Datasets:

Saelarien
/

saelarien-constraint-experiment-03-recovery-collapse-mismatch

noise_level float64 0.2 0.5	noise_type stringclasses 3 values	recovery_time int64 1 89	final_loss float64 0.5 49.3M	collapse bool 2 classes
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0.2	global	45	19.550369	false
0.2	global	33	51.652138	false
0.2	global	47	17.469118	false
0.2	global	60	155.650208	true
0.2	global	46	62.894981	true
0.2	global	41	41.788486	false
0.2	global	31	23.575369	true
0.2	global	57	45.841721	false
0.2	global	16	21.84367	false
0.2	global	71	45.474266	true
0.2	global	17	23.097691	false
0.2	global	44	10.132532	false
0.2	global	26	1.23419	false
0.2	global	48	44.919834	true
0.2	global	55	45.42852	true
0.2	global	47	33.568668	false
0.2	global	25	79.496429	true
0.2	global	55	2.83675	false
0.2	global	31	2.19679	false
0.2	global	74	65.479988	false
0.2	global	30	22.586075	false
0.2	global	32	12.375816	false
0.2	global	29	14.885314	false
0.2	global	25	24.884583	false
0.2	global	54	2.422494	false
0.2	global	20	12.856919	false
0.2	global	73	189.368118	true
0.2	global	22	67.330345	false
0.2	global	17	20.417339	false
0.2	global	34	10.015667	false
0.2	global	36	10.632219	false
0.2	global	5	4.73572	false
0.2	global	30	22.962425	true
0.2	global	34	1.099992	false
0.2	localized	33	204.196426	true
0.2	localized	57	266.5896	true
0.2	localized	22	41.016815	false
0.2	localized	6	9.322547	false
0.2	localized	30	16.199661	false
0.2	localized	86	17.264833	false
0.2	localized	48	8.193334	false
0.2	localized	50	116.917038	true
0.2	localized	26	30.778818	true
0.2	localized	3	1.817229	false
0.2	localized	1	4.177553	false
0.2	localized	32	27.566505	false
0.2	localized	16	3.650703	false
0.2	localized	40	204.145157	true
0.2	localized	35	287.695984	true
0.2	localized	44	51.354218	false
0.2	localized	16	2.650802	false
0.2	localized	6	9.223883	false
0.2	localized	8	3.735996	false
0.2	localized	16	7.932436	false
0.2	localized	32	0.495963	false
0.2	localized	27	4.575902	false
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0.2	localized	31	79.074249	false
0.2	localized	29	4.298552	false
0.2	localized	27	10.711732	false
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0.2	localized	43	3.314218	false
0.2	localized	58	108.491989	false
0.2	localized	9	8.743173	false
0.2	localized	24	1.510707	false
0.2	localized	23	9.523891	false
0.2	localized	13	1.659116	false
0.2	localized	35	28.859941	false
0.2	localized	5	17.666212	false
0.2	localized	17	0.509449	false
0.2	localized	59	420.226715	true
0.2	localized	64	84.773987	true
0.2	localized	23	30.37763	false
0.2	localized	9	16.767031	true
0.2	structured	74	915,199.5	true
0.2	structured	74	869,163.8125	true
0.2	structured	74	843,904.75	true
0.2	structured	74	665,032.75	true
0.2	structured	74	1,011,183.4375	true
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0.2	structured	74	1,115,466	true
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0.2	structured	74	955,468.5625	true
0.2	structured	74	808,375.4375	true
0.2	structured	74	739,763.6875	true
0.2	structured	74	1,005,467.25	true

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Saelariën Constraint Experiment 03: Recovery–Collapse Mismatch

Summary

This dataset extends Experiment 01, which established that collapse emerges when entropy injection exceeds a system’s capacity to maintain coherent state.

Experiment 03 isolates a different question: whether recovery dynamics uniquely characterize proximity to collapse.

The results show they do not.

Systems with indistinguishable recovery profiles can resolve into both stable and collapsed outcomes. Recovery behavior tracks aspects of the transition, but does not uniquely determine it.

Theoretical Foundation

This dataset is grounded in the Saelariën Constraint, a formal boundary condition governing instability in adaptive systems.

📄 Read the full paper
🔗 DOI (Zenodo)

The Saelariën Constraint establishes that system stability is limited by the relationship between entropy influx and interpretive capacity. Formally, it defines a rate bound:

dE/dt ≤ dI/dt

where entropy growth must not exceed the system’s ability to internally process and stabilize incoming perturbation. When this condition is violated, coherence cannot be maintained and collapse emerges as a consequence of unresolved structural overload.

