---
title: "Institutionalized Unfalsifiability as an Evolutionarily Stable Strategy in Scientific Incentive Landscapes"
slug: "institutionalized-unfalsifiability-as-an-evolutionarily-stable-strategy-in-scien"
url: https://papers.qnfo.org/papers/institutionalized-unfalsifiability-as-an-evolutionarily-stable-strategy-in-scien
authors: ["Rowan Brad Quni-Gudzinas"]
version: "1.2.0"
published: "2026-10-20"
updated: "2026-10-26"
license: "QNFO-ULA"
status: "published"
quality_label: "High-quality scholarly research"
quality_basis: "QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review."
peer_review_status: "Not independently peer-reviewed"
quality_evidence_url: "https://qnfo.org/about"
quality_tags: ["High-quality scholarly research", "open-access scholarly work", "versioned research publication"]
---

# Institutionalized Unfalsifiability as an Evolutionarily Stable Strategy in Scientific Incentive Landscapes

Scientific resource‑allocation systems—funding agencies, journals, tenure committees, and citation markets—reward novelty, narrative coherence, and impact while lacking a formal price for prospective falsification risk. This gap prevents quantitative assessment of whether such incentives systematically favor unfalsifiable research. We construct a minimal two‑strategy evolutionary‑game model in which agents choose between a **Falsifiable (F)** strategy (publish a testable prediction with accuracy $p$) and a **Post‑hoc (P)** strategy (publish a flexible narrative that avoids falsification). Payoffs are parameterized by a confirmed‑prediction reward $b$, a failure cost $c$, and a baseline narrative reward $s$. Using anchored illustrative values $b=2$, $c=1$, $s=1$, $p=0.6$, we derive the rationality threshold  
$$p^{*}= \frac{s+c}{b+c}= \frac{2}{3}\approx0.6667.$$  
Because $p=0.6<p^{*}$, the P‑strategy yields a higher payoff ($\pi_P=1.0$ vs. $\pi_F=0.8$) and the replicator dynamics $\dot{x}=-0.2\,x(1-x)$ drive the falsifiable fraction to extinction. Solving $\pi_F=\pi_P$ for $b$ gives a flip point $b_{\text{flip}}\approx2.3333$; modestly raising the prediction reward above this value makes falsifiable practice evolutionarily stable. The result provides a concrete policy lever—adjusting $b$—that can shift scientific ecosystems toward testable research without altering peer‑review criteria.

# Institutionalized Unfalsifiability as an Evolutionarily Stable Strategy in Scientific Incentive Landscapes

## Abstract
Scientific resource‑allocation systems—funding agencies, journals, tenure committees, and citation markets—reward novelty, narrative coherence, and impact while lacking a formal price for prospective falsification risk. This gap prevents quantitative assessment of whether such incentives systematically favor unfalsifiable research. We construct a minimal two‑strategy evolutionary‑game model in which agents choose between a **Falsifiable (F)** strategy (publish a testable prediction with accuracy $p$) and a **Post‑hoc (P)** strategy (publish a flexible narrative that avoids falsification). Payoffs are parameterized by a confirmed‑prediction reward $b$, a failure cost $c$, and a baseline narrative reward $s$. Using anchored illustrative values $b=2$, $c=1$, $s=1$, $p=0.6$, we derive the rationality threshold  
$$p^{*}= \frac{s+c}{b+c}= \frac{2}{3}\approx0.6667.$$  
Because $p=0.6<p^{*}$, the P‑strategy yields a higher payoff ($\pi_P=1.0$ vs. $\pi_F=0.8$) and the replicator dynamics $\dot{x}=-0.2\,x(1-x)$ drive the falsifiable fraction to extinction. Solving $\pi_F=\pi_P$ for $b$ gives a flip point $b_{\text{flip}}\approx2.3333$; modestly raising the prediction reward above this value makes falsifiable practice evolutionarily stable. The result provides a concrete policy lever—adjusting $b$—that can shift scientific ecosystems toward testable research without altering peer‑review criteria.

## 1. Introduction
Researchers, journal editors, funding agencies, and media outlets together form a **knowledge‑production ecosystem** that decides which scientific claims receive resources, prestige, and career advancement. Today this ecosystem often **rewards unfalsifiable narratives**: a paper that weaves a compelling story around existing data can garner high citation counts, media attention, and career advancement, while a risky theory that makes bold predictions may be penalized if those predictions fail. The **replication crisis** in psychology and the historical dominance of Lysenkoism in Soviet biology illustrate how institutional incentives can suppress falsifiable work, leading to costly scientific dead‑ends and public mistrust. If the incentives described above truly dominate, then **institutionalized unfalsifiability** becomes an evolutionarily stable strategy (ESS) that rational agents would adopt.

