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  "map_content": "Symmetrically, the trust equation's depletion term $-\\beta T D$ falls out of the aggregate loss honest agents suffer from being defrauded, and the logistic regeneration $rT(1-T/\\bar T)$ from the institutional replenishment of the default-cooperate prior. **The macro system is now microfounded.** This closes the consistency requirement I set in \u00a71.",
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  "map_content": "| Macro parameter | Micro meaning | Real-world lever |\n|---|---|---|\n| $\\gamma$ | exploit premium $T_p - R$ | product complexity, opacity |\n| $\\delta$ | detection \u00d7 penalty | regulator budget, audit tech, legal severity |\n| $\\beta$ | per-fraud trust damage | reputation propagation speed |\n| $r$ | trust-repair rate | institutional responsiveness |\n| $\\bar T$ | trust ceiling | rule of law, cultural baseline |",
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  "map_content": "Recall $\\mathcal{R}_0 = \\gamma\\bar T/\\delta$ and the immune-determined equilibrium $T^* = \\delta/\\gamma$. Three digital shocks:",
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  "map_content": "| Macro parameter | Micro meaning | Real-world lever |\n|---|---|---|\n| $\\gamma$ | exploit premium $T_p - R$ | product complexity, opacity |\n| $\\delta$ | detection \u00d7 penalty | regulator budget, audit tech, legal severity |\n| $\\beta$ | per-fraud trust damage | reputation propagation speed |\n| $r$ | trust-repair rate | institutional responsiveness |\n| $\\bar T$ | trust ceiling | rule of law, cultural baseline |",
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  "map_content": "Symmetrically, the trust equation's depletion term $-\\beta T D$ falls out of the aggregate loss honest agents suffer from being defrauded, and the logistic regeneration $rT(1-T/\\bar T)$ from the institutional replenishment of the default-cooperate prior. **The macro system is now microfounded.** This closes the consistency requirement I set in \u00a71.",
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  "map_content": "which is **exactly the macro deception equation** $\\dot D = \\gamma T D - \\delta D$ from Layer 2, with the aggregate parameters now *derived* rather than assumed:",
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  "map_content": "$$\n\\pi_D - \\pi_H \\;=\\; \\underbrace{T\\,(T_p - R)}_{\\text{exploitable trust surplus}} \\;-\\; \\underbrace{q^{*}(x)\\,\\phi\\,(k + T_p)}_{\\text{expected punishment}}\n$$",
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  "map_content": "### 4.3 Replicator dynamics \u2192 recovering the macro law",
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  "map_content": "Let $x = D/N$ be the **fraction of the population playing Deceptive** (this is the micro object that will become the macro $D$). Let $T \\in [0,1]$ now be reinterpreted as the population's **prior probability of transacting without verification** \u2014 i.e. the behavioral expression of the trust stock.",
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  "map_content": "where $q^{*}(x)$ is increasing in the perceived deception fraction $x$. **Trust is endogenous: it is the population's collective decision to lower its guard.**",
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  "map_content": "- Expected payoff to a deceiver meeting a verifying partner: $(1-\\phi)T_p - \\phi k$.\n- The population **verification intensity** $q$ is itself best-response: agents verify more when they expect more deception. This is the **screening response** (Stiglitz).",
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  "map_content": "3. **Reputation decoupling (anonymity, platform churn) lowers $\\beta$ and $r$.** Lower $\\beta$ paradoxically *raises* endemic deception $D^* = (r/\\beta)(1-1/\\mathcal R_0)$; lower $r$ slows recovery and, via the Jacobian, **destabilizes the spiral** \u2014 pushing the system from damped oscillation toward a **limit cycle** (sustained boom\u2013bust fraud waves that never settle).",
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  "map_content": "This is a **Prisoner's-Dilemma-structured** trade game: $T_p > R > P > S$. Deception is the one-shot dominant strategy \u2014 exactly Akerlof's problem.",
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  "map_content": "- **H (Honest):** truthful disclosure, delivers the promised value.\n- **D (Deceptive):** exploits information asymmetry to extract surplus it did not create.",
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  "map_content": "which is **exactly the macro deception equation** $\\dot D = \\gamma T D - \\delta D$ from Layer 2, with the aggregate parameters now *derived* rather than assumed:",
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  "map_content": "where $q^{*}(x)$ is increasing in the perceived deception fraction $x$. **Trust is endogenous: it is the population's collective decision to lower its guard.**",
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  "map_content": "$$\n\\pi_D - \\pi_H \\;=\\; \\underbrace{T\\,(T_p - R)}_{\\text{exploitable trust surplus}} \\;-\\; \\underbrace{q^{*}(x)\\,\\phi\\,(k + T_p)}_{\\text{expected punishment}}\n$$",
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  "map_content": "Let $x = D/N$ be the **fraction of the population playing Deceptive** (this is the micro object that will become the macro $D$). Let $T \\in [0,1]$ now be reinterpreted as the population's **prior probability of transacting without verification** \u2014 i.e. the behavioral expression of the trust stock.",
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  "map_content": "- Expected payoff to a deceiver meeting a verifying partner: $(1-\\phi)T_p - \\phi k$.\n- The population **verification intensity** $q$ is itself best-response: agents verify more when they expect more deception. This is the **screening response** (Stiglitz).",
