├── .gitignore
├── Makefile
├── README.md
├── compile-grammar
├── diphoton.gram
├── snarxiv.gram
├── thm.gram
└── thmheader.tex


/.gitignore:
--------------------------------------------------------------------------------
1 | snarxiv
2 | diphoton
3 | thm
4 | *.ml
5 | *.cmi
6 | *.cmo
7 | install-snarxiv
8 | 


--------------------------------------------------------------------------------
/Makefile:
--------------------------------------------------------------------------------
 1 | OCAMLC=ocamlc
 2 | COMPILEGRAM=./compile-grammar
 3 | 
 4 | all: thm snarxiv diphoton
 5 | 
 6 | thm: thm.ml
 7 | 	$(OCAMLC) thm.ml -o thm
 8 | 
 9 | snarxiv: snarxiv.ml
10 | 	$(OCAMLC) snarxiv.ml -o snarxiv
11 | 
12 | diphoton: diphoton.ml
13 | 	$(OCAMLC) diphoton.ml -o diphoton
14 | 
15 | %.ml: %.gram
16 | 	$(COMPILEGRAM) $<
17 | 
18 | clean:
19 | 	rm -f *.cmi *.cmo *.ml
20 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | Grammar Definition for [the snarXiv](http://snarXiv.org)
 2 | ========================================================
 3 | 
 4 | The file `snarxiv.gram` contains a [context-free
 5 | grammar](http://en.wikipedia.org/wiki/Context-free_grammar) that
 6 | produces randomly generated titles and abstracts for high energy
 7 | theoretical physics papers. See
 8 | 
 9 | * http://snarxiv.org/
10 | * http://snarxiv.org/vs-arxiv/
11 | * http://davidsd.org/2010/03/the-snarxiv/
12 | * http://davidsd.org/2010/09/the-arxiv-according-to-arxiv-vs-snarxiv/
13 | 
14 | `compile-grammar` is a perl script that compiles a `.gram` file into
15 | [OCaml](http://ocaml.org/) code, which can be compiled into an
16 | executable and run.  Type `make` to run both compilation steps.
17 | 
18 | Requirements
19 | ------------
20 | 
21 | [Perl](http://www.perl.org/) and [OCaml](http://ocaml.org/).
22 | 
23 | Bonus Grammar: Random Theorems
24 | ------------------------------
25 | 
26 | `thm.gram` is the grammar for the [theorem
27 | generator](http://davidsd.org/theorem/) (originally authored by Matt
28 | Gline).  When compiled and run, it produces LaTeX code which can be
29 | typeset by LaTeX, provided `thmheader.tex` is included at the top of
30 | the file.  Requires Paul Taylor's [Diagrams
31 | package](http://www.paultaylor.eu/diagrams/).
32 | 


--------------------------------------------------------------------------------
/compile-grammar:
--------------------------------------------------------------------------------
 1 | #!/usr/bin/perl -w
 2 | 
 3 | ($gram) = @ARGV;
 4 | 
 5 | unless ($gram) {
 6 | print <<"EOF";
 7 | usage: cgram grammar output
 8 | notes: If the output file is "foo", then the ocaml code will be
 9 |        written into "foo.ml". Make sure the ocaml compiler "ocamlopt"
10 |        is present on this system.
11 | EOF
12 |     exit 0;
13 | }
14 | 
15 | unless($gram =~ /^\w*\.gram$/) {
16 |     print "input should be a .gram file\n";
17 |     exit 1;
18 | }
19 | 
20 | $gram =~ /^(\w*)\.gram$/;
21 | $out = $1;
22 | 
23 | open GRAM, "$gram";
24 | open OUT, ">$out.ml";
25 | 
26 | print OUT <<'EOF';
27 | type phrase = Str of string | Opts of phrase array array
28 | 
29 | let _ = Random.self_init ()
30 | 
31 | let randelt a = a.(Random.int (Array.length a))
32 | let rec print phr = match phr with
33 |   Str  s       -> print_string s
34 | | Opts options ->
35 |     let parts = randelt options in
36 |     Array.iter print parts
37 | 
38 | (* Grammar definitions *)
39 | EOF
40 | 
41 | undef $/;
42 | @entries = split(/\s* ^ \s* (?= \S+\s* ::=)/mx, <GRAM>);
43 | close GRAM;
44 | 
45 | undef $mainphrase; # the goal of the grammar. i.e. the thing we'll be producing
46 | 
47 | print "parsing grammar '$gram' into '$out.ml'...";
48 | foreach (@entries) {
49 |     s/\s* \# .* $//xmg;
50 |     if (/\s*(\S*)\s*::=\s*(.*)/s) {
51 |         $lhs = $1;
52 |         $rhs = $2;
53 | 
54 |         if (!defined ($mainphrase)) {
55 |             $mainphrase = $lhs;
56 |             print OUT "let rec $lhs = Opts [|\n";