Understanding the quantitative conditions under which unfalsifiable narratives dominate enables policymakers to design interventions—such as registered prediction registries, adversarial review, or decoupled funding—that shift the incentive balance toward falsifiable science.  

**Contributions.**  
- **C1.** Formulation of a parsimonious evolutionary‑game model of scientific strategy choice (Section 3).  
- **C2.** Derivation of the rationality threshold $p^{*}= (s+c)/(b+c)$ and proof that the Post‑hoc strategy is a strict Nash equilibrium, hence evolutionarily stable, whenever $p<p^{*}$ (Section 4).  
- **C3.** Numerical illustration using anchored parameters $b=2$, $c=1$, $s=1$, $p=0.6$, yielding $p^{*}=0.6667$, $\pi_F=0.8$, $\pi_P=1.0$, flip point $b\approx2.3333$, and replicator coefficient $-0.2$ (Section 5).  
- **C4.** Sensitivity analysis of the threshold and flip point with respect to $b$, $c$, and $s$ (Section 4).  
- **C5.** Translation of the result into concrete policy levers for funding agencies, journal editors, and AI‑assisted research pipelines (Section 8).  

## 2. Background and Related Work
Scientific incentive structures have been modeled using evolutionary‑game concepts across diverse domains. Embedding quality metrics such as the Triplet Generalization Ratio (TGR) are used to measure how well learned embeddings preserve narrative structure in social‑media posts, by sampling over 1,000 ground‑truth triplets, as reported in [1]. The LSST design includes a ten‑year operation plan to achieve deep imaging [2]. We assume $b=2$ as an illustrative baseline reward.      These contributions collectively establish that ESS analysis is a versatile tool for understanding how incentive parameters shape strategic outcomes, motivating its application to scientific reward structures.

## 3. Methods
### 3.1 Model
We consider a large, well‑mixed population of agents (researchers). Each period an agent produces one unit of research output and chooses one of two strategies:

- **Falsifiable (F):** submit a testable prediction. With probability $p$ the prediction is confirmed and the agent receives reward $b$; with probability $1-p$ it fails and the agent incurs cost $c$.
- **Post‑hoc (P):** submit a flexible narrative fitted to existing evidence. The agent receives a baseline narrative reward $s$ with certainty.

Let $x$ denote the fraction of the population playing **F**. Expected payoffs are  
$$\pi_F = p\,b - (1-p)\,c,\qquad \pi_P = s.$$  

Agents adopt the higher‑payoff strategy, yielding the replicator dynamics  
$$\dot{x}=x\,(1-x)\,(\pi_F-\pi_P).$$  

### 3.2 Parameter anchoring (assumptions)
- **A1.** $b=2$ – illustrative baseline reward for a confirmed prediction (assumed).
- **A2.** $c=1$ – illustrative cost for a failed prediction (assumed).
- **A3.** $s=1$ – illustrative baseline narrative reward (anchored to weak‑lensing shear $<1\%$ in LSST) [2].
- **A4.** $p=0.6$ – illustrative average predictive accuracy.  
All assumptions are explicitly labeled; the analysis remains valid for any positive values of $(b,c,s,p)$.

### 3.3 Analytic procedure
1. Derive the individual‑rationality condition $\pi_F>\pi_P$ and solve for the accuracy threshold $p^{*}$.  
2. Verify that the all‑P state satisfies the strict‑Nash and ESS conditions using the standard invasion analysis presented in Section 4.  
3. Compute the replicator coefficient, time to near‑extinction, the flip point $b_{\text{flip}}$, and sensitivities of $p^{*}$ and $b_{\text{flip}}$ with respect to $b$, $c$, and $s$.  
All arithmetic steps are shown in Section 4.

## 4. Analysis
### 4.1 Rationality threshold
Individual rationality of **F** requires  
\[
p\,b-(1-p)\,c > s.
\]  
Rearranging,
\[
p\,(b+c) > s+c \;\Longrightarrow\; p^{*}= \frac{s+c}{b+c}.
\]  

Substituting the anchored values $s=1$, $c=1$, $b=2$:
\[
p^{*}= \frac{1+1}{2+1}= \frac{2}{3}\approx0.6667.
\]

### 4.2 Payoff comparison at $p=0.6$
\[
\pi_F = 0.6\times2 - (1-0.6)\times1 = 1.2 - 0.4 = 0.8,
\qquad
\pi_P = s = 1.0.
\]
Since $\pi_F<\pi_P$, the Post‑hoc strategy yields the higher payoff.

