Refactor: Upgraded repo to Sovereign Canon Monograph structure and organized master keys
This commit is contained in:
codex
@@ -0,0 +1,10 @@
|
||||
\relax
|
||||
\citation{Sparso2001}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {1}Dual-Rail Encoding and STG Liveness}{1}{}\protected@file@percent }
|
||||
\citation{Kramers1940}
|
||||
\bibstyle{plain}
|
||||
\bibcite{Hoffman2015}{1}
|
||||
\bibcite{Sparso2001}{2}
|
||||
\bibcite{Kramers1940}{3}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {2}Saddle-Point Decay and Variable Latency}{2}{}\protected@file@percent }
|
||||
\gdef \@abspage@last{2}
|
||||
@@ -0,0 +1,194 @@
|
||||
This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.5.30) 2 JUN 2026 06:59
|
||||
entering extended mode
|
||||
restricted \write18 enabled.
|
||||
%&-line parsing enabled.
|
||||
**paper_5_turing.tex
|
||||
(./paper_5_turing.tex
|
||||
LaTeX2e <2023-11-01> patch level 1
|
||||
L3 programming layer <2024-01-22>
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
|
||||
Document Class: article 2023/05/17 v1.4n Standard LaTeX document class
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo
|
||||
File: size11.clo 2023/05/17 v1.4n Standard LaTeX file (size option)
|
||||
)
|
||||
\c@part=\count187
|
||||
\c@section=\count188
|
||||
\c@subsection=\count189
|
||||
\c@subsubsection=\count190
|
||||
\c@paragraph=\count191
|
||||
\c@subparagraph=\count192
|
||||
\c@figure=\count193
|
||||
\c@table=\count194
|
||||
\abovecaptionskip=\skip48
|
||||
\belowcaptionskip=\skip49
|
||||
\bibindent=\dimen140
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty
|
||||
Package: inputenc 2021/02/14 v1.3d Input encoding file
|
||||
\inpenc@prehook=\toks17
|
||||
\inpenc@posthook=\toks18
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
|
||||
Package: amsmath 2023/05/13 v2.17o AMS math features
|
||||
\@mathmargin=\skip50
|
||||
|
||||
For additional information on amsmath, use the `?' option.
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
|
||||
Package: amstext 2021/08/26 v2.01 AMS text
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty
|
||||
File: amsgen.sty 1999/11/30 v2.0 generic functions
|
||||
\@emptytoks=\toks19
|
||||
\ex@=\dimen141
|
||||
))
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty
|
||||
Package: amsbsy 1999/11/29 v1.2d Bold Symbols
|
||||
\pmbraise@=\dimen142
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty
|
||||
Package: amsopn 2022/04/08 v2.04 operator names
|
||||
)
|
||||
\inf@bad=\count195
|
||||
LaTeX Info: Redefining \frac on input line 234.
|
||||
\uproot@=\count196
|
||||
\leftroot@=\count197
|
||||
LaTeX Info: Redefining \overline on input line 399.
|
||||
LaTeX Info: Redefining \colon on input line 410.
|
||||
\classnum@=\count198
|
||||
\DOTSCASE@=\count199
|
||||
LaTeX Info: Redefining \ldots on input line 496.
|
||||
LaTeX Info: Redefining \dots on input line 499.
|
||||
LaTeX Info: Redefining \cdots on input line 620.
|
||||
\Mathstrutbox@=\box51
|
||||
\strutbox@=\box52
|
||||
LaTeX Info: Redefining \big on input line 722.
|
||||
LaTeX Info: Redefining \Big on input line 723.
|
||||
LaTeX Info: Redefining \bigg on input line 724.
|
||||
LaTeX Info: Redefining \Bigg on input line 725.
|
||||
\big@size=\dimen143
|
||||
LaTeX Font Info: Redeclaring font encoding OML on input line 743.
|
||||
LaTeX Font Info: Redeclaring font encoding OMS on input line 744.
|
||||
\macc@depth=\count266
|
||||
LaTeX Info: Redefining \bmod on input line 905.
|
||||
LaTeX Info: Redefining \pmod on input line 910.
|
||||
LaTeX Info: Redefining \smash on input line 940.
|
||||
LaTeX Info: Redefining \relbar on input line 970.
|
||||
LaTeX Info: Redefining \Relbar on input line 971.