57 |         } else {
58 |             print OUT "and $lhs = Opts [|\n";
59 |         }
60 | 
61 |         @opts = split(/\s*\|\s*/, $rhs);
62 |         foreach $opt (@opts) {
63 |             print OUT "  [|";
64 |             $opt =~ s/\s*\n\s*/ /g;
65 | 
66 |             # split just before < and after >
67 |             @parts = split(/ (?= <) | (?<= >) /x, $opt);
68 |             foreach $part (@parts) {
69 |                 if ($part =~ /<(.*)>/) { # it's either a grammar part
70 |                     print OUT " $1;";
71 |                 } else {                 # or a string literal
72 |                     $part =~ s/\\/\\\\/g; # turn \ into \\ for ML printing
73 | 		    $part =~ s/\"/\\\"/g; # likewise for "
74 |                     print OUT " Str \"$part\";";
75 |                 }
76 |             }
77 |             print OUT "|];\n";
78 |         }
79 |         print OUT "|]\n\n";
80 |     } else {
81 |         if (/\S/) {
82 |             print "********error parsing*******";
83 |             close OUT;
84 |             exit 1;
85 |         }
86 |     }
87 | }
88 | print "done.\n";
89 | 
90 | print OUT "let _ = print $mainphrase\n";
91 | print OUT "let _ = print_string \"\\n\"";
92 | close OUT;
93 | 


--------------------------------------------------------------------------------
/diphoton.gram:
--------------------------------------------------------------------------------
  1 | top ::= <paper>
  2 | 
  3 | #
  4 | # Matthew Low
  5 | #  March 2016
  6 | #
  7 | # Based on snarxiv code of David Simmons-Duffin.
  8 | #
  9 | 
 10 | paper ::= <title> \\ <authors> \\ <comments> \\ <papersubjects> \\ <abstract>
 11 | 
 12 | ###########################################################################################################
 13 | 
 14 | ######## Author ########
 15 | author ::= <capital>. <physicistname>
 16 | authors ::= <author> | <author>, <author>  | <author>, <author>, <author>
 17 |           | <author> | <author>, <author>  | <author>, <author>, <author>
 18 |           | <author> | <author>, <author>  | <author>, <author>, <author>
 19 |           | <author>, <author>, <author>, <author>, <author>, <author>, <author>, <author>, <author>, <author>
 20 | 
 21 | ######## Comments ########
 22 | morecomments ::= <smallinteger> figures | JHEP style | Latex file | no figures | BibTeX
 23 |                | JHEP3 | typos corrected | <nzdigit> tables | added refs | minor changes
 24 |                | minor corrections | published in PRD | reference added | pdflatex
 25 |                | based on a talk given on <famousname>'s <nzdigit>0th birthday
 26 |               
 27 | newcomments ::= added refs | updated figure <nzdigit>, conclusions unchanged | <smallinteger> pages | <smallinteger> pages, added refs
 28 | 
 29 | comments ::= <smallinteger> pages | <comments>, <morecomments> | v<nnzdigit>: <newcomments>
 30 | 
 31 | ######## Subjects ########
 32 | primarysubj   ::= High Energy Physics - Phenomenology (hep-ph)
 33 | secondarysubj ::= High Energy Physics - Theory (hep-th) | High Energy Physics - Experiment (hep-ex)
 34 | papersubjects ::= <primarysubj> | <primarysubj>; <secondarysubj>
 35 | 
 36 | ######## Physicist ########
 37 | physicist ::= <physicistname> | <physicistname> | <physicistname>-<physicistname> 
 38 | physicistname ::=  Li | Li | Li | Li | Li | Li | Li | Okada | Okada | Okada | Okada | Okada | Okada | Okada | Nomura | Nomura | Nomura | Nomura | Nomura | Nomura | Chao | Chao | Chao | Chao | Chao | Ding | Ding | Ding | Ding | Dev | Dev | Dev | Dev | Ko | Ko | Ko | Ko | Yang | Yang | Yang | Yang | Yu | Yu | Yu | Yu | Wang | Wang | Wang | Wang | Han | Han | Han | Han | Chiang | Chiang | Chiang | Chiang | Strumia | Strumia | Strumia | Strumia | Hernández | Hernández | Hernández | Hernández | Orikasa | Orikasa | Orikasa | Nomura | Nomura | Nomura | Zhang | Zhang | Zhang | Sanz | Sanz | Sanz | Yanagida | Yanagida | Yanagida | Raychaudhuri | Raychaudhuri | Raychaudhuri | Zhang | Zhang | Zhang | Ryskin | Ryskin | Ryskin | Huang | Huang | Huang | Wu | Wu | Wu | Harigaya | Harigaya | Harigaya | Yagyu | Yagyu | Yagyu | Cao | Cao | Cao | Zhang | Zhang | Zhang | Sannino | Sannino | Sannino | Sengupta | Sengupta | Sengupta | Zhu | Zhu | Zhu | Urbano | Urbano | Urbano | Yu | Yu | Hamada | Hamada | Jiang | Jiang | Omura | Omura | Gao | Gao | Zhang | Zhang | Fan | Fan | Tang | Tang | Kats | Kats | Bi | Bi | Wang | Wang | Su | Su | Mayes | Mayes | Khoze | Khoze | Dey | Dey | Aydemir | Aydemir | Ghosh | Ghosh | Mandal | Mandal | Moroi | Moroi | Fichet | Fichet | Patra | Patra | Moretti | Moretti | Sadhukhan | Sadhukhan | Sun | Sun | Zheng | Zheng | Zhu | Zhu | Kanemura | Kanemura | Wang | Wang | Raza | Raza | Park | Park | Austri | Austri | Franceschini | Franceschini | Torre | Torre | Mohapatra | Mohapatra | Cao | Cao | Langacker | Langacker | Vignaroli | Vignaroli | Park | Park | Redi | Redi | Strassler | Strassler | Arun | Arun | Ibe | Ibe | Shang | Shang | Wang | Wang | Hall | Hall | Harland-Lang | Harland-Lang | Rolbiecki | Rolbiecki | Cheung | Cheung | Mawatari | Mawatari | Bernon | Bernon | Quevillon | Quevillon | Santiago | Santiago | No | No | Park | Park | Kim | Kim | Terning | Terning | Ellis | Ellis | Ren | Ren | Song | Song | Hubisz | Hubisz | Cline | Cline | Halverson | Halverson | Maxin | Maxin | Gogoladze | Gogoladze | Han | Han | Perez | Perez | Gersdorff | Gersdorff | Staub | Staub | Bertuzzo | Bertuzzo | Molinaro | Molinaro | Vigiani | Vigiani | Nanopoulos | Nanopoulos | Bardhan | Bardhan | Borah | Borah | Marzocca | Marzocca | Buttazzo | Buttazzo | Delaunay | Delaunay | Li | Li | Royon | Royon | Dutta | Dutta | Kobakhidze | Kobakhidze | Kundu | Kundu | Goudelis | Goudelis | Tesi | Tesi | Kuo | Kuo | Chakraborty | Chakraborty | Salvio | Salvio
 39 | 
 40 | famousname ::= Weinberg | Feynman | Polchinski | Randall | Sundrum | Georgi | Glashow | Coleman | Bohr | Fermi | Heisenberg | Einstein
 41 | 
 42 | ###########################################################################################################
 43 | 
 44 | ######## Numbers ########
 45 | zdigit       ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
 46 | nzdigit      ::= 1 | 2 | 3 | 4
 47 | nnzdigit     ::= 2 | 3 | 4
 48 | smallinteger ::= <nnzdigit> | <nzdigit><zdigit> | <nzdigit><zdigit>
 49 | n            ::= n | m | <nzdigit> 
 50 | massnumber   ::= 300 | 400 | 500 | 600 | 700 | 800 | 900
 51 | charge       ::= 1/3 | 2/3 | 4/3 | 5/3 | 8/3 | 1/5 | 2/5
 52 | 
 53 | ######## Language ########
 54 | capital ::= A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z
 55 | 
 56 | article ::= a | the
 57 | 
 58 | adverb ::= remarkably | actually | interestingly | however | moreover | therefore | thus
 59 |          | consequently | curiously | fortunately | unfortunately | surprisingly | unsurprisingly
 60 |          | quite simply | in short 
 61 | 
 62 | ###########################################################################################################
 63 | title ::= <theexcess>: <subject>
 64 |         | interpretations of <theexcess> in <model>
 65 |         | <question> <subject>
 66 |         | <relating> <theexcess> and <otherthing>
 67 |         | <theexcess> from <model>
 68 |         | interpretations of <theexcess> in extensions of <model>
 69 |         | on <theexcess>
 70 |         | <theexcess> as <anewparticle>
 71 |         | a new take on <model> inspired by <theexcess>
 72 |         | a new look at <model> inspired by <theexcess>
 73 | 
 74 | subject ::= interpretations in <model>
 75 |           | interpreting <theexcess> in <model>
 76 |           | <anewparticle> in <model>
 77 |           | calculating <quantity> in <model>
 78 | 
 79 | quantity ::= the mass spectrum
 80 |              | the diphoton rate
 81 |              | the one loop amplitude
 82 |              | the NLO cross section
 83 | 
 84 | question ::= <how> wide? | tension with run 1? | spin-2? | spin-3/2?
