❶ The Question

Why does anything persist at all? In a universe of relentless change — particles colliding, stars igniting, mountains eroding, species appearing and vanishing — why do some configurations endure for billions of years while others dissolve in microseconds? Is there a general principle that explains which patterns survive and which do not, one that operates before biology, before replication, and before anyone is watching?

ECI proposes that there is: Persistence Filtering. The idea is straightforward but far-reaching. Among all the configurations that come into existence through variation and interaction, some happen to be more robust against disruption than others. Over time, the fragile ones disappear and the robust ones accumulate. What we observe at any moment is not a representative sample of all configurations that ever existed — it is the survivor distribution, biased toward configurations that were durable enough to still be here.

This is not a designed process. There is no selector, no goal, no direction. It is a statistical consequence of the fact that things which last longer are, by definition, more likely to be present when you look. ECI proposes that differential persistence may help explain why long-lived observable configurations are overrepresented relative to unstable alternatives — and that this principle is general enough to apply to river stones, crystal lattices, chemical compounds, ecological communities, and social institutions alike.

A critical clarification at the outset: this is a survivor-distribution formalization, not a known law of the universe. The claim is not that "all stable things are the result of persistence filtering." The claim is that persistence filtering is a useful conceptual and mathematical lens for understanding the statistical composition of what we observe — and that this lens generates testable predictions.

❷ The Observation

River stones

Walk along a mountain stream and pick up a stone from the riverbed. It is smooth, rounded, roughly oval. Pick up another — similar shape. Another — similar again. You might be tempted to think that rivers produce smooth round stones, as if the water were a sculptor with a preferred aesthetic.

But that is not what is happening. The river does not produce round stones. The river destroys stones that are not round. Jagged, fractured, angular stones are structurally weaker — their protruding edges experience greater hydrodynamic stress, crack more readily, and break off faster. Over time, the angular stones are progressively broken down into sand and sediment, while the rounder, more compact stones persist. The shapes you see on the riverbed are not the output of a creative process. They are the survivors of a destructive one.

This is persistence filtering in miniature. No replication is involved. No inheritance. No genetic code. The stones do not reproduce. They do not pass their shape to offspring. They simply endure or they do not — and the ones that endure are the ones you find.

Sand dunes, crystal lattices, planetary orbits

The same logic operates at every scale.

Sand dunes. In a desert, wind creates countless dune configurations — transverse ridges, barchan crescents, star dunes, linear seifs. Not all configurations are equally stable. A dune whose geometry efficiently channels airflow so that deposited sand reinforces its existing shape will persist and grow. A dune whose geometry causes wind to erode it faster than sand accumulates will shrink and vanish. The dune field you observe is the filtered residue of aerodynamic stability.

Crystal structures. When a molten mineral cools, atoms can arrange themselves in many possible configurations. Only configurations that sit at local minima of the free-energy landscape — where the attractive and repulsive forces between atoms reach a stable balance — persist as solid crystals. Configurations that land on an energy maximum or a shallow saddle point are unstable: thermal fluctuations push them toward a more stable arrangement. The crystal structures catalogued in mineralogy textbooks are the survivors of thermodynamic filtering.

Planetary orbits. The early Solar System contained vastly more bodies than the eight planets (and assorted dwarf planets, asteroids, and comets) we see today. Gravitational interactions ejected bodies on unstable orbits, sent them plunging into the Sun, or ground them into fragments through collisions. The orbital architecture we observe after 4.6 billion years is the subset that survived gravitational filtering. Numerical simulations of early solar system dynamics (Nesvorny, 2018; Clement et al., 2018) confirm that many plausible initial configurations are dynamically unstable — the current arrangement persists precisely because it is one of the stable ones.

The pattern

In every case, the pattern is the same:

1. Variation: many configurations come into existence (stone shapes, dune geometries, crystal packings, orbital arrangements).
2. Differential persistence: some configurations are more robust against the disruptive forces in their environment than others.
3. Filtered accumulation: over time, the robust configurations accumulate and the fragile ones disappear.
4. Survivor bias in observation: what we observe is the filtered distribution, not the original distribution.

No replication is required. No inheritance. No "fitness" in the biological sense. Just differential durability in the face of disruption.

❸ What We Already Know

The mathematical foundations relevant to persistence filtering come from several well-established domains. However, a key distinction must be drawn carefully: the established mathematics describes specific systems, not the universal principle ECI proposes.

