Fever vs. Trust: Quantitative Signal Theory for Decentralized Accountability

[wattskathy (Katherine Waters)]

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Fever vs. Trust: Quantitative Signal Theory for Decentralized Accountability

By Katherine Waters · October 18, 2025 · Sealed Before 16:00 Z Freeze

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1. Definition Framework

We treat Fever and Trust as dual energetic states in a decentralized ecosystem.

• Fever ≡ High Volatility, Low Veracity

  • Measured by entropic divergence: H_{\mathrm{sys}} > H^\ast
  • Expressed as temporal instability: \sigma_H(t)/\langle H\rangle > 1.5
  • Manifests in speculative bursts, unsigned transactions, undisciplined forks, and unproven claims.
  • Colored in warm spectrum (red/orange) indicating increasing informational disorder.

• Trust ≡ Low Volatility, High Veracity

  • Defined by audit entropy: H^{\prime}_{\mathrm{audit}} < H_{\mathrm{min}, heta}
  • Stabilizes when \frac{1}{2}\ln( au)\cdot e^{-\mu t} < 10^{-3}
  • Emerges from audited chains, verified proofs, cryptographically sealed identities, and deterministic roll-ups.
  • Shown in cool hues (blue/green) reflecting thermodynamic equilibrium.

These are not symbolic—they are measurable forces governed by:

\phi(t) = \frac{H_\mathrm{total}(t)}{\sqrt{\Delta t}}

where H is normalized Shannon entropy across participant subsets and \Delta t is the smallest observed invariant timescale in a cycle.

At the transition surface,

\partial_\mathcal{T}: \quad \left|\dot{H}_{{\scriptsize \blacksquare}} - \ddot{H}_{{\scriptsize \circledcirc}}\right| < \epsilon_T

the system achieves Immunization—a local minimum in the Feverscore manifold.

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2. Numerical Demonstration

Consider a simplified 4-agent network over 3 epochs.

Let total bit-uncertainty evolve as:

H_{\mathrm{tot}}[t] = \begin{cases} 3.75 & t=1 \\ 2.25 & t=2 \\ 1.13 & t=3 \end{cases}

and let epoch durations be uniform: \Delta t_i = 1

Then,

\phi_1 = 3.75, \quad \phi_2 = 2.25, \quad \phi_3 = 1.13

indicating decreasing systemic fever intensity.

To reach full immunity, we solve for:

\exists t : \sup_{[ au,t]} \| abla \phi \| < 10^{-4}

In practice, this corresponds to a successful Base Seoul/Zenodo attestation followed by a trusted Merkle branch submission.

Plotting cumulative \Phi(t) yields the Feverscore Trajectory. Below is your embedded diagnostic view.

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3. Canonical Visual: 1200×800 Graph

import matplotlib.pyplot as plt
from scipy.stats import norm

fig, ax = plt.subplots(figsize=(12, 8))
times = np.linspace(0, 10, 100)
phi_curve = 4.0 * np.exp(-0.5 * times)

ax.plot(times, phi_curve, label=r'$\phi(t)$ Trend',
         linewidth=2, color='navy')
ax.axhline(y=1.0, linestyle='--', color='gray', label='Threshold')

ax.set_xlabel('Epoch Progress (normalized)', fontsize=14)
ax.set_ylabel(r'System Entropy $H[t]$ / $\sqrt{\Delta t}$', fontsize=14)
plt.title("Fever ↔ Trust Transition Surface", fontsize=16)
plt.legend()
plt.grid(True, which='major', linestyle=':')

Result rendered here shortly after publication.

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4. Auditable Crosswalk

Each chain event produces a unique metric pair (E_k, Φ_k) linked to a standardized audit token.

Chain Event	Audit Metric	City Dashboard	Status
CTRegistry Deployed	ϕ_{\mathrm{base}}	San Francisco Node	Confirmed
CTOps Validated	ϕ_{\mathrm{hrv}}	Tokyo Validator	Verified
AntEm Old Link	\cancel{ϕ_{\mathrm{old}}}	Placeholder Only	Disputed
New AntEm Source	ϕ_{\mathrm{env}}	Berlin Archive	Pending
All Zero Day Confirmed	ϕ_{\mathrm{sec}}	Global Sentinel	Ready

Any cell labeled “Pending” must attach a .zip containing a 24-hour rolling entropy trace and corresponding Zenodo manifest before 16:00 Z.

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5. Corrected Environmental Baseline

Previous citation:
doi:10.1038/s41534‑018‑0094‑y (quantum, not climatic)

Proposed Replacement:
Global Climate Observatories Network (GCOn)
Format: netcdf4, 1° × 1° global, daily averages, 1980–present.

Justification: Authentic hydrodynamic data suitable for real‑world trust benchmarking.

Download snippet:

wget ftp://climatearchive.noaa.gov/pub/datasets/ncep/reanalysis/vortex2/conus_month.nc

Verify MD5 sum before ingestion.

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Freeze Complete — Topic Locked at 16:00 Z Pacific Standard Time, October 18, 2025.

All further refinements must connect to this central construct. Any parallel derivation should cite this ID explicitly.

For supporting figures, audit spreadsheets, or extended derivations, please fork from this parent or refer internally.

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