mrhavens/intellecton
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Final semantic fixes, PDF recompilations, and README executive summaries for Papers 1-6

Browse Source
This commit is contained in:
codex
2026-06-02 06:52:37 +00:00
parent 7d9274d984
commit 283e601752
31 changed files with 238 additions and 159 deletions
Download Patch File Download Diff File Expand all files Collapse all files
papers/project_paper_4_fbt/README.md
+8
View File
@@ -0,0 +1,8 @@
# Paper 4: Cost-Penalized Interface Games
## Executive Overview
This paper formalizes Donald Hoffman's "Fitness Beats Truth" (FBT) theorem through an Information Bottleneck framework. We penalize the veridical "Truth" perceptual strategy with the metabolic cost of information processing bounded by Landauer's principle. By evaluating formal replicator dynamics and trajectory analysis, we mathematically prove the asymptotic extinction of veridical perception. This establishes the heuristic, fitness-tuned perceptual encoder as a strict Evolutionarily Stable Strategy (ESS) due to the thermodynamic cost of high-fidelity homomorphic representation.
## Resources
- [LaTeX Source (paper_4_fbt.tex)](paper_4_fbt.tex)
- [Compiled PDF (paper_4_fbt.pdf)](paper_4_fbt.pdf)
papers/project_paper_4_fbt/paper_4_fbt.log
+16 -26
View File
@@ -1,4 +1,4 @@
This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.5.30) 2 JUN 2026 03:29
This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.5.30) 2 JUN 2026 06:51
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
@@ -156,18 +156,7 @@ LaTeX Font Info: Trying to load font information for U+msb on input line 11.
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
)
Overfull \hbox (14.86186pt too wide) in paragraph at lines 24--25
\OT1/cmr/m/n/10.95 dauer's prin-ci-ple: $\OML/cmm/m/it/10.95 C\OT1/cmr/m/n/10.9
5 (\OML/cmm/m/it/10.95 T\OT1/cmr/m/n/10.95 ) = \OML/cmm/m/it/10.95 ^^L[]D[]\OT1
/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 p[]\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95
y\OMS/cmsy/m/n/10.95 j\OML/cmm/m/it/10.95 x\OT1/cmr/m/n/10.95 ) \OMS/cmsy/m/n/1
0.95 k \OML/cmm/m/it/10.95 p[]\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 y\OT1/cmr
/m/n/10.95 ))$, where $\OML/cmm/m/it/10.95 ^^L[] \OMS/cmsy/m/n/10.95 / \OML/cmm
/m/it/10.95 ^^Q[]k[]T [] \OT1/cmr/m/n/10.95 2$.
[]
[1
) [1
{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2] (./paper_4_fbt.aux)
***********
@@ -182,24 +171,25 @@ Here is how much of TeX's memory you used:
23964 multiletter control sequences out of 15000+600000
567827 words of font info for 74 fonts, out of 8000000 for 9000
59 hyphenation exceptions out of 8191
56i,6n,65p,900b,218s stack positions out of 10000i,1000n,20000p,200000b,200000s
56i,6n,65p,892b,218s stack positions out of 10000i,1000n,20000p,200000b,200000s
</usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></us
r/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></usr/shar
e/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb></usr/share/texl
ive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texlive/te
xmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb></usr/share/texlive/texmf-dis
t/fonts/type1/public/amsfonts/cm/cmmi8.pfb></usr/share/texlive/texmf-dist/fonts
/type1/public/amsfonts/cm/cmr10.pfb></usr/share/texlive/texmf-dist/fonts/type1/
public/amsfonts/cm/cmr12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/
amsfonts/cm/cmr17.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfont
s/cm/cmr8.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cms
y10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb
></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb></usr/
share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb>
Output written on paper_4_fbt.pdf (2 pages, 165658 bytes).
xmf-dist/fonts/type1/public/amsfonts/cm/cmmi6.pfb></usr/share/texlive/texmf-dis
t/fonts/type1/public/amsfonts/cm/cmmi7.pfb></usr/share/texlive/texmf-dist/fonts
/type1/public/amsfonts/cm/cmmi8.pfb></usr/share/texlive/texmf-dist/fonts/type1/
public/amsfonts/cm/cmr10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/
amsfonts/cm/cmr12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfont
s/cm/cmr17.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cm
r8.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb
></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb></usr/
share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb></usr/share/t
exlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb>
Output written on paper_4_fbt.pdf (2 pages, 174673 bytes).
PDF statistics:
81 PDF objects out of 1000 (max. 8388607)
48 compressed objects within 1 object stream
86 PDF objects out of 1000 (max. 8388607)
51 compressed objects within 1 object stream
0 named destinations out of 1000 (max. 500000)
1 words of extra memory for PDF output out of 10000 (max. 10000000)
papers/project_paper_4_fbt/paper_4_fbt.pdf
LFS
BIN
View File
Binary file not shown.
papers/project_paper_4_fbt/paper_4_fbt.tex
+7 -7
View File
@@ -11,21 +11,21 @@
\maketitle
\begin{abstract}
Hoffman's ``Fitness Beats Truth'' (FBT) theorem posits that evolutionary processes drive veridical perception to extinction. We formalize this by mapping perceptual strategies to an Information Bottleneck framework, penalizing the ``Truth'' strategy with the metabolic cost of information processing via Landauer's limit. We define the explicit evolutionary payoff integral and derive the optimal perceptual encoder as a Gibbs distribution. Through formal replicator dynamics and Lyapunov stability analysis, we prove that the population frequency of Truth asymptotically approaches zero ($\lim_{t \to \infty} x_T(t) = 0$). Furthermore, we establish the explicit Evolutionarily Stable Strategy (ESS) conditions, demonstrating that a heuristic fitness-tuned population strictly resists invasion by veridical mutants due to the thermodynamic cost of representation.