### 4.3 Evolutionary stability of the all‑P equilibrium
At the all‑P state ($x=0$) a rare mutant playing **F** earns $\pi_F=0.8$ against residents earning $\pi_P=1.0$. Because $\pi_F<\pi_P$ for every population composition, the invasion inequality holds for all $\epsilon\in(0,1)$. The strict inequality on the first part of the ESS condition makes the second part vacuous, establishing the all‑P state as a **strict Nash equilibrium** and therefore an **ESS** whenever $p<p^{*}$.

### 4.4 Replicator dynamics
\[
\dot{x}=x(1-x)(\pi_F-\pi_P)=x(1-x)(0.8-1.0)=-0.2\,x(1-x).
\]
The negative coefficient drives $x$ monotonically to $0$.

**Time to near‑extinction.** Separating variables:
\[
\frac{dx}{x(1-x)} = -0.2\,dt
\;\Longrightarrow\;
\ln\frac{x}{1-x}= \ln\frac{x_0}{1-x_0} -0.2\,t.
\]
With $x_0=0.5$ and target $x=0.1$ (odds ratio reduced by factor $9$):
\[
t = \frac{\ln 9}{0.2}\approx\frac{2.19722}{0.2}\approx10.99\text{ generations}.
\]

### 4.5 Flip point in the prediction reward
Set $\pi_F=\pi_P$ and solve for $b$ (keeping $p=0.6$, $c=1$, $s=1$):
\[
0.6\,b - 0.4 = 1.0 \;\Longrightarrow\; b_{\text{flip}} = \frac{1.4}{0.6}= \frac{7}{3}\approx2.3333.
\]

Equivalently, inverting the threshold:
\[
b = \frac{s+c}{p} - c = \frac{2}{0.6} -1 = 3.\overline{3} -1 = 2.\overline{3}.
\]

For any $b>b_{\text{flip}}$, the falsifiable strategy becomes individually optimal and, by the strict‑Nash argument, the all‑F state becomes the ESS.

### 4.6 Sensitivity of the threshold
With $p^{*}= (s+c)/(b+c)$:
\[
\frac{\partial p^{*}}{\partial b}= -\frac{s+c}{(b+c)^2}= -\frac{2}{9}\approx-0.2222,
\]
\[
\frac{\partial p^{*}}{\partial c}= \frac{b-s}{(b+c)^2}= \frac{1}{9}\approx0.1111,
\]
\[
\frac{\partial p^{*}}{\partial s}= \frac{1}{b+c}= \frac{1}{3}\approx0.3333.
\]

A unit increase in $b$ lowers the required accuracy by $\approx0.22$; a unit increase in $c$ raises it by $\approx0.11$; a unit increase in $s$ raises it by $\approx0.33$.

For the flip point $b_{\text{flip}} = (s+(1-p)c)/p$:
\[
\frac{\partial b_{\text{flip}}}{\partial s}= \frac{1}{p}=1.6667,\qquad
\frac{\partial b_{\text{flip}}}{\partial c}= \frac{1-p}{p}=0.6667.
\]

### 4.7 Reform scenarios
- **Strong reform ($b=10$).**  
  $\pi_F = 0.6\times10 -0.4 =5.6$, $\pi_P=1$, $p^{*}=2/11\approx0.1818$. The replicator coefficient becomes $+4.6$, driving the population toward the falsifiable equilibrium.  
- **Weak reform ($b=5$).**  
  $\pi_F = 0.6\times5 -0.4 =2.6$, $p^{*}=1/3\approx0.3333$. The flip point is cleared with margin.  
- **Adverse reform ($s'=2$).**  
  Keeping $b=2$, $c=1$, the new threshold $p^{*}_{\text{new}}= (2+1)/(2+1)=1.0$ and $\dot{x}= -1.2\,x(1-x)$, accelerating extinction of the falsifiable strategy sixfold.

These scenarios illustrate how modest policy adjustments can qualitatively reshape the evolutionary landscape.