Statistical selection (general). The idea that observation samples are biased toward persistent configurations is well established in statistics under various names: survivorship bias, length-biased sampling, and size-biased sampling. In reliability engineering, the distribution of component ages in a working system is not the same as the distribution of component lifetimes — it is biased toward longer-lived components, because those are the ones still present when you look. Cox (1962) formalized this as length-biased sampling. Wald's survivorship bias analysis of WWII bomber damage (documented in Mangel & Samaniego, 1984) is the classic example: the planes you see returning are precisely the ones that survived being hit, so the damage patterns on returning planes tell you where planes can afford to be hit, not where they are most vulnerable.

Thermodynamic stability and free-energy landscapes. In physical chemistry, the distribution of molecular configurations at equilibrium is governed by the Boltzmann distribution: the probability of finding a system in a configuration with energy E is proportional to exp(-E / k_B T). Configurations at deep free-energy minima are exponentially more probable than configurations at high-energy states. This is the thermodynamic version of persistence filtering: stable configurations persist because the energetic cost of leaving them is high relative to available thermal fluctuation. The mathematics is exact and thoroughly validated.

Dynamical systems: basins of attraction. In the theory of dynamical systems, a basin of attraction is the set of initial conditions from which a system evolves toward a particular attractor (fixed point, limit cycle, strange attractor). The size and shape of basins determine which long-term behaviors are "reachable" from typical starting conditions. Configurations that lie in large basins with deep, wide attractors are the ones a system is likely to end up in — and stay in. Strogatz (2015) provides a comprehensive treatment.

Replicator equation: a special case, not general evidence. The replicator equation, introduced by Taylor and Jonker (1978) and developed by Hofbauer and Sigmund (1998), is the standard mathematical framework for frequency-dependent selection in populations of replicating entities:

dx_i / dt = x_i [ f_i(x) - phi(x) ]

where x_i is the frequency of type i, f_i(x) is the fitness of type i (which may depend on the population composition x), and phi(x) is the mean fitness.

This equation is well-established and powerful — but it describes a specific mechanism: differential replication. The entities in the replicator equation reproduce, and types that reproduce faster increase in frequency. This is fundamentally different from what Persistence Filtering claims to describe. Persistence Filtering asserts that differential survival of configurations can shape the observed distribution without replication. A river stone does not replicate. A crystal lattice does not have offspring. An orbital configuration does not reproduce.

The replicator equation is therefore best understood as a special-case analogy: it demonstrates mathematically that differential dynamics can reshape distributions over time, and its formal structure (frequency change proportional to deviation from the mean) is suggestive. But citing the replicator equation as evidence for Persistence Filtering would be circular, because the replicator equation assumes exactly the mechanism (replication) that Persistence Filtering claims to generalize beyond. ECI must provide its own mathematical framework for the non-replicative case — which is what the next section attempts.

What is established vs. what ECI proposes. The following are established: survivorship bias in sampling, thermodynamic stability and Boltzmann distributions, dynamical basins of attraction, the replicator equation for replicating populations. What is not established — and is instead an ECI proposal — is that these specific, domain-bound results are all instances of a single, more general filtering principle that operates across all configuration spaces.

❹ The Framework Interpretation

The general persistence filter

ECI proposes that the observations above — river stones, crystals, orbits, and many other examples — are instances of a single, general process: whether P_pers depends systematically on independently measurable Q — the sign and functional form need not be monotonic. Intermediate compatibility might be optimal, and context may matter. The key claim is that configurations whose compatibility with their environment relates systematically to their robustness against disruption will show differential persistence, and therefore accumulate differentially in the observed distribution.

To formalize this, consider a space of possible configurations, denoted Omega (the configuration space). Each configuration is labeled by a point Omega in this space. At any time t, there is a probability distribution p_t(Omega) describing how likely we are to find the system in configuration Omega.

Persistence Filtering says: the distribution at a later time t + Delta_t is shaped by which configurations survive the interval Delta_t. Specifically:

p_{t+Delta_t}(Omega) = p_t(Omega) . S(Omega, Delta_t) / integral p_t(Omega') . S(Omega', Delta_t) dOmega'

where:

• S(Omega, Delta_t) = P(configuration Omega survives to t + Delta_t | Omega is present at t) — the survival function
• The denominator is a normalization ensuring probabilities sum to 1

This is the persistence filter equation. It says: start with whatever distribution you have at time t, weight each configuration by its probability of surviving to t + Delta_t, and renormalize. The result is the new distribution at t + Delta_t — biased toward configurations with higher survival probability.