Experiment 03 extends this framework by testing whether observable recovery dynamics uniquely encode proximity to that boundary.

The results indicate they do not.

Recovery behavior captures aspects of the system’s response to instability, but does not uniquely determine whether the underlying constraint has been violated. Systems with equivalent recovery profiles can diverge in outcome, implying that the governing boundary condition is not fully recoverable from response dynamics alone.

This supports a constraint-first interpretation of instability. Collapse is governed by a structural limit on interpretive capacity rather than by recovery behavior itself, and observable dynamics provide only a partial projection of that limit.

Motivation

Standard approaches to instability treat recovery time as a primary observable. As systems approach failure, recovery time inflates in a consistent manner, providing a measurable signal of weakening stability.

This framing implicitly assumes that recovery dynamics encode the underlying boundary condition.

The present dataset tests that assumption directly.

The goal is not to measure collapse indirectly, but to evaluate whether recovery behavior alone is sufficient to predict it.

Key Result

Recovery time does not uniquely parameterize collapse behavior.

Across the dataset, multiple recovery_time values correspond to both collapse = True and collapse = False outcomes under controlled perturbations.

This establishes a mismatch between observable recovery dynamics and final system state.

This establishes that the governing stability boundary is not uniquely recoverable from observable recovery dynamics.

The implication is structural. Recovery inflation is a projection of the transition, not the transition itself.

Figure

Figure 1: Recovery vs Collapse Mismatch

Recovery time is plotted against final system loss under controlled entropy injection.

Collapsed trials (collapse = True) and stable trials (collapse = False) occupy overlapping regions along the recovery_time axis. Identical or near-identical recovery times correspond to both outcomes.

This demonstrates that recovery dynamics do not uniquely parameterize collapse behavior.

The mapping from recovery time to final system state is non-injective. Observable recovery inflation reflects aspects of system response, but does not encode the governing stability boundary.

This provides empirical evidence that collapse is determined by a constraint on system capacity, not by recovery behavior alone.

Dataset Structure

Each row represents a single trial under controlled entropy injection.

Column	Description
noise_level	Magnitude of entropy injection
noise_type	Type of perturbation (`global`, `localized`, `structured`)
recovery_time	Time required to return to baseline under admissible dynamics
final_loss	Terminal deviation of the system
collapse	Binary outcome indicating loss of coherence

Experimental Design

The system is subjected to controlled entropy injection across multiple regimes:

global noise
localized noise
structured perturbations

Recovery time is measured under bounded perturbation protocols prior to full system divergence.

Final system state is evaluated independently of recovery dynamics.

Interpretation

Two regimes emerge:

1. Recovery-consistent regime

Systems exhibit increasing recovery time as instability is approached. Collapse may or may not occur.

2. Recovery-degenerate regime

Systems share identical or near-identical recovery profiles yet diverge in final outcome.

The second regime invalidates recovery time as a sufficient statistic for collapse prediction.

This supports a constraint-based interpretation of instability. Collapse occurs when a boundary condition is crossed, not when recovery dynamics reach a particular value.

Relation to Experiment 01

Experiment 01 demonstrated that collapse emerges under excessive entropy relative to system capacity.

[View Experiment 01 Dataset] (https://huggingface.co/datasets/Saelarien/saelarien-constraint-experiment-01-entropy-capacity-collapse)

Experiment 03 shows that observable recovery behavior does not fully encode that capacity.

Together, these results support the Saelarien Constraint:

A system cannot sustain coherence when the rate of incoming entropy exceeds its interpretive capacity, and this boundary is not uniquely recoverable from recovery dynamics alone.

Implications

Recovery time is a useful observable but not a complete descriptor
Stability boundaries cannot be reduced to response dynamics
Collapse prediction requires identifying the governing constraint directly

This reframes instability from a response-based problem to a boundary-identification problem.

Limitations

Interpretive capacity is not yet directly measured.

The dataset isolates the existence of the boundary condition, not its explicit functional form.

Future work will focus on operationalizing capacity as a measurable quantity.

Files

saelarien_constraint_experiment_03.csv Main dataset containing all trial results
saelarien_constraint_experiment_03.ipynb Experimental notebook with full simulation pipeline
saelarien_constraint_experiment_03_figure_1.png Recovery vs collapse mismatch visualization

Citation

Saelariën X, (2026). Saelariën Constraint Experiment 03: Recovery–Collapse Mismatch. The Saela Field.

License

CC BY-NC-ND 4.0

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