# SIM1 Adaptive Budget Toy

Status:

```text
SIM1_ADAPTIVE_BUDGET_TOY_PASS__FINITE_INFORMATION_ADAPTIVE_SIMULATION__NO_PHYSICAL_CLAIM
```

SIM1 is the first practical ITHKOR-SIM experiment. It asks whether a simple
information-adaptive update policy can preserve a synthetic finite toy world
better than fixed controls under the same compute budget.

This is an engineering diagnostic. It is not a claim that ITHKOR is a physical
law, not a claim that the universe is a simulation, and not a replacement for
physics engines.

## Question

```text
Can ITHKOR-inspired information diagnostics place a limited update budget more
effectively than uniform, gradient, source-only, random and shuffled controls?
```

## Setup

- scalar 2D synthetic field;
- deterministic moving source plus weak static source;
- full update used as the reference trajectory;
- approximate simulators can update only 25% of cells per step;
- all policies use the same update fraction;
- oracle-delta is included only as an upper benchmark.

Policies:

| Policy | Meaning |
| --- | --- |
| `ithkor_sim` | weighted finite information score: model delta, source-response, record stability and coherence/laplacian pressure |
| `uniform_round_robin` | fixed deterministic uniform update pattern |
| `geometric_gradient` | update high-gradient cells |
| `source_only` | update strongest source cells |
| `random` | random cells, deterministic seed |
| `shuffled_ithkor` | same information-score distribution, spatially shuffled |
| `oracle_delta` | upper benchmark using true one-step delta |

## Command

```powershell
python -m py_compile ithkor_sim1_adaptive_budget_toy.py
python ithkor_sim1_adaptive_budget_toy.py --output-dir experiments\216_sim1_adaptive_budget_toy\raw\sim1_adaptive_budget_toy_2026-06-23
```

## Result

Raw outputs:

```text
experiments/216_sim1_adaptive_budget_toy/raw/sim1_adaptive_budget_toy_2026-06-23/
```

Key numbers:

| Metric | Value |
| --- | ---: |
| grid size | 48 |
| steps | 72 |
| trials | 8 |
| update budget | 0.25 |
| `ithkor_sim` mean combined error | 0.068936 |
| best non-oracle control | `source_only` |
| margin over best control | 0.074887 |
| wins over controls | 5/5 |
| oracle gap | 0.001964 |

Policy ranking by mean combined error:

| Policy | Mean Combined Error |
| --- | ---: |
| `oracle_delta` | 0.066972 |
| `ithkor_sim` | 0.068936 |
| `source_only` | 0.143822 |
| `geometric_gradient` | 0.157783 |
| `uniform_round_robin` | 0.380004 |
| `random` | 0.420109 |
| `shuffled_ithkor` | 0.422857 |

## Interpretation

SIM1 supports a narrow practical statement:

```text
In this synthetic finite toy world, an ITHKOR-inspired information-adaptive
budget policy preserved target observables better than simple controls at the
same update fraction.
```

The shuffled-information control is important: it shows that the policy did not
win merely because it had a convenient score distribution. Spatial placement of
the information score mattered.

## Boundaries

SIM1 does not show:

- better physical accuracy in real simulations;
- a universal adaptive simulation method;
- a proof of an information-based universe;
- gravity, spacetime, physical time or quantum-gravity support.

## Next Step

SIM2 should test whether the same idea works as a checkpoint/record-placement
policy:

```text
Can record-stability and response pressure select save/checkpoint locations
that improve replay and rollback quality at fixed storage budget?
```