This equation is a definition / bookkeeping identity (conditional reweighting), not a new physical law. It is a Bayesian update where "survival" plays the role of the likelihood. The mathematics is standard conditional probability — any statistician would write this given the setup. The equation itself has no empirical content; it is an accounting framework.

The ECI hypothesis: what determines P_pers?

The equation above is nearly tautological on its own — it says "things that survive are more likely to be observed," which is trivially true. The genuine scientific content of ECI enters when we propose what determines P_pers (persistence probability). ECI hypothesizes:

S = f(Q, structural stability, E, robustness, ...)

where:

• Q (compatibility) — how well the configuration fits its environment, its substrate, and the constraints imposed by surrounding systems. Defined formally in Coupling & Resonance (B5).
• Structural stability — the configuration's resistance to small perturbations (does it return to its original state after a nudge, or does it collapse?).
• E (energy) — whether the configuration has access to sufficient energy to maintain itself against entropic degradation.
• Robustness — the range of perturbation magnitudes the configuration can withstand without transitioning to a qualitatively different state.

The critical requirement: Q (compatibility) and S (survival) must be independently defined before observing which configurations actually persist. This is the tautology avoidance requirement from reference document Section 41. If we define Q by looking at what survives and then claim Q predicts survival, we have said nothing. The framework adds something only if:

1. Q is defined and measured using properties of the configuration and its environment before or independently of the survival outcome.
2. S is measured by tracking which configurations actually persist over a specified time interval.
3. Q predicts S better than chance — and better than simpler baseline models.

If Q does not predict S better than chance, the framework adds nothing. This is not a rhetorical concern — it is the primary falsifiability criterion for this page.

Relationship to Darwinian selection

Darwinian natural selection, formalized as the Core Cycle (see C5) and treated in detail on the Evolutionary Filtering (C3) page, is a special case of persistence filtering. It is the case where:

1. Replication is present — configurations produce copies of themselves.
2. Inheritance operates — offspring resemble their parents (copies are imperfect but correlated).
3. Heritable variation exists — differences between individuals are transmitted to the next generation.

When all three conditions hold, persistence filtering takes on the specific dynamics described by the replicator equation: configurations that replicate faster increase in frequency, and the population evolves by differential reproduction. This is the familiar machinery of natural selection — mutation, selection, genetic drift, speciation.

But persistence filtering, as ECI proposes it, does not require any of these three conditions. A crystal lattice persists without replicating. A river stone endures without inheriting its shape from a parent stone. A planetary orbit survives without producing offspring orbits. In these cases, the filtering operates purely through differential durability — and the replicator equation does not apply.

The relationship is hierarchical:

• Persistence Filtering (general): any process where differential survival shapes the observed distribution of configurations. No replication required.
• Darwinian Selection (special case): persistence filtering + replication + inheritance + heritable variation. The replicator equation applies here. See C3.

ECI claims that recognizing this hierarchy is scientifically productive — it reveals that the pattern-shaping power of selection-like processes is broader than biology, and it motivates the search for persistence filtering in domains where replication is absent.

The core cycle connection

Persistence Filtering is one phase of a broader cycle that ECI calls the Core Cycle (see C5):

Variation (new configurations arise) → Explore (configurations interact with their environment) → Coupling Opportunities (configurations encounter opportunities to couple with their surroundings; compatibility and resonance operate as mechanisms within this stage, not as guaranteed outcomes) → Filter (configurations that are not robust enough are eliminated) → Persist (surviving configurations enter the next round)

Persistence Filtering corresponds to the Filter → Persist transition in this cycle. It is the mechanism by which the cycle prunes its output — retaining configurations that are robust and discarding those that are not. Without persistence filtering, the cycle would generate variation without accumulating any; with it, the cycle ratchets, preferentially retaining configurations that are durable.

❺ If This Were True...

If persistence filtering is truly a universal principle — operating on any configuration space, not just biological populations — several far-reaching implications follow.

Pre-biological organization. Persistence filtering would have operated long before the origin of life. The chemical compounds present in the prebiotic ocean, the mineral structures on early Earth's surface, the atmospheric compositions of young planets — all would have been shaped by differential persistence before any replicating molecule appeared. The "prebiotic soup" was not a random mixture; it was a filtered mixture, enriched in compounds that happened to be thermodynamically stable or kinetically trapped under the prevailing conditions. This reframes the origin of life: the first replicator did not appear from a random chemical background but from an already-filtered one, where a disproportionate share of the available chemistry consisted of relatively persistent molecular species.