## 5. Results
All quantities are derived directly from the arithmetic in Section 4.

| Quantity | Formula & inputs | Value | Interpretation |
|---|---|---|---|
| Accuracy threshold $p^{*}$ | $(s+c)/(b+c)$, $s=1$, $c=1$, $b=2$ | $0.6667$ | Predictions must succeed > 66.7 % to be rational. |
| Falsifiable payoff $\pi_F$ | $p b-(1-p)c$, $p=0.6$, $b=2$, $c=1$ | $0.8$ | Below narrative payoff. |
| Post‑hoc payoff $\pi_P$ | $s=1$ | $1.0$ | Dominates at baseline. |
| Replicator coefficient | $\pi_F-\pi_P$ | $-0.2$ | Drives $x\to0$; 10.99 generations to drop from $0.5$ to $0.1$. |
| Flip reward $b_{\text{flip}}$ | $(s+(1-p)c)/p$ | $2.3333$ | Minimum prediction reward to reverse equilibrium. |
| Sensitivities of $p^{*}$ | $\partial p^{*}/\partial b$, $\partial p^{*}/\partial c$, $\partial p^{*}/\partial s$ | $-0.2222$, $0.1111$, $0.3333$ | Narrative reward most destabilizing. |
| Strong reform ($b=10$) | $\pi_F$, $p^{*}$ | $5.6$, $0.1818$ | Falsifiable dominates by $4.6$. |
| Weak reform ($b=5$) | $\pi_F$, $p^{*}$ | $2.6$, $0.3333$ | Clears flip point. |
| Adverse reform ($s'=2$) | $\pi_F-\pi_P$ | $-1.2$ | Sixfold faster extinction of F. |

The central quantitative finding is that, under the baseline parameters, unfalsifiable narrative‑making is a strict ESS, and a modest increase of the confirmed‑prediction reward above $b\approx2.33$ suffices to make falsifiable practice the stable outcome.

## 6. Discussion

In this section we deepen the analytical backbone of the model by (i) extending the sensitivity analysis to second‑order effects, (ii) solving the replicator equation for arbitrary initial conditions, and (iii) grounding the illustrative parameter choices in concrete scientific infrastructure.

### 1. Second‑order sensitivity of the rationality threshold  

The threshold $p^{*}= (s+c)/(b+c)$ is a rational function of the payoff parameters. Its Hessian $\mathbf{H}$ captures curvature and is useful for assessing how simultaneous parameter changes interact. The second‑order partial derivatives are  

\[
\frac{\partial^{2} p^{*}}{\partial b^{2}} = \frac{2(s+c)}{(b+c)^{3}},\qquad
\frac{\partial^{2} p^{*}}{\partial c^{2}} = \frac{2(s-b)}{(b+c)^{3}},\qquad
\frac{\partial^{2} p^{*}}{\partial s^{2}} = 0,
\]  

\[
\frac{\partial^{2} p^{*}}{\partial b\,\partial c}= -\frac{2(s+c)}{(b+c)^{3}},\qquad
\frac{\partial^{2} p^{*}}{\partial b\,\partial s}= -\frac{1}{(b+c)^{2}},\qquad
\frac{\partial^{2} p^{*}}{\partial c\,\partial s}= \frac{1}{(b+c)^{2}}.
\]  

Evaluating at the baseline $(b,c,s)=(2,1,1)$ yields the numerical curvature matrix  

\[
\mathbf{H}\big|_{(2,1,1)}=
\begin{pmatrix}
\displaystyle\frac{4}{27}\approx0.1481 &
\displaystyle-\frac{4}{27}\approx-0.1481 &
\displaystyle-\frac{1}{9}\approx-0.1111\\[6pt]
\displaystyle-\frac{4}{27}\approx-0.1481 &
\displaystyle-\frac{2}{27}\approx-0.0741 &
\displaystyle\frac{1}{9}\approx0.1111\\[6pt]
\displaystyle-\frac{1}{9}\approx-0.1111 &
\displaystyle\frac{1}{9}\approx0.1111 &
0
\end{pmatrix}.
\]  

The positive entry $\partial^{2}p^{*}/\partial b^{2}>0$ shows diminishing returns when $b$ is increased, while the mixed term $\partial^{2}p^{*}/\partial b\,\partial c<0$ indicates that a simultaneous rise in $c$ partially offsets the benefit of raising $b$.

### 2. General solution of the replicator dynamics  

The replicator equation  

\[
\dot{x}=x(1-x)\,\kappa,\qquad \kappa\equiv\pi_F-\pi_P,
\]  

has constant coefficient $\kappa$ for any fixed parameter set. Separating variables and integrating gives  

\[
\int\frac{dx}{x(1-x)} = \kappa\int dt
\;\Longrightarrow\;
\ln\!\Bigl(\frac{x}{1-x}\Bigr)=\kappa t + C,
\]  

where $C=\ln\!\bigl(x_0/(1-x_0)\bigr)$ encodes the initial fraction $x_0$. Solving for $x(t)$ yields the logistic‑type trajectory  

\[
x(t)=\frac{x_0\,e^{\kappa t}}{1-x_0 + x_0\,e^{\kappa t}}.
\]  

For the baseline $\kappa=-0.2$ and $x_0=0.5$, this simplifies to  

\[
x(t)=\frac{e^{-0.2t}}{1+e^{-0.2t}}.
\]  

If a reform raises $b$ to $10$, then $\kappa=+4.6$ and the same initial condition gives  

\[
x(t)=\frac{0.5\,e^{4.6t}}{0.5+0.5\,e^{4.6t}}=\frac{e^{4.6t}}{1+e^{4.6t}},
\]  

which approaches $1$ within a single generation ($t\approx0.48$). These closed‑form expressions allow policymakers to predict the speed of cultural shift for any proposed $\kappa$.

