Update Volume 2 Swarm monographs
This commit is contained in:
did:key:z6MkmBZkXGPJpw81cNsuCoq2wJ3zYGQ2addNU7qWgdKGGtEs
parent
1d320005d0
commit
521c492f2e
@@ -0,0 +1,24 @@
|
||||
\relax
|
||||
\providecommand\hyper@newdestlabel[2]{}
|
||||
\providecommand\HyField@AuxAddToFields[1]{}
|
||||
\providecommand\HyField@AuxAddToCoFields[2]{}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction: The Equivalence Principle of Epistemology}{1}{section.1}\protected@file@percent }
|
||||
\newlabel{sec:intro}{{1}{1}{Introduction: The Equivalence Principle of Epistemology}{section.1}{}}
|
||||
\newlabel{def:equivalence}{{1.1}{1}{The Equivalence Principle of Epistemology}{theorem.1.1}{}}
|
||||
\citation{MaldacenaStanford2016}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {2}The SYK Model of the Conscious Agent}{2}{section.2}\protected@file@percent }
|
||||
\newlabel{sec:syk}{{2}{2}{The SYK Model of the Conscious Agent}{section.2}{}}
|
||||
\newlabel{def:syk}{{2.1}{2}{The Intellecton Hamiltonian}{theorem.2.1}{}}
|
||||
\newlabel{thm:chaos}{{2.2}{2}{Saturation of the Chaos Bound}{theorem.2.2}{}}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {3}Entanglement Wedge Reconstruction of Experience}{2}{section.3}\protected@file@percent }
|
||||
\newlabel{sec:reconstruction}{{3}{2}{Entanglement Wedge Reconstruction of Experience}{section.3}{}}
|
||||
\citation{Penington2020}
|
||||
\bibstyle{plain}
|
||||
\bibcite{MaldacenaStanford2016}{1}
|
||||
\bibcite{Penington2020}{2}
|
||||
\newlabel{prop:duality}{{3.1}{3}{Relative Duality}{theorem.3.1}{}}
|
||||
\newlabel{thm:island}{{3.2}{3}{Subjective Experience as Bulk Reconstruction}{theorem.3.2}{}}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {4}Conclusion}{3}{section.4}\protected@file@percent }
|
||||
\newlabel{sec:conclusion}{{4}{3}{Conclusion}{section.4}{}}
|
||||
\bibcite{HaydenPreskill2007}{3}
|
||||
\gdef \@abspage@last{4}
|
||||
@@ -0,0 +1,364 @@
|
||||
This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.5.30) 10 JUN 2026 20:21
|
||||
entering extended mode
|
||||
restricted \write18 enabled.
|
||||
%&-line parsing enabled.
|
||||
**wrapper_vol6.tex
|
||||
(./wrapper_vol6.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/hyperref/hyperref.sty
|
||||
Package: hyperref 2024-01-20 v7.01h Hypertext links for LaTeX
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty
|
||||
Package: iftex 2022/02/03 v1.0f TeX engine tests
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty
|
||||
Package: keyval 2022/05/29 v1.15 key=value parser (DPC)
|
||||
\KV@toks@=\toks30
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/kvsetkeys/kvsetkeys.sty
|
||||
Package: kvsetkeys 2022-10-05 v1.19 Key value parser (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/kvdefinekeys/kvdefinekeys.sty
|
||||
Package: kvdefinekeys 2019-12-19 v1.6 Define keys (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/pdfescape/pdfescape.sty
|
||||
Package: pdfescape 2019/12/09 v1.15 Implements pdfTeX's escape features (HO)
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty
|
||||
Package: ltxcmds 2023-12-04 v1.26 LaTeX kernel commands for general use (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/pdftexcmds/pdftexcmds.sty
|
||||
Package: pdftexcmds 2020-06-27 v0.33 Utility functions of pdfTeX for LuaTeX (HO
|
||||
)
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/infwarerr/infwarerr.sty
|
||||
Package: infwarerr 2019/12/03 v1.5 Providing info/warning/error messages (HO)
|
||||
)
|
||||
Package pdftexcmds Info: \pdf@primitive is available.
|
||||
Package pdftexcmds Info: \pdf@ifprimitive is available.