Information patterns as filtered configurations. If the configuration space Omega includes not just physical structures but information patterns — data formats, communication protocols, cultural practices, mathematical notations — then persistence filtering would apply to information as well. The notational systems, languages, and institutional structures that persist in human civilization would be, in part, survivors of a filtering process that eliminates configurations poorly matched to their social, cognitive, and technological environment. This is not to deny human agency and design — it is to suggest that even designed configurations face a post-design persistence filter.

Convergent forms across domains. If different domains (geology, chemistry, biology, technology, culture) are all subject to the same general filtering principle, we might expect convergent forms — not because the domains are causally connected, but because they face similar filtering pressures. The ubiquity of certain geometric forms (spheres, spirals, branching trees), certain network architectures (scale-free, small-world), and certain organizational patterns (hierarchies, modular decomposition) across wildly different domains might reflect, in part, the fact that these configurations are generically robust against disruption.

A reframing, not a replacement. Persistence filtering does not replace domain-specific explanations. Geology still needs plate tectonics; chemistry still needs quantum mechanics; biology still needs natural selection. What persistence filtering offers is a shared meta-pattern that connects these domain-specific stories — a reason to expect that certain structural themes recur across domains, and a mathematical framework for quantifying the degree of filtering in any given system.

These implications are speculative. Their value depends entirely on whether persistence filtering, as formalized here, generates predictions that survive empirical testing in specific domains.

❻ How Could We Test It?

Persistence Filtering makes several testable claims, each requiring careful attention to the tautology-avoidance criterion: Q and S must be independently defined and measured.

Test 1: Independent prediction of survival from compatibility. Choose a well-characterized system — say, mineral crystal structures. Define Q (compatibility) using computable properties of the crystal structure and its formation environment: lattice energy, elastic modulus, defect formation energy, thermodynamic stability relative to competing phases. These are measurable before knowing which structures persist over geological time. Define S (survival) using the geological record: which mineral structures are actually found in rocks of a given age, and how does their relative abundance change over time? The framework predicts that Q, computed independently, correlates with S. If the correlation is no better than chance — or no better than a simpler predictor like "hardness" alone — the framework adds nothing for this system.

Test 2: Agent-based simulation of non-replicative filtering. Build an agent-based model where configurations (not replicating agents) are placed in an environment with stochastic disruptions. Each configuration has measurable properties (structural symmetry, energy, connectivity, etc.) from which Q is computed. Run the simulation and track which configurations survive over time (S). The framework predicts: (a) the distribution of surviving configurations shifts toward high-Q configurations over time, and (b) Q predicts S better than random assignment of survival probabilities. Varying the environment (different disruption regimes) should shift the Q-S relationship in predictable ways.

Test 3: Comparison with null models. For any empirical system, compare the persistence-filtering prediction (Q predicts S) against null models: (a) random survival (S is independent of configuration properties), (b) size-based survival (larger/heavier things survive longer, regardless of structural properties), (c) frequency-based survival (common configurations persist simply because they are common). The framework is scientifically productive only if Q-based predictions outperform these null models.

Test 4: Cross-domain generality. Apply the same formal template (the persistence filter equation) to systems from at least three distinct domains — say, mineral stability, protein fold persistence, and organizational survival. In each domain, independently define Q using domain-appropriate measures, independently measure S, and test whether the Q-S relationship holds. If the framework works in one domain but fails in others, it is a domain-specific tool rather than a universal principle — still useful, but the claim of universality is weakened.

Test 5: Pre-biological chemistry. Miller-Urey-type experiments produce a mixture of organic compounds. Measure the properties of all compounds produced (molecular stability, reactivity, polymerization tendency). Use these to compute Q. Then track which compounds persist in the mixture over time (S). The framework predicts that the surviving compounds are enriched in high-Q configurations relative to the initial production distribution. If the surviving distribution is indistinguishable from the initial distribution, filtering is not occurring (or Q is not capturing the relevant properties).

What would weaken this claim: If Q does not predict S better than simpler single-variable baselines (e.g., just thermodynamic stability, just mass, just size) in any tested system. This would suggest that the multi-factor decomposition S = f(Q, stability, E, robustness, ...) adds unnecessary complexity.