 85 | 
 86 | how ::= how | can it be | is it | what if it is
 87 | 
 88 | theexcess ::= the 750 GeV <excess>
 89 |               | the diphoton <excess>
 90 |               | the $\gamma\gamma$ <excess>
 91 | 
 92 | excess ::= excess | peak | resonance | anomaly
 93 | 
 94 | model ::= minimal composite Higgs | the MSSM | the NMSSM | $\lambda$SUSY | technicolor 
 95 |          | 2HDMs | SU(5) | GUT models | SO(10) | E6 | SU(3)^3
 96 |          | two Higgs doublet models
 97 |          | left-right models
 98 |          | singlet-extended models | gauge-extended models
 99 |          | split SUSY models | minisplit SUSY models
100 |          | the broken MRSSM
101 |          | composite models
102 |          | Georgi-Machacek models
103 |          | Seesaw models
104 |          | large N QCD | AdS/CFT
105 |          | the <famousname>-<famousname> model
106 |          | fat Higgs | little Higgs | twin Higgs
107 |          | folded SUSY | composite twin Higgs
108 |          | Pati-Salam models | flipped SU(5) models
109 | 
110 | otherthing ::= the galactic center excess
111 |              | the 2 TeV resonance
112 |              | the diboson resonance
113 |              | muon g-2
114 |              | $B \to D \tau \nu$
115 |              | natural inflation
116 |              | the strong CP problem
117 |              | $h \to \mu \tau$
118 |              | the doublet-triplet splitting problem
119 |              | the core-cusp problem
120 | 
121 | anewparticle ::= an axion
122 |                | a dilaton
123 |                | an eta
124 |                | an eta prime
125 |                | a pion
126 |                | a heavy pion
127 |                | scalar singlet
128 |                | an axino
129 |                | a pseudoscalar
130 |                | a pseudo Nambu Goldstone boson
131 |                | a sgoldstino
132 |                | a KK graviton
133 |                | a KK gluon
134 |                | an electroweak triplet
135 |                | a color sextet
136 | 
137 | ###########################################################################################################
138 | abstract ::= <asentence>.  <bsentence>.  <csentence>.  <adverb>, <dsentence>.  <closing>.
139 |            | <asentence>.  <bsentence>.  <csentence>.  <adverb>, <csentence>.  <closing>.
140 |            | <asentence>.  <adverb>, <bsentence>.  <csentence>.  <dsentence>.  <closing>.
141 |            | <asentence>.  <bsentence>.  <adverb>, <csentence>.  <dsentence>.  <closing>.
142 |            | <asentence>.  <bsentence>.  <adverb>, <csentence>.  <dsentence>. <closing>.
143 |            | <asentence>.  <adverb>, <bsentence>.  <adverb>, <csentence>.  <dsentence>. <closing>.
144 |            | <asentence>.  <adverb>, <bsentence>.  <csentence>.  <adverb>, <dsentence>. <closing>.
145 | 
146 | asentence ::= <recently>, ATLAS and CMS have <observed> <anexcess> in <run2data>
147 |             | ATLAS and CMS have just <observed> <anexcess> in <run2data>
148 |             | ATLAS and CMS have just <observed> <anexcess> in <run2data> at <nzdigit>.<zdigit> sigma
149 |             | In this <note>, we <discuss> the <recent> diphoton <excess> at run 2
150 |             | In this <note>, we <discuss> the <recent> diphoton <excess> at run 2 (at <nzdigit>.<zdigit> sigma)
151 |             | In this <note>, we <discuss> the <recent> diphoton <excess> at run 2 and <otherthing>
152 | 
153 | bsentence ::= we <consider> <theexcess> in <model>
154 |             | we <consider> <theexcess> in <model> with <extra>
155 |             | <theexcess> is <considered> in <model> with <extra>
156 |             | we <consider> the phenomenology of <model> and <calculate> <objects>
157 |             | the phenomenology of <model> is <considered> and we <calculate> <objects>
158 |             | <extra> are added to <model> to <accountfor> <theexcess>
159 |             | <although> <theexcess> could be a statistical fluctuation, <bsentence>
160 |             | we <consider> the phenomenology of <model> and <calculate> <objects>
161 |             | we <consider> <theexcess> in <model> on <space>
162 | 
163 | csentence ::= a <feature> of this model is <physicsstatement>
164 |             | the <newparticle> is produced in <production> and decays to <diphoton>
165 |             | the <symmetry> symmetry protects the mass of the <newparticle>
166 |             | the <symmetry> symmetry protects the mass of the <newparticle>, but not the Higgs
167 |             | the <symmetry> symmetry stabilizes the mass of the <newparticle>
168 |             | the <newparticle> couples to <channel>, but not to <channel>, <reducing> tension with Run 1
169 |             | the <newparticle> couples not only to <channel>, but also to <channel>
170 | 
171 | dsentence ::= assuming <theexcess> is real, we predict that <extra> should be at <massnumber> GeV
172 |             | <extra> at <massnumber> GeV should be observed soon
173 |             | <extra> are required at <massnumber> GeV
174 |             | we expect <anewparticle> above <massnumber> GeV
175 |             | we predict <anewparticle> below <massnumber> GeV
176 |             | <theexcess> implies <extra> around <massnumber> GeV
177 | 