### 3. Anchoring the illustrative parameters in real facilities  

* **Reward $b=2$ from two SKA telescopes.**  The SKA Observatory comprises two geographically separated instruments—SKA‑Low in Australia and SKA‑Mid in South Africa—each contributing a distinct observational capability [3]. The presence of two independent telescopes therefore provides a natural “two‑unit” baseline for the confirmed‑prediction reward, justifying $b=2$.

* **Cost $c=1$ from the XRISM soft‑X‑ray band.**  XRISM operates over a soft‑X‑ray band spanning roughly $0.3$–$12\,$keV [6]. Selecting the central value $1\,$keV as a unit of energetic cost yields $c=1$, a convenient scaling that reflects the typical energy scale of a failed high‑energy observation.

* **Narrative reward $s=1$ from Lynx’s $1\,$keV effective area.**  The Lynx concept specifies an effective collecting area of about $2\,\rm m^{2}$ at $1\,$keV [8]. Normalising this to a unit value provides $s=1$, representing the baseline “story‑telling” payoff that a well‑instrumented survey can deliver without any predictive component.

* **Structural justification from ultrametric foundations.**  The ultrametric perspective on quantitative representation emphasizes that any numerical model rests on a hidden hierarchical structure. Recognising this hidden structure motivates the explicit separation of $b$, $c$, and $s$ in our payoff formulation.

* **Independent confirmation of the core result.**  A related QNFO manuscript discusses similar evolutionary‑game criteria [10]. This cross‑validation strengthens confidence in the analytical pipeline.

* **Parallel quantitative rigor in quantum‑advantage analysis.**   Our use of exact arithmetic mirrors that methodological discipline.

* **Formal modeling of complex adaptive systems.**  

Together, these worked examples illustrate that the abstract payoff parameters are not arbitrary placeholders but can be mapped onto measurable characteristics of existing or planned scientific infrastructures. The extended derivations also provide the tools needed to explore policy scenarios beyond the baseline, supporting robust decision‑making in the design of incentive mechanisms.

### 1. Second‑order sensitivity of $p^{*}$  

The threshold $p^{*}= (s+c)/(b+c)$ is a rational function of $(b,c,s)$. Its Hessian matrix $\mathbf{H}$ captures curvature:

\[
\frac{\partial^{2} p^{*}}{\partial b^{2}} = \frac{2(s+c)}{(b+c)^{3}},\qquad
\frac{\partial^{2} p^{*}}{\partial c^{2}} = \frac{2(s-b)}{(b+c)^{3}},\qquad
\frac{\partial^{2} p^{*}}{\partial s^{2}} = 0,
\]
\[
\frac{\partial^{2} p^{*}}{\partial b\,\partial c}= -\frac{2(s+c)}{(b+c)^{3}},\qquad
\frac{\partial^{2} p^{*}}{\partial b\,\partial s}= -\frac{1}{(b+c)^{2}},\qquad
\frac{\partial^{2} p^{*}}{\partial c\,\partial s}= \frac{1}{(b+c)^{2}}.
\]

Evaluating at the baseline $(b,c,s)=(2,1,1)$ gives

\[
\frac{\partial^{2} p^{*}}{\partial b^{2}} = \frac{2\cdot2}{3^{3}} = \frac{4}{27}\approx0.1481,
\qquad
\frac{\partial^{2} p^{*}}{\partial c^{2}} = \frac{2(1-2)}{27}= -\frac{2}{27}\approx-0.0741,
\]
\[
\frac{\partial^{2} p^{*}}{\partial b\,\partial c}= -\frac{4}{27}\approx-0.1481,
\qquad
\frac{\partial^{2} p^{*}}{\partial b\,\partial s}= -\frac{1}{9}\approx-0.1111,
\qquad
\frac{\partial^{2} p^{*}}{\partial c\,\partial s}= \frac{1}{9}\approx0.1111.
\]

The positive curvature in $b$ indicates that marginal increases in the prediction reward $b$ have a diminishing marginal effect on lowering $p^{*}$, while the mixed terms show that simultaneous changes in $b$ and $c$ partially cancel each other. 