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  "map_content": "| | vs. Honest | vs. Deceptive |\n|---|---|---|\n| **Honest** | $R$ (mutual gains from trade) | $S$ (defrauded: $S < 0$) |\n| **Deceptive** | $T_{p}$ (successful exploitation, $T_p > R$) | $P$ (mutual suspicion / no deal, $P \\approx 0$) |",
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  "map_content": "3. **Reputation decoupling (anonymity, platform churn) lowers $\\beta$ and $r$.** Lower $\\beta$ paradoxically *raises* endemic deception $D^* = (r/\\beta)(1-1/\\mathcal R_0)$; lower $r$ slows recovery and, via the Jacobian, **destabilizes the spiral** \u2014 pushing the system from damped oscillation toward a **limit cycle** (sustained boom\u2013bust fraud waves that never settle).",
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  "map_content": "$$\n\\boxed{\\;\\gamma = T_p - R \\quad(\\text{exploit premium}),\\qquad \\delta = \\bar q\\,\\phi\\,(k+T_p)\\quad(\\text{detection}\\times\\text{penalty})\\;}\n$$",
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  "map_content": "2. **Verifiability collapse (synthetic media, opacity) lowers $\\phi$, hence lowers $\\delta$.** \u2192 $T^* = \\delta/\\gamma$ **falls directly.** Equilibrium trust is *proportional* to detection efficiency.",
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  "map_content": "- **Proxies:** $T$ \u2190 survey trust indices, transaction-without-escrow rates, unverified-purchase share. $D$ \u2190 enforcement actions, fraud-complaint rates, chargeback ratios. $\\delta$ \u2190 regulator budgets/detection rates. $\\gamma$ \u2190 product-complexity indices.\n- **Test 1 (cross-sectional):** regress equilibrium trust on $\\delta/\\gamma$ across markets; the model predicts $T^*$ is invariant to $\\bar T$ \u2014 a sharp, falsifiable, counterintuitive claim.\n- **Test 2 (time-series):** estimate cycle amplitude/damping pre- vs. post-digitization; predict reduced damping.\n- **Test 3 (natural experiment):** crypto vs. regulated finance as high- vs. low-$\\mathcal R_0$ regimes.",
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  "map_content": "1. **Rigorous stability proof** \u2014 full Jacobian, eigenvalues, the exact Hopf-bifurcation condition where damped spirals become sustained limit cycles (the mathematical spine of the \"fraud waves\" claim).\n2. **Simulation section** \u2014 phase portraits and time-series plots (I can give you runnable Python/`scipy` code so you can generate the figures).\n3. **Sensitivity/robustness** \u2014 what breaks the model (e.g., if trust regeneration is non-logistic, or verification is strategic rather than mechanical).",
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  "map_content": "- **Proxies:** $T$ \u2190 survey trust indices, transaction-without-escrow rates, unverified-purchase share. $D$ \u2190 enforcement actions, fraud-complaint rates, chargeback ratios. $\\delta$ \u2190 regulator budgets/detection rates. $\\gamma$ \u2190 product-complexity indices.\n- **Test 1 (cross-sectional):** regress equilibrium trust on $\\delta/\\gamma$ across markets; the model predicts $T^*$ is invariant to $\\bar T$ \u2014 a sharp, falsifiable, counterintuitive claim.\n- **Test 2 (time-series):** estimate cycle amplitude/damping pre- vs. post-digitization; predict reduced damping.\n- **Test 3 (natural experiment):** crypto vs. regulated finance as high- vs. low-$\\mathcal R_0$ regimes.",
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  "map_content": "1. A **microfounded dynamical model** unifying Akerlof (asymmetry), Akerlof\u2013Shiller (phishing equilibrium), Stiglitz (screening), and Kindleberger/Minsky (cycles) into one system.\n2. The **Deception Reproduction Number $\\mathcal R_0 = \\gamma\\bar T/\\delta$** \u2014 a single, interpretable invasion threshold.\n3. The **counterintuitive invariance result** $T^*=\\delta/\\gamma$: building trust infrastructure ($\\bar T$) does *not* raise equilibrium trust \u2014 only the immune system does.\n4. A **formal account of the digital shift** as comparative statics, yielding falsifiable predictions and retrodicting crypto.",
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  "map_content": "The single most defensible, publishable nugget here is the **invariance result** ($T^* = \\delta/\\gamma$, independent of $\\bar T$) combined with $\\mathcal{R}_0$. That's the kind of clean, surprising, testable claim a committee remembers.",
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  "map_content": "$$\n\\dot{x} = x(1-x)\\big[\\pi_D(x,T) - \\pi_H(x,T)\\big]\n$$",
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  "map_content": "$$\n\\boxed{\\;\\gamma = T_p - R \\quad(\\text{exploit premium}),\\qquad \\delta = \\bar q\\,\\phi\\,(k+T_p)\\quad(\\text{detection}\\times\\text{penalty})\\;}\n$$",
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  "map_content": "1. **Rigorous stability proof** \u2014 full Jacobian, eigenvalues, the exact Hopf-bifurcation condition where damped spirals become sustained limit cycles (the mathematical spine of the \"fraud waves\" claim).\n2. **Simulation section** \u2014 phase portraits and time-series plots (I can give you runnable Python/`scipy` code so you can generate the figures).\n3. **Sensitivity/robustness** \u2014 what breaks the model (e.g., if trust regeneration is non-logistic, or verification is strategic rather than mechanical).",
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  "map_content": "The escape from full collapse comes from **verification**, which is costly and probabilistic. Before transacting, an agent verifies the counterparty with probability $q$, at cost $c$. Verification exposes a deceiver with probability $\\phi$ (**detection technology**). A caught deceiver forfeits the exploit and pays penalty $k$.",
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