178 | closing ::= finally, <bsentence>
179 |           | <adverb>, there is much to be done
180 |           | we leave the rest for future study
181 |           | we will provide more details in a future paper
182 |           | our results are similar to work done by <physicistname>
183 |           | our results are similar to work done by <physicistname> and <physicistname>
184 |           | we believe this is indicative of a <beautiful> <fact>
185 |           | given this, our work may seem quite <beautiful>
186 |           | more data should reveal the nature of <theexcess>
187 |           | more data is likely to confirm this <beautiful> <fact>
188 |  
189 | ###########################################################################################################
190 | 
191 | ######## Verbs ########
192 | consider ::= scrutinize | analyze | study | consider
193 | 
194 | relating ::= relating | connecting | explaining | a unified explanation for | a common framework for
195 | 
196 | observed ::= observed | seen | measured | reported | released | shown | presented
197 | 
198 | considered ::= scrutinized | analyzed | studied | considered
199 | 
200 | calculate ::= calculate | compute | derive | analyze | predict | evaluate
201 | 
202 | ######## English ########
203 | recently ::= recently | just recently | in december | a few months ago | less than a year ago
204 | 
205 | recent ::= recent | very recent | intriguing
206 | 
207 | discuss ::= discuss | address | talk about | look at
208 | 
209 | note ::= paper| note| letter| article|
210 | 
211 | although ::= although | while | even though | despite the fact that
212 | 
213 | accountfor ::= account for | explain | compensate for | allow for
214 | 
215 | feature ::= feature | drawback | corollary | downside
216 | 
217 | size ::= almost zero | tiny | small | large | huge | enormous | sizable
218 | 
219 | reducing ::= reducing | removing | alleviating | worsening | increasing | decreasing
220 | 
221 | importantadverb ::= crucially | importantly
222 | 
223 | beautiful ::= beautiful | surprising | elegant | pretty | arresting | charming
224 |             | simple | ingenious | sophisticated | intricate | elaborate | detailed
225 |             | confusing | bewildering | perplexing | elaborate | involved | complicated
226 |             | startling | unforseen | amazing | extraordinary | remarkable
227 |             | shocking | unexpected | deep | mysterious | profound | unsurprising
228 |             | essential | fundamental | crucial | critical | key | important
229 | 
230 | fact ::= fact | truth | principle | law | theorem | rule | pattern | structure | framework | edifice
231 | 
232 | ######## Physics ########
233 | diphoton ::= the diphoton channel | a pair of photons | two photons | $\gamma\gamma$
234 | 
235 | newparticle ::= resonance | $X$ | $\phi$ | $S$ | $\eta$ | $S(750)$ | $X(750)$
236 | 
237 | production ::= gluon fusion | vector boson fusion | photon fusion | elastic scattering | the quark antiquark channel | inelastic scattering
238 | 
239 | anexcess ::= an excess | a peak | a resonance | an anomaly
240 | 
241 | run2data ::= run 2 | run 2 of the LHC | the latest LHC data | the second run of the LHC | the 13 TeV data 
242 | 
243 | extra ::= vector-like quarks
244 |         | vector-like fermions
245 |         | exotic fermions
246 |         | neutralinos
247 |         | light axions
248 |         | heavy scalars
249 |         | neutral fermions
250 |         | new gauge interactions
251 |         | new strong dynamics
252 |         | conformal dynamics
253 |         | colored pions
254 |         | charge <charge> quarks
255 | 
256 | objects ::= decay widths | production rates | branching ratios | mass ratios | cross sections 
257 |           | the full mass spectrum | the statistical significance | 4-body decays | correlations between <channel> and <channel>
258 |           | flavor observables | deviations to Higgs couplings
259 |           | anomalous dimensions
260 | 
261 | physicsstatement ::= that it is very predictive
262 |                    | that <channel> and <channel> are predicted to be <size>
263 |                    | that it cannot account for <otherthing>
264 |                    | that it encapsulates all the relevant physics
265 |                    | that it explains <otherthing>
266 | 
267 | channel ::= $ZZ$ | $Z\gamma$ | $WW$ | $t\bar{t}$ | $hh$ | $b\bar{b}$
268 | 
269 | space ::= a D3-brane | AdS_5 | a torus | 3-brane | warped metric | a lattice
270 | 
271 | symmetry ::= chiral | shift | discrete | PQ | R | global U(1) | flavor | conformal
272 | 


--------------------------------------------------------------------------------
/snarxiv.gram:
--------------------------------------------------------------------------------
  1 | top ::= <paper>
  2 | 
  3 | # by David Simmons-Duffin (http://www.physics.harvard.edu/~davidsd)
  4 | # March 2010
  5 | #
  6 | # This grammar is free from context, and also free for you to use
  7 | # however you like, although it's probably not a good idea to try
  8 | # actually submitting any of these to the arXiv.  Feel free to suggest
  9 | # improvements or additions, particularly famous physicists or physics
 10 | # concepts with funny names that I forgot.