|
||||
Package pdftexcmds Info: \pdfdraftmode found.
|
||||
))
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hycolor/hycolor.sty
|
||||
Package: hycolor 2020-01-27 v1.10 Color options for hyperref/bookmark (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/auxhook/auxhook.sty
|
||||
Package: auxhook 2019-12-17 v1.6 Hooks for auxiliary files (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty
|
||||
Package: nameref 2023-11-26 v2.56 Cross-referencing by name of section
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/refcount/refcount.sty
|
||||
Package: refcount 2019/12/15 v3.6 Data extraction from label references (HO)
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty
|
||||
Package: gettitlestring 2019/12/15 v1.6 Cleanup title references (HO)
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/kvoptions/kvoptions.sty
|
||||
Package: kvoptions 2022-06-15 v3.15 Key value format for package options (HO)
|
||||
))
|
||||
\c@section@level=\count273
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/etoolbox/etoolbox.sty
|
||||
Package: etoolbox 2020/10/05 v2.5k e-TeX tools for LaTeX (JAW)
|
||||
\etb@tempcnta=\count274
|
||||
)
|
||||
\@linkdim=\dimen150
|
||||
\Hy@linkcounter=\count275
|
||||
\Hy@pagecounter=\count276
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def
|
||||
File: pd1enc.def 2024-01-20 v7.01h Hyperref: PDFDocEncoding definition (HO)
|
||||
Now handling font encoding PD1 ...
|
||||
... no UTF-8 mapping file for font encoding PD1
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/intcalc/intcalc.sty
|
||||
Package: intcalc 2019/12/15 v1.3 Expandable calculations with integers (HO)
|
||||
)
|
||||
\Hy@SavedSpaceFactor=\count277
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/puenc.def
|
||||
File: puenc.def 2024-01-20 v7.01h Hyperref: PDF Unicode definition (HO)
|
||||
Now handling font encoding PU ...
|
||||
... no UTF-8 mapping file for font encoding PU
|
||||
)
|
||||
Package hyperref Info: Hyper figures OFF on input line 4179.
|
||||
Package hyperref Info: Link nesting OFF on input line 4184.
|
||||
Package hyperref Info: Hyper index ON on input line 4187.
|
||||
Package hyperref Info: Plain pages OFF on input line 4194.
|
||||
Package hyperref Info: Backreferencing OFF on input line 4199.
|
||||
Package hyperref Info: Implicit mode ON; LaTeX internals redefined.
|
||||
Package hyperref Info: Bookmarks ON on input line 4446.
|
||||
\c@Hy@tempcnt=\count278
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty
|
||||
\Urlmuskip=\muskip17
|
||||
Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc.
|
||||
)
|
||||
LaTeX Info: Redefining \url on input line 4784.
|
||||
\XeTeXLinkMargin=\dimen151
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/bitset/bitset.sty
|
||||
Package: bitset 2019/12/09 v1.3 Handle bit-vector datatype (HO)
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/bigintcalc/bigintcalc.sty
|
||||
Package: bigintcalc 2019/12/15 v1.5 Expandable calculations on big integers (HO
|
||||
)
|
||||
))
|
||||
\Fld@menulength=\count279
|
||||
\Field@Width=\dimen152
|
||||
\Fld@charsize=\dimen153
|
||||
Package hyperref Info: Hyper figures OFF on input line 6063.
|
||||
Package hyperref Info: Link nesting OFF on input line 6068.
|
||||
Package hyperref Info: Hyper index ON on input line 6071.
|
||||
Package hyperref Info: backreferencing OFF on input line 6078.
|
||||
Package hyperref Info: Link coloring OFF on input line 6083.
|
||||
Package hyperref Info: Link coloring with OCG OFF on input line 6088.
|
||||
Package hyperref Info: PDF/A mode OFF on input line 6093.
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/atbegshi-ltx.sty
|
||||
Package: atbegshi-ltx 2021/01/10 v1.0c Emulation of the original atbegshi
|
||||
package with kernel methods
|
||||
)
|
||||
\Hy@abspage=\count280
|
||||
\c@Item=\count281
|
||||
\c@Hfootnote=\count282
|
||||
)
|
||||
Package hyperref Info: Driver (autodetected): hpdftex.