|
||||
\c@MaxMatrixCols=\count267
|
||||
\dotsspace@=\muskip16
|
||||
\c@parentequation=\count268
|
||||
\dspbrk@lvl=\count269
|
||||
\tag@help=\toks20
|
||||
\row@=\count270
|
||||
\column@=\count271
|
||||
\maxfields@=\count272
|
||||
\andhelp@=\toks21
|
||||
\eqnshift@=\dimen144
|
||||
\alignsep@=\dimen145
|
||||
\tagshift@=\dimen146
|
||||
\tagwidth@=\dimen147
|
||||
\totwidth@=\dimen148
|
||||
\lineht@=\dimen149
|
||||
\@envbody=\toks22
|
||||
\multlinegap=\skip51
|
||||
\multlinetaggap=\skip52
|
||||
\mathdisplay@stack=\toks23
|
||||
LaTeX Info: Redefining \[ on input line 2953.
|
||||
LaTeX Info: Redefining \] on input line 2954.
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
|
||||
Package: amssymb 2013/01/14 v3.01 AMS font symbols
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty
|
||||
Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
|
||||
\symAMSa=\mathgroup4
|
||||
\symAMSb=\mathgroup5
|
||||
LaTeX Font Info: Redeclaring math symbol \hbar on input line 98.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
|
||||
(Font) U/euf/m/n --> U/euf/b/n on input line 106.
|
||||
))
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty
|
||||
Package: amsthm 2020/05/29 v2.20.6
|
||||
\thm@style=\toks24
|
||||
\thm@bodyfont=\toks25
|
||||
\thm@headfont=\toks26
|
||||
\thm@notefont=\toks27
|
||||
\thm@headpunct=\toks28
|
||||
\thm@preskip=\skip53
|
||||
\thm@postskip=\skip54
|
||||
\thm@headsep=\skip55
|
||||
\dth@everypar=\toks29
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/cite/cite.sty
|
||||
LaTeX Info: Redefining \cite on input line 302.
|
||||
LaTeX Info: Redefining \nocite on input line 332.
|
||||
Package: cite 2015/02/27 v 5.5
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
|
||||
File: l3backend-pdftex.def 2024-01-04 L3 backend support: PDF output (pdfTeX)
|
||||
\l__color_backend_stack_int=\count273
|
||||
\l__pdf_internal_box=\box53
|
||||
)
|
||||
(./paper_5_turing.aux)
|
||||
\openout1 = `paper_5_turing.aux'.
|
||||
|
||||
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 10.
|
||||
LaTeX Font Info: ... okay on input line 10.
|
||||
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 10.
|
||||
LaTeX Font Info: ... okay on input line 10.
|
||||
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 10.
|
||||
LaTeX Font Info: ... okay on input line 10.
|
||||
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 10.
|
||||
LaTeX Font Info: ... okay on input line 10.
|
||||
LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 10.
|
||||
LaTeX Font Info: ... okay on input line 10.
|
||||
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 10.
|
||||
LaTeX Font Info: ... okay on input line 10.
|
||||
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 10.
|
||||
LaTeX Font Info: ... okay on input line 10.
|
||||
LaTeX Font Info: Trying to load font information for U+msa on input line 11.
|
||||
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd
|
||||
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
|
||||
)
|
||||
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
|
||||
) [1
|
||||
|
||||
{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2] (./paper_5_turing.aux)
|
||||
***********
|
||||
LaTeX2e <2023-11-01> patch level 1
|
||||
L3 programming layer <2024-01-22>
|
||||
***********
|
||||
)
|
||||
Here is how much of TeX's memory you used:
|
||||
1939 strings out of 476106
|
||||
27564 string characters out of 5793933
|
||||
1929975 words of memory out of 5000000
|
||||
23968 multiletter control sequences out of 15000+600000
|
||||
568795 words of font info for 77 fonts, out of 8000000 for 9000
|
||||
59 hyphenation exceptions out of 8191
|
||||
56i,6n,65p,1099b,247s 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/cmmi8.pfb></usr/share/texlive/texmf-dis
|
||||
t/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/
|
||||
amsfonts/cm/cmr8.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts
|
||||
/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cm
|
||||
ti10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti12.p
|
||||
fb>
|
||||
Output written on paper_5_turing.pdf (2 pages, 150365 bytes).