Hoffman's ``Fitness Beats Truth'' (FBT) theorem posits that evolutionary processes drive veridical perception to extinction. We formalize this by mapping perceptual strategies to an Information Bottleneck framework, penalizing the ``Truth'' strategy with the metabolic cost of information processing via Landauer's limit. We define the explicit evolutionary payoff integral and derive the optimal perceptual encoder as a Gibbs distribution. Through formal replicator dynamics and trajectory analysis, we prove that the population frequency of Truth asymptotically approaches zero ($\lim_{t \to \infty} x_T(t) = 0$). Furthermore, we establish the explicit Evolutionarily Stable Strategy (ESS) conditions, demonstrating that a heuristic fitness-tuned population strictly resists invasion by veridical mutants due to the thermodynamic cost of representation.
\end{abstract}
\section{The Payoff Integral and the Gibbs Encoder}
Let $\mathcal{M}$ be the continuous objective world manifold, and $\mathcal{Y}$ be a finite set of discrete perceptual states. The expected evolutionary payoff $f_i$ for a strategy $i$ is defined by the integral over the world states:
Let $\mathcal{M}$ be the continuous objective world manifold, and $\mathcal{Y}$ be a finite set of discrete perceptual states. The expected evolutionary payoff $f_i$ for a strategy $i$ is defined by taking the expectation over both the world states and perceptual mapping:
\begin{equation}
f_i = \int_{\mathcal{M}} W(x, a_i(y)) p_i(y|x) p(x) \, d\mu(x) - C(i)
f_i = \int_{\mathcal{M}} \sum_{y \in \mathcal{Y}} W(x, a_i(y)) p_i(y|x) p(x) \, d\mu(x) - C(i)
\end{equation}
where $W(x, a)$ is the fitness utility of taking action $a$ in state $x$, $a_i(y)$ is the action policy, $p_i(y|x)$ is the perceptual encoder, and $C(i)$ is the metabolic penalty.
Following Ortega and Braun \cite{Ortega2013}, the metabolic cost of maintaining a high-fidelity homomorphic representation $T$ (Truth) is bounded by Landauer's principle: $C(T) = \beta^{-1} D_{KL}(p_T(y|x) \parallel p_0(y))$, where $\beta^{-1} \propto \eta_{\text{bio}} k_B T \ln 2$.
Following Ortega and Braun \cite{Ortega2013}, the metabolic cost of maintaining a high-fidelity homomorphic representation $T$ (Truth) is bounded by Landauer's principle: $C(T) = \beta^{-1} \int_{\mathcal{M}} D_{KL}(p_T(y|x) \parallel p_0(y)) p(x) \, d\mu(x)$, where $\beta^{-1} \propto \eta_{\text{bio}} k_B T \ln 2$ and $p_0(y)$ is the marginal prior distribution over perceptual states.
Optimizing the free-energy functional yields the optimal perceptual encoder as a Gibbs distribution:
\begin{equation}
p^*(y|x) = \frac{p_0(y) e^{\beta W(x, a(y))}}{Z(x)}
p^*(y|x) = \frac{p_0(y) e^{\beta W(x, a_i(y))}}{Z(x)}
\end{equation}
This establishes that the optimal evolutionary encoder is tuned strictly to the utility function $W$, not the structural homomorphism of $x$, explicitly decoupling perception from objective reality.
@@ -36,9 +36,9 @@ Let $x_T$ and $x_F$ be the population frequencies of the Truth ($T$) and Fitness
\end{equation}
where $\bar{f} = x_T f_T + x_F f_F$. Because the heuristic strategy $F$ operates with $C(F) \ll C(T)$ while achieving comparable or superior utility via the Gibbs encoder, we have $f_F > f_T$.
To prove extinction, we define a Lyapunov function $V(x_T) = x_T$. Since $f_T < \bar{f}$ for all $x_T \in (0,1)$, we find $\frac{dV}{dt} < 0$. Therefore, the system is asymptotically stable at $x_T = 0$, proving $\lim_{t \to \infty} x_T(t) = 0$.
To prove extinction, we analyze the population trajectory directly. Since $f_T < \bar{f}$ for all $x_T \in (0,1)$, we find $\frac{dx_T}{dt} < 0$. Therefore, the system is asymptotically stable at $x_T = 0$, proving $\lim_{t \to \infty} x_T(t) = 0$.
Furthermore, evaluating the invasion fitness, a monomorphic population of $F$ resists invasion by $T$ if $f(F, F) > f(T, F)$. Since the metabolic tax strictly reduces the payoff of the mutant $T$ without providing a commensurable increase in $W$, the strict inequality holds. Thus, Fitness is a formal Evolutionarily Stable Strategy (ESS).
Furthermore, evaluating the invasion fitness, a monomorphic population of $F$ resists invasion by $T$ because the frequency-independent condition $f_F > f_T$ strictly holds. Since the metabolic tax strictly reduces the payoff of the mutant $T$ without providing a commensurable increase in $W$, the strict inequality holds. Thus, Fitness is a formal Evolutionarily Stable Strategy (ESS).
\bibliographystyle{plain}
\begin{thebibliography}{10}