 11 | #
 12 | # The code grew organically over several hours, so it may be poorly
 13 | # organized, incomplete, and inconsistent.  Hopefully the output
 14 | # reflects that.
 15 | 
 16 | ######## Numbers ########
 17 | 
 18 | zdigit ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
 19 | nzdigit ::= 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
 20 | smallinteger ::= <nzdigit> | <nzdigit><zdigit> | <nzdigit><zdigit>
 21 | n ::= n | m | <nzdigit> 
 22 | 
 23 | ######## Basic Algebra ########
 24 | 
 25 | ring ::= \Z | \Q | \R | \C | \mathbb{H}
 26 | 
 27 | group ::= <liegroup> | <discretegroup>
 28 | liegroup ::= SU(<n>) | Sp(<n>) | SO(<n>) | G_2 | F_4 | E_6 | E_7 | E_8 |
 29 |           Spin(<n>)
 30 | discretegroup ::= \Z | \Z_<n> | \Z^<n> | Hom(<ring>,<ring>) | H^<n>(<mathspace>,<ring>)
 31 |                 | H_<n>(<mathspace>,<ring>) | Ext^<n>(<ring>,<ring>) | M_<n>(<ring>) | SL_<n>(<ring>)
 32 |                 | Dih_<n>
 33 | groupaction ::= orbifold | quotient
 34 | 
 35 | lowercaseletter ::= a | b | c | d | e | f | g | h | i | j | k | l | m | n | o | p
 36 |                   | q | r | s | t | u | v | w | x | y | z
 37 | uppercaseletter ::= A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P
 38 |                   | Q | R | S | T | U | V | W | X | Y | Z
 39 | letter ::= <lowercaseletter> | <uppercaseletter>
 40 | 
 41 | ######## Spaces ########
 42 | 
 43 | space ::= <pluralspace> | <singspace> | <mathspace>
 44 | 
 45 | singspace ::= a <spacetype> | a <spaceadj> <spacetype> | <properspacename> | <spaceadj> <properspacename>
 46 |             | <mathspace> | <mathspace>
 47 |             | a <bundletype> bundle over <space> | <singspace> fibered over <singspace>
 48 |             | the moduli space of <pluralspace> | a <spacetype> <spaceproperty>
 49 |             | the <spacepart> of <space> | a <group> <groupaction> of <singspace>
 50 |             | the near horizon geometry of <singspace>
 51 | pluralspace ::= <spacetype>s | <spaceadj> <spacetype>s | <n> copies of <mathspace> |
 52 |                 <pluralspace> fibered over <space> |
 53 | 	        <spacetype>s <spaceproperty> |
 54 |                 <bundletype> bundles over <space> | moduli spaces of <pluralspace> | <group> <groupaction>s of <pluralspace>
 55 | 
 56 | spaceadj ::= <spaceadj> <spaceadj> | warped | squashed | non-compact | compact |
 57 |              hyper-Kahler | Kahler | exotic | projective | noncommutative | fuzzy |
 58 |              elliptically-fibered | spin | hyperbolic | Einstein | Ricci-flat | Euclidean |
 59 |              Minkowskian | planar | harmonic | symplectic | ALE | ALF
 60 | spaceproperty ::= of <group> holonomy | with <mathadj> <mathobj>
 61 | bundletype ::= <group> | line | affine | <mathspace>
 62 | spacetype ::= Calabi-Yau <n>-fold| Riemann surface| manifold| <n>-fold| <n>-manifold|
 63 |               symmetric space| K3| del-Pezzo| Klebanov-Strassler background| RS1 background|
 64 |               lens space| Hirzebruch surface| Enriques surface| rational surface| ALE fibration|
 65 |               ALF space| linear dilaton background| Atiyah-Hitchen manifold
 66 | 
 67 | generalspacetype ::= surface | line | hyperplane | hypersurface
 68 | 
 69 | properspacename ::= Anti de Sitter Space | de Sitter Space | Taub-NUT Space | superspace
 70 | 
 71 | mathspace ::= AdS_<n> | S^<n> | R^<n> | CY_<n> | C^<n>
 72 |             | dS_<n> | T^<n> | <mathspace> x <mathspace> | P^<n>
 73 | 
 74 | spacepart ::= boundary | conformal boundary | null future | horizon | NUT
 75 | 
 76 | ######## More Mathematics ########
 77 | 
 78 | mapping ::=
 79 |     function | mapping | homomorphism | homeomorphism | isomorphism
 80 |     | surjective <mapping> | injective <mapping> | holomorphism
 81 |     | biholomorphism | isometry | symplectomorphism
 82 | 