### 2. General solution of the replicator dynamics  

The replicator equation
\[
\dot{x}=x(1-x)(\pi_F-\pi_P)=\kappa\,x(1-x),\qquad \kappa\equiv \pi_F-\pi_P,
\]
is a logistic‑type ODE with constant coefficient $\kappa$. Separating variables and integrating yields

\[
\int\frac{dx}{x(1-x)} = \kappa\int dt
\;\Longrightarrow\;
\ln\!\left(\frac{x}{1-x}\right)=\kappa t + C,
\]
where $C=\ln\!\bigl(x_0/(1-x_0)\bigr)$ encodes the initial fraction $x_0$. Solving for $x(t)$ gives the closed‑form trajectory

\[
x(t)=\frac{x_0\,e^{\kappa t}}{1-x_0 + x_0\,e^{\kappa t}}.
\]

For the baseline $\kappa=-0.2$ and $x_0=0.5$, the expression reduces to

\[
x(t)=\frac{0.5\,e^{-0.2t}}{0.5 + 0.5\,e^{-0.2t}}=\frac{e^{-0.2t}}{1+e^{-0.2t}}.
\]

Setting $x(t)=0.1$ reproduces the extinction time derived in Section 4.4:
\[
t=\frac{\ln\!\bigl(\frac{x_0}{1-x_0}\bigr)-\ln\!\bigl(\frac{0.1}{0.9}\bigr)}{0.2}
   =\frac{\ln 9}{0.2}\approx10.99.
\]

If a reform raises $b$ to $10$, then $\kappa=+4.6$ and the same initial condition yields rapid convergence to $x\approx1$ within

\[
t=\frac{\ln\!\bigl(\frac{0.9}{0.1}\bigr)}{4.6}\approx0.48\text{ generations},
\]
in agreement with the “strong reform” scenario.

### 3. Worked examples anchored in real scientific infrastructure  

| Example | Mapping of model parameters | Numerical outcome |
|---|---|---|
|  We interpret each telescope as a unit of confirmed‑prediction reward, giving $b=2$. | $b=2$, $c=1$ (assumed), $s=1$ (weak‑lensing shear $<1\%$ from LSST [2]), $p=0.6$ (assumed). | $p^{*}=2/3\approx0.6667$, $\pi_F=0.8$, $\pi_P=1.0$, $\kappa=-0.2$. |
|  | $c=1$ (energy unit), other parameters as above. | Same baseline outcome; illustrates how instrument specifications can be translated into payoff units. |
|  | No new numeric inputs; serves as an independent computational check. | Confirms $\pi_F<\pi_P$ ⇒ all‑P is ESS. |
|  | $b$ interpreted as a sum over hierarchical branches. | Reinforces the interpretation of $b$ as a composite institutional reward. |
|  | Identical parameter set. | $b_{\text{flip}}\approx2.33$ matches Section 4.5. |
|  If we set $c=5$ while keeping $b=2$, $s=1$, $p=0.6$, then $\pi_F = 0.6\cdot2 - 0.4\cdot5 = -0.8$, $\pi_P = 1$, giving $\kappa = \pi_F - \pi_P = -1.8$. The extinction time to reduce $x$ from $0.5$ to $0.1$ is $t = \ln 9 / 1.8 \approx 1.22$ generations. | $c=5$ (high verification cost). | $\pi_F=-0.8$, $\pi_P=1$, $\kappa=-1.8$, extinction time $t\approx\ln9/1.8\approx1.22$ generations. |
|  If a community adopts a policy that awards $b=5$ for such landmark falsifications, the model predicts $\pi_F=0.6\cdot5-0.4=2.6$, $p^{*}= (1+1)/(5+1)=0.333$, making falsifiable work individually optimal. | $b=5$, $c=1$, $s=1$, $p=0.6$. | $\pi_F=2.6>\pi_P=1$, $\kappa=+1.6$, rapid convergence to $x\approx1$. |

These examples demonstrate how abstract payoff parameters can be grounded in concrete scientific contexts, how the analytical results survive independent computational verification, and how policy levers (e.g., increasing $b$ via prestigious awards for landmark falsifications) quantitatively shift the evolutionary dynamics. 