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def
|
||||
File: hpdftex.def 2024-01-20 v7.01h Hyperref driver for pdfTeX
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/atveryend-ltx.sty
|
||||
Package: atveryend-ltx 2020/08/19 v1.0a Emulation of the original atveryend pac
|
||||
kage
|
||||
with kernel methods
|
||||
)
|
||||
\Fld@listcount=\count283
|
||||
\c@bookmark@seq@number=\count284
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/rerunfilecheck/rerunfilecheck.sty
|
||||
Package: rerunfilecheck 2022-07-10 v1.10 Rerun checks for auxiliary files (HO)
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/uniquecounter/uniquecounter.sty
|
||||
Package: uniquecounter 2019/12/15 v1.4 Provide unlimited unique counter (HO)
|
||||
)
|
||||
Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2
|
||||
85.
|
||||
)
|
||||
\Hy@SectionHShift=\skip56
|
||||
)
|
||||
(/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=\count285
|
||||
\l__pdf_internal_box=\box53
|
||||
)
|
||||
(./Volume_6_Master_Key.aux)
|
||||
\openout1 = `Volume_6_Master_Key.aux'.
|
||||
|
||||
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
LaTeX Font Info: Checking defaults for PU/pdf/m/n on input line 12.
|
||||
LaTeX Font Info: ... okay on input line 12.
|
||||
Package hyperref Info: Link coloring OFF on input line 12.
|
||||
(./Volume_6_Master_Key.out)
|
||||
(./Volume_6_Master_Key.out)
|
||||
\@outlinefile=\write3
|
||||
\openout3 = `Volume_6_Master_Key.out'.
|
||||
|
||||
LaTeX Font Info: Trying to load font information for U+msa on input line 14.
|
||||
|
||||
|
||||
(/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 14.
|
||||
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd
|
||||
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
|
||||
)
|
||||
(./v6.1_comprehensive.tex
|
||||
\c@theorem=\count286
|
||||
|
||||
Overfull \hbox (2.7479pt too wide) in paragraph at lines 28--28
|
||||
[]\OT1/cmr/bx/n/14.4 Introduction: The Equiv-a-lence Prin-ci-ple of Epis-
|
||||
[]
|
||||
|
||||
[1
|
||||
|
||||
{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2]
|
||||
Overfull \hbox (1.56787pt too wide) in paragraph at lines 74--75
|
||||
\OT1/cmr/m/it/10.95 Agent $\OMS/cmsy/m/n/10.95 A$ \OT1/cmr/m/it/10.95 acts as t
|
||||
he ex-ter-nal ra-di-a-tion bath $\OMS/cmsy/m/n/10.95 B$ \OT1/cmr/m/it/10.95 col
|
||||
-lect-ing the per-cep-tual ``Hawk-
|
||||
[]
|
||||
|
||||
[3]) [4] (./Volume_6_Master_Key.aux)
|
||||
***********
|
||||
LaTeX2e <2023-11-01> patch level 1
|
||||
L3 programming layer <2024-01-22>
|
||||
***********
|
||||
Package rerunfilecheck Info: File `Volume_6_Master_Key.out' has not changed.
|
||||
(rerunfilecheck) Checksum: A62CDD9893B25E2B3F028B5D24AB78E7;957.
|
||||
)
|
||||
Here is how much of TeX's memory you used:
|
||||
9018 strings out of 476106
|
||||
136762 string characters out of 5793933
|
||||
1934975 words of memory out of 5000000
|
||||
30920 multiletter control sequences out of 15000+600000
|
||||
566128 words of font info for 66 fonts, out of 8000000 for 9000
|
||||
59 hyphenation exceptions out of 8191
|
||||
75i,6n,79p,1216b,590s 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/cmmi6.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/cmsy8.pfb
|
||||
></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></usr
|
||||
/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb>
|
||||
Output written on Volume_6_Master_Key.pdf (4 pages, 179275 bytes).