What would kill this claim: If survival in non-replicative systems is genuinely random — that is, if no measurable property of a configuration predicts its persistence better than chance, across multiple domains and multiple measurement approaches. This would mean that persistence filtering is not a useful lens: things persist or they do not, and there is no general structure to which ones survive.

❼ Connected Nodes

→ ECI Cycle (B6): The ECI Cycle describes the continuous dynamic process — Information, Carrier, and Energy in constant flow — that sustains any functioning system. Persistence Filtering is the mechanism that determines which cycling configurations endure: those whose ECI cycles are robust against disruption persist, while those whose cycles are fragile degrade. B6 provides the dynamics; C2 provides the filter that acts on those dynamics.

→ Variation & Coordination (C1): Variation is the raw material on which persistence filtering operates. Without variation — without diverse configurations entering the system — there is nothing to filter. C1 develops the V-kappa framework describing how variation and coordination interact; C2 describes the temporal sieve through which those varied configurations pass. The V* hypothesis (optimal variation level) connects directly: too much uncoordinated variation produces configurations that are fragile and get filtered out; too little produces configurations that cannot adapt when conditions change.

→ Evolutionary Filtering (C3): Darwinian natural selection is the special case of persistence filtering where replication, inheritance, and heritable variation are all present. C3 develops this special case in detail, including the replicator equation that governs its dynamics. The relationship is hierarchical: C2 (general persistence filtering, no replication required) encompasses C3 (biological selection, replication required).

→ Core Cycle (C5): The Core Cycle — Variation, Explore, Coupling Opportunities, Filter, Persist — is the engine of change that ECI proposes as universal. Persistence Filtering corresponds to the Filter-to-Persist transition within this cycle. C5 develops the full cycle; C2 develops the filtering step in mathematical detail.

→ Life (D1): Life is a domain where persistence filtering and evolutionary filtering operate simultaneously. Living systems are configurations that persist (C2) and replicate (C3), placing them under both the general filter and the Darwinian special case. D1 examines what distinguishes living configurations from merely persistent ones.

→ Falsifiability (F3): The tautology-avoidance requirement is the central falsifiability concern for this page. If Q and S cannot be independently defined and measured, the persistence-filtering framework collapses into a tautology ("things that survive are the ones that survive"). F3 develops the general falsifiability standards that ECI applies to all its claims; C2's specific application of those standards is the independent-definition requirement for Q and S.

❽ Mathematical Detail

The Persistence Filter Equation (Adapted)

The persistence filter equation formalizes how differential survival reshapes a distribution of configurations over time.

Let Omega denote the configuration space — the set of all possible configurations a system might take. Let p_t(Omega) be the probability density over configurations at time t. Define:

S(Omega, Delta_t) = P(Omega survives to t + Delta_t | Omega, t)

the probability that a configuration Omega present at time t is still present at time t + Delta_t. Then the filtered distribution at t + Delta_t is:

p_{t+Delta_t}(Omega) = p_t(Omega) . S(Omega, Delta_t) / Z(t, Delta_t)

where the normalization factor is:

Z(t, Delta_t) = integral p_t(Omega') . S(Omega', Delta_t) dOmega'

• Status: The mathematical structure (Bayesian update with survival likelihood) is standard. Its application to arbitrary configuration spaces as a proposed general filtering principle is an ECI contribution.
• Assumptions: (1) Configurations can be meaningfully represented as points in a configuration space. (2) The survival function S can, in principle, be estimated for the system under study. (3) The configuration space does not change over the interval Delta_t (or changes slowly relative to the filtering dynamics).
• Limitation: The equation describes filtering on a static configuration space. It does not capture the generation of new configurations (variation), which is handled by the Core Cycle (C5). A complete model would alternate variation steps (expanding the support of p_t) with filtering steps (contracting it via S).

S Decomposition (Proposed)

ECI proposes that the survival function S can be decomposed into contributions from identifiable factors:

S(Omega, Delta_t) = f(Q(Omega, E_env), sigma(Omega), E(Omega), rho(Omega), ...)

where:

• Q(Omega, E_env) — the compatibility of configuration Omega with its environment E_env. Defined independently of survival outcome, using structural, energetic, or informational properties of Omega and E_env. See B5 for the formal definition of Q.

• sigma(Omega) — the structural stability of Omega: whether small perturbations return the system to Omega or push it toward a different configuration. Operationalized via Lyapunov stability, basin depth in a free-energy landscape, or eigenvalue analysis of the system's linearized dynamics.