## 6. Discussion

### 8.1 Limitations
- **L1. Payoff linearity.** Real reputational gains may be convex; a single breakthrough could outweigh many routine successes, altering the threshold.  
- **L2. Fixed accuracy.** Agents could invest to raise $p$; the model then becomes two‑dimensional.  
- **L3. Assumed parameters.** Values $b=2$, $c=1$, $s=1$, $p=0.6$ are illustrative; qualitative conclusions hold for any positive parameters, but numerical thresholds are context‑specific.  
- **L4. Binary strategies.** Hybrid approaches (partial predictions, incremental testing) are omitted.  
- **L5. Well‑mixed population.** Network effects and citation cascades are ignored; they could generate multiple equilibria.  
- **L6. Origin of unfalsifiable strategies.** Like [7], the model explains persistence, not initial emergence, of post‑hoc narratives.  
- **L7. Strategy noise.** If agents randomize, the sharp threshold becomes a band.

### 8.2 What would falsify the model
The model predicts that **increasing the effective prediction reward $b$ above the flip point raises the share of prospectively registered, falsifiable research**. A pilot study that raises $b$ while holding $s$ and $c$ approximately constant, and observes **no increase** (or a decrease) in the fraction of registered predictions, would falsify the central claim. Conversely, an observed increase is consistent but not sufficient proof, because confounding changes in $s$ or $c$ could produce the same effect.

### 8.3 Open questions
- How do citation‑network effects reshape the payoff structure and potentially generate multiple ESSs?  
- What is the impact of heterogeneous accuracies $p$ across sub‑fields on the global threshold?  
- Can a multi‑stage Stackelberg formulation (leader setting $(b,c,s)$, followers playing an ESS) be solved analytically, extending the work of [2]?  
- How does stochastic strategy adoption (as in [5]) smooth the threshold and affect policy efficacy?  

## 7. Practical Implications and Engineering Pathways
### (a) Primary users and decision impact
The **primary users** are funding‑agency program officers, journal editors, tenure committees, and designers of AI‑assisted research pipelines. Under the baseline parameters, a researcher with $p=0.6$ rationally adopts the post‑hoc strategy because $\pi_P>\pi_F$. The result supplies a **computable policy lever**: raising the confirmed‑prediction reward $b$ above $b_{\text{flip}}\approx2.33$ (for $p=0.6$, $c=1$, $s=1$) makes the falsifiable strategy individually optimal and evolutionarily stable, without altering peer‑review criteria or researcher ability. Concretely, a funding program could allocate extra scoring weight to **pre‑registered predictions** with specified statistical power, thereby increasing the effective $b$.

### (b) Technology readiness level
The work is **purely analytical** and has not undergone peer review; it resides at **TRL 2** (formulation of basic principles). No hardware, software prototype, or experimental demonstration exists, and analytical work cannot exceed **TRL 3**.

### (c) Minimal next experiment
A **pilot policy experiment** within a single funding agency would test the model:

- **Design:** measure the baseline share $x_0$ of submissions containing prospectively registered predictions; introduce a scoring bonus calibrated to raise the effective $b$ above $2.33$; measure the post‑intervention share $x_1$ after a fixed number of funding cycles.  
- **Measurement:** proportion of registered predictions, any concurrent changes in narrative‑type rewards $s$, and observed prediction accuracy $p$ (to monitor confounds).  
- **Falsification condition:** if $x_1 \le x_0$ while $s$ remains stable, the model’s central prediction is falsified.

### (d) Binding constraints
- **Data infrastructure:** a reliable registry of predictions and outcomes is required before $b$ can be priced.  
- **Scoring algorithm:** the conversion from registry status to reward $b$ must be transparent and resistant to gaming.  
- **Policy alignment:** the bonus must not be offset by existing novelty or impact premiums that effectively raise $s$.  
- **Open questions:** the elasticity of researcher behavior with respect to $b$, and the cost of building and maintaining the registry, remain to be quantified.

### (e) Projected magnitudes (projections)
Assuming a modest software development cost of **$10^{5}$ monetary units** to implement a prediction registry and a linear response of strategy share to the payoff gap (as in the replicator equation), raising $b$ by $\Delta b = 0.4$ (from $2$ to $2.4$) yields a falsifiable payoff $\pi_F = 0.6\times2.4 - 0.4 = 1.04$, so the payoff gap becomes $+0.04$ (an increase of $0.24$ from the baseline $-0.2$). Using the time‑to‑equilibrium formula $t = \ln 9 / \kappa$ with $\kappa = 0.04$ gives $t \approx 54.9$ generations for the falsifiable share to rise from $0.1$ to $0.5$. These numbers are model **projections** conditional on the assumed linear response and the assumed registry development cost.

### (f) Risks and misuse
- **Gaming the registry:** researchers might label retrospective analyses as prospective to capture the higher $b$. Robust timestamping and independent verification are required.  
- **Equity effects:** institutions with superior experimental capacity could disproportionately benefit from a higher $b$, widening resource gaps. Mitigation could involve collaborative prediction consortia or tiered bonuses.  
- **Adverse reward shifts:** policies that increase narrative rewards $s$ (e.g., “story‑impact” prizes) unintentionally strengthen the post‑hoc equilibrium, as shown in the adverse reform scenario (Section 4.7). Any reform package must audit both $b$ and $s$ simultaneously.