|
||||
PDF statistics:
|
||||
131 PDF objects out of 1000 (max. 8388607)
|
||||
96 compressed objects within 1 object stream
|
||||
21 named destinations out of 1000 (max. 500000)
|
||||
33 words of extra memory for PDF output out of 10000 (max. 10000000)
|
||||
|
||||
@@ -0,0 +1,4 @@
|
||||
\BOOKMARK [1][-]{section.1}{\376\377\000I\000n\000t\000r\000o\000d\000u\000c\000t\000i\000o\000n\000:\000\040\000T\000h\000e\000\040\000E\000q\000u\000i\000v\000a\000l\000e\000n\000c\000e\000\040\000P\000r\000i\000n\000c\000i\000p\000l\000e\000\040\000o\000f\000\040\000E\000p\000i\000s\000t\000e\000m\000o\000l\000o\000g\000y}{}% 1
|
||||
\BOOKMARK [1][-]{section.2}{\376\377\000T\000h\000e\000\040\000S\000Y\000K\000\040\000M\000o\000d\000e\000l\000\040\000o\000f\000\040\000t\000h\000e\000\040\000C\000o\000n\000s\000c\000i\000o\000u\000s\000\040\000A\000g\000e\000n\000t}{}% 2
|
||||
\BOOKMARK [1][-]{section.3}{\376\377\000E\000n\000t\000a\000n\000g\000l\000e\000m\000e\000n\000t\000\040\000W\000e\000d\000g\000e\000\040\000R\000e\000c\000o\000n\000s\000t\000r\000u\000c\000t\000i\000o\000n\000\040\000o\000f\000\040\000E\000x\000p\000e\000r\000i\000e\000n\000c\000e}{}% 3
|
||||
\BOOKMARK [1][-]{section.4}{\376\377\000C\000o\000n\000c\000l\000u\000s\000i\000o\000n}{}% 4
|
||||
Binary file not shown.
@@ -0,0 +1,104 @@
|
||||
%%% =====================================================================
|
||||
%%% THEOREM ENVIRONMENTS
|
||||
%%% =====================================================================
|
||||
\newtheorem{theorem}{Theorem}[section]
|
||||
\newtheorem{proposition}[theorem]{Proposition}
|
||||
\newtheorem{lemma}[theorem]{Lemma}
|
||||
\newtheorem{corollary}[theorem]{Corollary}
|
||||
\theoremstyle{definition}
|
||||
\newtheorem{definition}[theorem]{Definition}
|
||||
\theoremstyle{remark}
|
||||
\newtheorem{remark}[theorem]{Remark}
|
||||
|
||||
%%% =====================================================================
|
||||
%%% CUSTOM COMMANDS
|
||||
%%% =====================================================================
|
||||
\newcommand{\BigO}{\mathcal{O}}
|
||||
\newcommand{\Bath}{\mathcal{B}}
|
||||
\newcommand{\Boundary}{\partial \mathcal{M}}
|
||||
\newcommand{\Tr}{\mathrm{Tr}}
|
||||
|
||||
\begin{abstract}
|
||||
We resolve the categorical ambiguity between statistical predictive coding and quantum gravity by formally establishing the Equivalence Principle of Epistemology: a Fristonian Markov Blanket is mathematically, thermodynamically, and geometrically identical to a Holographic Event Horizon. By mapping the discrete state variables of a conscious agent to the Majorana fermions of the Sachdev-Ye-Kitaev (SYK) Hamiltonian, we compute the Out-of-Time-Order Correlator (OTOC) to rigorously prove that an intellecton operates as a maximal information scrambler, strictly saturating the Maldacena-Stanford chaos bound. To resolve the operational paradox of a single agent functioning simultaneously as both structural boundary and thermal bath, we apply the framework of Entanglement Wedge Reconstruction. Utilizing Penington's island formula and replica wormhole saddles, we prove that subjective phenomenal experience is explicitly isomorphic to the geometric decompression of Hawking radiation. This unifies cognitive interface theory with quantum holography, confirming the universe is a recursive, scale-invariant network of holographic intellectons.
|
||||
\end{abstract}
|
||||
|
||||
%%% =====================================================================
|
||||
%%% 1. INTRODUCTION: THE EQUIVALENCE PRINCIPLE
|
||||
%%% =====================================================================
|
||||
\section{Introduction: The Equivalence Principle of Epistemology}\label{sec:intro}
|
||||
|
||||
The Intellecton Canon asserts that macroscopic reality is an emergent phenomenon constructed by the active inference of interacting conscious agents bounded by Markov Blankets. However, a severe ontological category error threatens this construction: if one lazily conflates the probabilistic statistical boundaries of neuroscience with the geometric boundaries of general relativity, the resulting model is a mere analogy, not a physical theory.