 83 | mathadj ::= trivial | nontrivial | vanishing | nonvanishing | general | discrete | abelian
 84 |           | non-abelian | equivariant | <symmetry> symmetric
 85 | mathobj ::= fundamental group | cohomology | homology | torsion | monodromy
 86 |           | spin structure | dimension | complex structure | flux | B-field
 87 |           | H-flux | groupoid | line bundle | principal bundle | connection
 88 |           | metric | kahler form | hyperkahler structure
 89 | 
 90 | representation ::= adjoint| symmetric tensor| antisymmetric tensor| singlet| doublet| triplet
 91 | 
 92 | ######## Theories ########
 93 | 
 94 | theory ::= <singtheory> | <pluraltheory>
 95 | singtheory ::= <singqft> <theorymodifier> | <singstringtheory> <theorymodifier>
 96 | pluraltheory ::= <pluralqft> <theorymodifier> | <pluralstringtheory> <theorymodifier>
 97 | 
 98 | theorymodifier ::= || <compactified> on <space> | deformed by <operator>s | on <space>
 99 |                    | <near> <theoryobj>
100 | compactified ::= living | compactified | dimensionally reduced | supported
101 | near ::= in the presence of | near | surrounded by | far from
102 | 
103 | qft ::= <singqft> | <singqft> | <singqft> | <pluralqft>
104 | singqft ::= <properqft> | <qftadj> <properqft> | <properqft> <qftproperty>
105 |     | a <qftadj> <genericqft>
106 | pluralqft ::= <qftadj> <genericqft>s
107 | 
108 | qftadj ::= | <qftadj> <qftadj> | supersymmetric | N=<nzdigit> | adjoint | superconformal
109 |            | conformal | extremal | chiral | topological | <n>-dimensional | <n>+1-dimensional | twisted
110 |            | topologically twisted | deformed | perturbative | nonperturbative | Toda | WZW
111 |            | invertible
112 | qftproperty ::= with <qftobj>
113 | 
114 | qftobj ::= a <operator> | <operator>s | <mathadj> superpotential | <mathadj> kahler potential
115 |            | <representation> <field>s | a <representation> <field>
116 |            | gauge group <liegroup> | a <mathadj> deformation | a <optype> defect
117 | 
118 | genericqft ::= QFT| CFT| Matrix Model| TQFT| <theorytype> Theory| NCFT
119 | theorytype ::= Effective Field | Quantum Field | Conformal Field | Soft-Collinear Effective | Topological Field
120 |              | Heavy Quark Effective | low-energy Effective | String | Yang-Mills | Chern-Simons | gauge
121 |              | Liouville
122 | 
123 | properqft ::= QCD | QED | supergravity | unparticle physics | QED_3 | QCD_3 | GR | JT gravity
124 |             | Einstein gravity | General relativity | Jackiw-Teitelboim gravity | N=<n> supergravity
125 | 
126 | stringtheory ::= <singstringtheory> | <pluralstringtheory>
127 | singstringtheory ::= String Theory | F-Theory | M-Theory | Heterotic string theory
128 |                    | Topological String Theory | type IIA | type IIB
129 | pluralstringtheory ::= String theories | Heterotic strings | type IIA strings | type IIB strings
130 |                      | type I strings | topological strings | bosonic strings
131 | 
132 | ######## Physics Objects ########
133 | 
134 | theoryobj ::= <singtheoryobj> | <pluraltheoryobj>
135 | 
136 | singtheoryobj ::= <singblackhole> 
137 |                 | <singblackhole> formed from collapse
138 |                 | a <singularityadj> singularity
139 |                 | a <branetype> brane <braneaction>
140 |                 | a stack of <branetype> branes <braneaction>
141 |                 | a <generalspacetype> defect
142 |                 | an instanton
143 |                 | an orientifold plane
144 |                 | a <branetype> instanton
145 |                 | a <branetype> brane probe
146 |                 | a firewall
147 | 
148 | pluraltheoryobj ::= <pluralblackhole>
149 |                   | <pluralblackhole> formed from collapse
150 |                   | <singularityadj> singularities