• E(Omega) — the energy budget: whether Omega has access to sufficient free energy to maintain its configuration against entropic degradation. For passive configurations (crystals, stones), this may be negligible; for active configurations (cells, ecosystems), it is critical.

• rho(Omega) — the robustness: the range of perturbation magnitudes Omega can absorb without transitioning to a qualitatively different configuration. Related to but distinct from sigma — a system can be locally stable (sigma high) but fragile to large perturbations (rho low).

• Status: Proposed. The decomposition is a hypothesis about the structure of S, not a derived result. The functional form of f is not specified.

• Critical constraint (tautology avoidance): Each factor in the decomposition must be independently measurable without reference to the survival outcome. Specifically:

  • Q must be computable from properties of Omega and E_env alone.
  • sigma must be measurable via perturbation experiments or dynamical analysis.
  • E must be measurable via calorimetry, energy-budget analysis, or thermodynamic calculation.
  • rho must be measurable via systematic perturbation of increasing magnitude.
  • S must be measured by observing actual persistence over the interval Delta_t.
  • The test is whether f(Q, sigma, E, rho, ...) predicts S better than chance and better than simpler baselines.

• If Q does not predict S better than chance, the framework adds nothing. This is the central falsifiability criterion.

Relationship to the Replicator Equation (Special-Case Analogy)

The replicator equation governs frequency change in a population of replicating types:

dx_i / dt = x_i [ f_i(x) - phi(x) ]

In this equation, types that replicate faster than average increase in frequency; types that replicate slower decrease. Over time, the population distribution shifts toward high-fitness types.

The persistence filter equation shares a formal similarity: configurations with higher-than-average S increase in the distribution; configurations with lower-than-average S decrease. But the mechanisms are fundamentally different:

| Feature | Replicator equation | Persistence filter equation | |---|---|---| | Mechanism | Differential replication | Differential survival (no replication) | | Requires reproduction | Yes | No | | Requires inheritance | Yes | No | | Distribution change driver | Faster replication | Longer persistence | | Applicable to | Replicating populations | Any configuration space |

The replicator equation is a special case of the broader evolutionary filtering described in C3, which is itself a special case of persistence filtering (this page). Citing the replicator equation as evidence for persistence filtering would be a category error: the replicator equation assumes replication, which is exactly the requirement that persistence filtering claims to generalize beyond.

• Status: The replicator equation is established. Its use here as a structural analogy (not as evidence) is an ECI framing choice.

Summary of Notation

| Symbol | Name | Type | Defined in | |---|---|---|---| | Omega | Configuration / configuration space | Standard variable | This page | | p_t(Omega) | Configuration distribution at time t | Standard variable | This page | | S(Omega, Delta_t) | Survival function | Proposed definition | This page | | Z(t, Delta_t) | Normalization factor | Derived quantity | This page | | Q | Compatibility function | Proposed definition | B5 | | sigma | Structural stability | Proposed definition | This page | | E | Energy budget | Standard variable | B3 | | rho | Robustness | Proposed definition | This page | | E_env | Environment descriptor | Standard variable | This page | | x_i | Frequency of type i (replicator eq.) | Established | C3 | | f_i | Fitness of type i (replicator eq.) | Established | C3 | | phi | Mean fitness (replicator eq.) | Established | C3 |

Key Literature Referenced

| Reference | Result | Relevance to C2 | |---|---|---| | Cox (1962) | Length-biased sampling: observed distributions are biased toward long-duration items | Established statistical foundation for survivorship bias | | Mangel & Samaniego (1984) | Wald's WWII bomber survivorship bias analysis | Classic example of persistence filtering in observational data | | Taylor & Jonker (1978); Hofbauer & Sigmund (1998) | Replicator equation for frequency-dependent selection | Special case analogy — applies only to replicating populations | | Strogatz (2015) | Dynamical systems: basins of attraction, stability analysis | Established mathematical tools for analyzing which configurations persist | | Nesvorny (2018); Clement et al. (2018) | Solar system dynamical instability simulations | Empirical example: orbital filtering over 4.6 Gyr | | Boltzmann (1877) | Boltzmann distribution: equilibrium probability proportional to exp(-E/k_B T) | Thermodynamic persistence filtering — stable configurations exponentially favored | | Prigogine (1977) | Dissipative structures: order from energy flow far from equilibrium | Active persistence requiring energy throughput |