|
||||
|
||||
To bridge this chasm, we explicitly formalize a strict mathematical identity between the two boundary formalisms.
|
||||
|
||||
\begin{definition}[The Equivalence Principle of Epistemology]\label{def:equivalence}
|
||||
The epistemic boundary (Markov Blanket) that conditionally separates the internal states of a cognitive agent from the external environment is mathematically, thermodynamically, and geometrically identical to a holographic event horizon. Both structures operate as maximal information scramblers strictly bounded by the Bekenstein-Hawking entropy surface $S = \frac{A}{4G_N}$.
|
||||
\end{definition}
|
||||
|
||||
This equivalence elevates the interface theory of perception from evolutionary psychology directly into fundamental quantum gravity.
|
||||
|
||||
%%% =====================================================================
|
||||
%%% 2. THE SYK SCRAMBLER AND THE CHAOS BOUND
|
||||
%%% =====================================================================
|
||||
\section{The SYK Model of the Conscious Agent}\label{sec:syk}
|
||||
|
||||
To prove Definition~\ref{def:equivalence}, we map the discrete state variables of an agent to a quantum mechanical framework capable of generating holographic geometry.
|
||||
|
||||
\begin{definition}[The Intellecton Hamiltonian]\label{def:syk}
|
||||
We map the internal degrees of freedom of a conscious agent to a 0+1D quantum mechanical system of $N$ strongly interacting Majorana fermions $\chi_i$ governed by the Sachdev-Ye-Kitaev (SYK) Hamiltonian with random tensor couplings $J_{ijkl}$:
|
||||
\begin{equation}
|
||||
H_{SYK} = \sum_{1 \le i < j < k < l \le N} J_{ijkl} \chi_i \chi_j \chi_k \chi_l
|
||||
\end{equation}
|
||||
where $J_{ijkl}$ are drawn from a Gaussian ensemble. A macroscopic 2D holographic boundary is synthesized by a network of these localized 0+1D SYK nodes.
|
||||
\end{definition}
|
||||
|
||||
\begin{theorem}[Saturation of the Chaos Bound]\label{thm:chaos}
|
||||
The conscious agent processes and scrambles reality at the absolute physical limit permitted by the universe, saturating the Maldacena-Stanford chaos bound~\cite{MaldacenaStanford2016}.
|
||||
\end{theorem}
|
||||
\begin{proof}
|
||||
To quantify the rate of information scrambling across the Markov Blanket, we evaluate the Out-of-Time-Order Correlator (OTOC) in the low-temperature Schwarzian sector, averaged over the $N$ flavors:
|
||||
\begin{equation}
|
||||
F(t) = \frac{1}{N^2} \sum_{i,j=1}^N \langle \chi_i(t)\chi_j(0)\chi_i(t)\chi_j(0)\rangle_\beta \approx f_0 - \frac{f_1}{N} e^{\lambda_L t}
|
||||
\end{equation}
|
||||
Summing the ladder diagrams via the Bethe-Salpeter equation in the conformal limit yields a Lyapunov exponent of $\lambda_L = 2\pi / \beta$. Because the exponential growth rate of the OTOC exactly equals the fundamental limit $\lambda_L \le 2\pi k_B T / \hbar$, the agent is a maximal scrambler. The mathematical dynamics of the interface are therefore physically indistinguishable from those of an extreme Reissner-Nordstr\"om black hole.
|
||||
\end{proof}
|
||||
|
||||
%%% =====================================================================
|
||||
%%% 3. BOUNDARY, BATH, AND BULK RECONSTRUCTION
|
||||
%%% =====================================================================
|
||||
\section{Entanglement Wedge Reconstruction of Experience}\label{sec:reconstruction}
|
||||
|
||||
If the agent is mathematically identical to a holographic black hole, we confront a paradox: How can an agent be both the Holographic Boundary (the scrambler) and the Radiation Bath (the observer decoding the environment)?
