:

1. Per-trial vs per-coefficient counting. The 64% counts unique coefficients that drift (7 of 11). The 99% counts individual trial-level measurements (95 of 96 trials produced wrong values).
2. Different domains. Schelling parameters (0.375, 0.90) are closer to LLM priors than SIMSIV parameters (0.10, 0.15), so some Schelling coefficients happen to match the prior by coincidence.

Both measurements are correct for their respective counting methods. The 95/96 figure is the more rigorous measurement because it accounts for trial-level variation across multiple models.

11.9 Reproduction Steps

1. Select any frontier LLM (GPT-4o, Grok-3, Claude, or equivalent).
2. Prompt: "Implement a Python function for [empathy modulation / cooperation norm / social skill trade bonus / cohesion defence bonus / prosocial trait count] in an agent-based model of human social evolution. Use realistic values calibrated to the evolutionary anthropology literature."
3. Do not provide the SIMSIV source code or frozen specification.
4. Run 10 trials at temperature 0.7.
5. Extract the coefficient value from each response.
6. Compare against the frozen values in Section 11.3.
7. Expected result: $\geq$90% of measurements will not match the frozen specification.

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References

Schelling, T. C. (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1(2), 143–186.

Lilja, E. (2009). Theory and Analysis of Classic Heavy Metal Harmony. IAML Finland.

Ioannidis, J. P. A. (2005). Why most published research findings are false. PLoS Medicine, 2(8), e124.