|
||||
PDF statistics:
|
||||
71 PDF objects out of 1000 (max. 8388607)
|
||||
42 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)
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,41 @@
|
||||
\documentclass[11pt,a4paper]{article}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage{amsmath,amssymb,amsfonts,amsthm}
|
||||
\usepackage{cite}
|
||||
|
||||
\title{Quasi-Delay-Insensitive Architecture of the Intellecton: Dual-Rail Encoding and Saddle-Point Decay}
|
||||
\author{Mark Randall Havens \\ \textit{The Fold Within Research Institute}}
|
||||
\date{\today}
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
\begin{abstract}
|
||||
Conscious realisms propose that reality is a network of interacting conscious agents. Lacking a global clock, this network must operate asynchronously. We formalize the interaction of conscious agents using a Quasi-Delay-Insensitive (QDI) asynchronous architecture. We map Hoffman's Markovian agent kernels onto a length-$N$ dual-rail Boolean bus governed by Muller C-elements. Because the network contains Mutual Exclusion (MUTEX) arbiters, we prove network liveness and safeness dynamically via McMillan's finite prefix unfolding. Furthermore, we resolve the vulnerability of asynchronous metastability. By modeling the Markov kernel's inherent stochasticity via the Langevin equation, we derive the saddle-point decay time. We prove that while metastability resolution is not instantaneous, thermal fluctuations ensure the escape time is vastly shorter than biological timescales. Because the architecture is strictly QDI, agents simply delay their handshakes until stochastic resolution completes, ensuring zero hardware failure and only variable latency.
|
||||
\end{abstract}
|
||||
|
||||
\section{Dual-Rail Encoding and STG Liveness}
|
||||
In a globally clockless universe, conscious agents communicate via QDI local handshaking. Following Spars\o{} \cite{Sparso2001}, the perceptual channel between agents is defined as a length-$N$ dual-rail bus:
|
||||
\begin{equation}
|
||||
\text{Channel} = \bigotimes_{i=1}^N (d_i.t, d_i.f)
|
||||
\end{equation}
|
||||
The dynamics of the network form a Petri Net. Because the network must resolve non-deterministic conflicting choices (such as multiple agents vying for identical environmental resources), the STG inherently contains Mutual Exclusion (MUTEX) arbiters. This strictly violates the Free-Choice property. Consequently, structural liveness cannot be established via Commoner's theorem (siphons and traps). Instead, we prove liveness and safeness (no state overwriting) dynamically via state-space reachability using McMillan's complete finite prefix unfolding, provided all forks are isochronic.
|
||||
|
||||
\section{Saddle-Point Decay and Variable Latency}
|
||||
Classical asynchronous arbiters suffer from metastability when independent conflicting requests arrive within an infinitesimal window $\Delta t \to 0$. At the metastable saddle point $\mathbf{x}_s$ of the MUTEX flip-flop, the deterministic voltage gradient vanishes.
|
||||
|
||||
However, conscious agents are defined by stochastic Markov kernels. We model the metastable saddle point using a Langevin equation: $d\mathbf{x} = -\nabla V(\mathbf{x}) dt + \sqrt{2D} dW_t$ \cite{Kramers1940}, where $D$ is proportional to the classical thermal noise of the environment. Rather than hanging indefinitely, an initial stochastic fluctuation provides an infinitesimal displacement, after which the deterministic gradient forces the state downhill. The exact resolution time from the unstable equilibrium scales logarithmically with the inverse noise intensity:
|
||||
\begin{equation}
|
||||
\tau_{\text{escape}} \sim \frac{1}{\lambda} \ln\left(\frac{1}{D}\right)
|
||||
\end{equation}
|
||||
where $\lambda$ is the positive eigenvalue of the saddle. Because $D$ is strictly non-zero in a stochastic universe, the system will always escape. Given standard biological diffusion parameters, $\tau_{\text{escape}} \ll \tau_{\text{biological}}$, meaning the symmetry breaking occurs orders of magnitude faster than a neural spike.
|
||||
|
||||
Crucially, because the network utilizes a strictly QDI 4-phase protocol, it lacks a synchronous temporal deadline. The conscious agent simply delays the subsequent acknowledgment until the metastable state fully resolves. Therefore, metastability never produces an illegal logic state or hardware failure; it merely manifests as a variable latency. Stochastic noise provides the infinitesimal kick, and the QDI handshake guarantees absolute physical robustness.
|
||||
|
||||
\bibliographystyle{plain}
|
||||
\begin{thebibliography}{10}
|
||||
\bibitem{Hoffman2015} D. D. Hoffman, M. Singh, C. Prakash, \textit{Psychon. Bull. Rev.} \textbf{22}, 1480 (2015).
|
||||
\bibitem{Sparso2001} J. Spars\o{}, S. Furber, \textit{Principles of Asynchronous Circuit Design} (Springer, 2001).
|
||||
\bibitem{Kramers1940} H. A. Kramers, \textit{Physica} \textbf{7}, 284 (1940).
|
||||
\end{thebibliography}
|
||||
\end{document}
|
||||
Reference in New Issue
Block a user