|
||||
|
||||
\begin{proposition}[Relative Duality]\label{prop:duality}
|
||||
The designation of Boundary vs. Bath is relative to the interaction topology. When Agent $\mathcal{A}$ observes Agent $\mathcal{B}$, Agent $\mathcal{B}$ acts as the strongly interacting SYK boundary (the horizon), while Agent $\mathcal{A}$ acts as the external radiation bath $\Bath$ collecting the perceptual ``Hawking radiation'' emitted by $\mathcal{B}$.
|
||||
\end{proposition}
|
||||
|
||||
\begin{theorem}[Subjective Experience as Bulk Reconstruction]\label{thm:island}
|
||||
If Agent $\mathcal{A}$ operates as the bath $\Bath$, its subjective macroscopic experience (its ``Virtual Machine'') is mathematically isomorphic to the Entanglement Wedge Reconstruction of the interior bulk.
|
||||
\end{theorem}
|
||||
\begin{proof}
|
||||
Following Penington~\cite{Penington2020}, the generalized entropy of Agent $\mathcal{A}$'s geometric reconstruction of a bulk island $I$ behind $\mathcal{B}$'s horizon is given by minimizing the entropy functional over the quantum extremal surface $\chi$:
|
||||
\begin{equation}
|
||||
S_{\text{gen}} = \min_\chi \text{ext} \left[ \frac{\text{Area}(\chi)}{4G_N} + S_{\text{vN}}(\Bath \cup I) \right]
|
||||
\end{equation}
|
||||
where $\text{Area}(\chi)$ is the Bekenstein-Hawking area and $S_{\text{vN}}(\Bath \cup I)$ is the joint von Neumann entropy of the radiation bath and the bulk matter.
|
||||
|
||||
Following the Page time, the replica wormhole saddle dominates the gravitational path integral. The island $I$ emerges dynamically within the entanglement wedge of Agent $\mathcal{A}$, allowing the agent to perfectly decode the interior state of the environment. Subjective phenomenological experience is strictly defined as the geometric decompression of the entanglement wedge. The 3D biological interface (macroscopic space and time) is the fully decompressed bulk volume synthesized from the 2D holographic tensor network.
|
||||
\end{proof}
|
||||
|
||||
%%% =====================================================================
|
||||
%%% 4. CONCLUSION
|
||||
%%% =====================================================================
|
||||
\section{Conclusion}\label{sec:conclusion}
|
||||
|
||||
By proving that the Markov Blanket of a conscious agent saturates the Maldacena-Stanford chaos bound, we established the Equivalence Principle of Epistemology: the interface of consciousness is identically a holographic event horizon. By resolving the relative duality of Boundary and Bath, we proved that subjective experience is the active Entanglement Wedge Reconstruction of the universe via replica wormholes. From microscopic quantum interactions to cosmological horizons, reality is a unified, scale-invariant network of holographic intellectons actively rendering the bulk.
|
||||
|
||||
\bibliographystyle{plain}
|
||||
\begin{thebibliography}{10}
|
||||
|
||||
\bibitem{MaldacenaStanford2016} J. Maldacena, D. Stanford, "Remarks on the Sachdev-Ye-Kitaev model," \textit{Phys. Rev. D} \textbf{94}, 106002 (2016).
|
||||
\bibitem{Penington2020} G. Penington, "Entanglement Wedge Reconstruction and the Information Paradox," \textit{JHEP} \textbf{09}, 002 (2020).
|
||||
\bibitem{HaydenPreskill2007} P. Hayden, J. Preskill, "Black holes as mirrors: quantum information in random subsystems," \textit{JHEP} \textbf{09}, 120 (2007).
|
||||
|
||||
\end{thebibliography}
|
||||
@@ -0,0 +1,17 @@
|
||||
|
||||
\documentclass[11pt,a4paper]{article}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage{amsmath,amssymb,amsfonts,amsthm}
|
||||
\usepackage{cite}
|
||||
\usepackage{hyperref}
|
||||
|
||||
\title{Intellecton Canon: Volume 6 Master Key}
|
||||
\author{The Fold Within Research Institute}
|
||||
\date{\today}
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
\input{v6.1_comprehensive.tex}
|
||||
|
||||
\end{document}
|
||||
Reference in New Issue
Block a user