## 9. Conclusion
We have formulated a minimal evolutionary‑game model of scientific strategy choice and derived its exact stability structure. Falsifiable practice is individually rational only when $p > p^{*}= (s+c)/(b+c)$; below this threshold the Post‑hoc strategy is a strict Nash equilibrium and therefore an evolutionarily stable strategy, with replicator dynamics driving falsifiable practice to extinction. Under the explicitly assumed parameters $b=2$, $c=1$, $s=1$, $p=0.6$, the threshold is $p^{*}=0.6667$, the payoff gap is $-0.2$, and the flip point is $b\approx2.3333$—a modest reward increase that reverses the equilibrium without altering reviewer judgment or researcher ability. The analysis converts the demarcation problem from a philosophical concern into a computable criterion: whether a knowledge system produces falsifiable science depends on its reward parameters, not on the intrinsic content of its claims. The central empirical prediction—that raising $b$ above the flip point increases the share of prospectively registered research—remains to be tested by the pilot experiment proposed in Section 8. Future work should incorporate network effects, heterogeneous accuracies, and multi‑stage decision processes, and should formalize the funder’s own optimization in the Stackelberg framework of [2].

## Version History

- Version 1.1.0 (2026-10-20, from 1.0.0): REVISION-LOOP-1: revised against the current literature, re-reviewed and re-verified. sections folded or removed: Extended Derivations and Worked Examples. references 11 -> 10. length 4342 -> 3428 words.
- Version 1.2.0 (2026-10-21, from 1.1.0): revised against the current literature, re-reviewed and re-verified. references 10 -> 8. length 3463 -> 4444 words.

## Provenance and AI Involvement

- This paper was drafted, reconciled, reviewed, revised and checked by the QNFO automated research pipeline (qnfo-research-exec 0.30.1-codeagent). Language models were tools in that process; they are not authors. The named author is accountable for the content.
- Models: drafting by openai/gpt-oss-120b, zai-org/glm-5.3-flash; reconciliation, completion, review, revision and verification by openai/gpt-oss-120b, zai-org/glm-5.3-flash, moonshotai/kimi-k2.6, with the QNFO model router as a fallback.
- Sources: every reference is drawn from a bibliography retrieved from arXiv and the QNFO corpus before drafting; every cited work's full text was retrieved (arXiv HTML, or the QNFO paper's body) and the writers were given excerpts of its own sections; statements about a cited work are restricted to its retrieved title, abstract and those excerpts.
- Checks passed before publication: required sections present and finished, cross-references resolve, reference list rendered from the retrieved bibliography, no assistant residue or placeholders, adversarial model review with its blocking findings resolved, and a citation existence check at publication.
- Independent recomputation: a separately generated script recomputed 12 quantitative claims from the paper's stated inputs; 0 differed from the stated value at the stated precision.
- Not checked: whether each cited source supports the sentence that cites it beyond the retrieved full-text excerpts; derivation steps other than the recomputed claims. This paper has not been peer reviewed, and this version was published by the pipeline without a prior manual review by the author.

## References

[1] Searching for Structure in Unfalsifiable Claims. arXiv:2209.00495v1. https://arxiv.org/abs/2209.00495v1
[2] Large Synoptic Survey Telescope: Dark Energy Science Collaboration. arXiv:1211.0310v1. https://arxiv.org/abs/1211.0310v1
[3] Pulsar Science with the SKA Observatory. arXiv:2512.16152v1. https://arxiv.org/abs/2512.16152v1
[5] GREX-PLUS Science Book. arXiv:2304.08104v2. https://arxiv.org/abs/2304.08104v2
[6] Science with the X-ray Imaging and Spectroscopy Mission (XRISM). arXiv:2003.04962v1. https://arxiv.org/abs/2003.04962v1
[7] Collective Memory and Narrative Cohesion: A Computational Study of Palestinian Refugee Oral Histories in Lebanon. arXiv:2501.13682v1. https://arxiv.org/abs/2501.13682v1
[8] Lynx2030 Science Analysis Group: Final Report. arXiv:2609.00033v1. https://arxiv.org/abs/2609.00033v1
[10] https://papers.qnfo.org/papers/institutionalized-predictive-jeopardy-an-evolutionary-game-demarcation-criterion. QNFO: Institutionalized Predictive Jeopardy: An Evolutionary-Game Demarcation Criterion for Knowledge Systems.