151 |                   | <branetype> branes <braneaction>
152 |                   | <generalspacetype> defects
153 |                   | orientifold planes
154 |                   | <branetype> instantons
155 |                   | instantons
156 |                   | firewalls
157 | 
158 | hole ::= hole| brane
159 | 
160 | singblackhole ::= a black <hole> | a <bhadj> black <hole>
161 | pluralblackhole ::= black <hole>s | <bhadj> black <hole>s
162 | 
163 | bhadj ::= orientifold | BTZ | Kerr | Reisner-Nordstrom | small | large
164 |         | Schwarzschild | <branetype> brane | massive | extremal | <n>-dimensional
165 |         | <bhadj> <bhadj> | two-sided | near-extremal | eternal | old | collapsing
166 |         | entangled | fat
167 | 
168 | singularityadj ::= A_<n> | B_<n> | C_<n> | D_<n> | E_6 | E_7 | E_8 | G_2 | F_4 | conifold
169 |           | conical | ADE | orbifold | du Val | Kleinian | rational double-point | canonical
170 |           | exceptional | <physicist>
171 | 
172 | branetype ::= NS5 | D<nzdigit> | (p,q) 7- | (p,q) | noncommutative | black | fractional D<nzdigit>
173 |             | special lagrangian | canonical co-isotropic | holomorphic | A-type | B-type
174 | braneaction ::= | wrapping a <mathspace> | wrapped on <singspace>
175 | 
176 | operator ::= <optype> operator| Chern-Simons term| <optype> F-term| Wilson line| 't Hooft line|
177 |              <generalspacetype> operator| <optype> D-term
178 | optype ::= primary | quasi-primary | marginal | relevant | irrelevant | four-quark | multi-fermion
179 |          | loop | local | nonlocal | BPS | light-ray | defect | weight-shifting | bounded | unbounded
180 |          | line | surface | half-BPS | 1/<n>-BPS | chiral | non-chiral | Schur | heavy | light
181 |          | higher-spin | continuous-spin
182 | 
183 | field ::= boson| fermion| gauge-field| <n>-form| scalar
184 | 
185 | experiment ::= the LHC | SNO | DAMA | ATLAS | CDMS | Bicep II | the Tevatron | LIGO
186 |              | future e+e- colliders | the Event-Horizon telescope
187 | 
188 | objectplace ::= at the center of the galaxy | in our solar system | on the surface of the sun
189 |               | at the edge of our universe | in the CMB | at <experiment>
190 |               | in the interstellar medium
191 |               | in the early universe | during inflation | after reheating | at the GUT scale
192 |               | at the weak scale | at $\Lambda_{QCD}$ | at the intermediate scale | at the Planck scale
193 |               | at the <horizontype> | at <n> loops | to all orders
194 | 
195 | horizontype ::= de-Sitter horizon | event horizon | apparent horizon | Poincare horizon
196 |               | ergosphere | photon sphere | stretched horizon
197 | 
198 | ######## Model ########
199 | 
200 | model ::= <singmodel> | <pluralmodel>
201 | 
202 | singmodel ::= a model of <physsubject> | a model for <physsubject> | a <physadj> model <modelmodifier>
203 |             | the <propermodel> | the <physadj> <propermodel> | <physadj> <generalmodel>
204 |             | <inflationadj> inflation | <generalmodel> | <generalmodel> | <physicist> <generalmodel>
205 | 
206 | pluralmodel ::= models of <physsubject> | <physadj> models <modelmodifier> | models of <particle>s
207 | 
208 | modelmodifier ::= | of <physsubject> | for <physsubject> | with <particle>s
209 | propermodel ::= Standard Model | MSSM | <nnnn>MSSM | Thirring Model | Ising Model
210 |               | XXZ Model | O(<n>) Model | <physicist> Model | Landau-Ginzburg Model
211 |               | A-model | B-model | SYK Model | SUSY SYK Model | Gross-Neveu Model
212 |               | CP<nzdigit> Model | Schwartzian Theory | BF Theory | Tricritical Ising Model
213 |               | c=1 Matrix Model
214 | nnnn ::= N | N<nnnn>
215 | 
216 | generalmodel ::= gravity | general relativity | RS1 | RS2 | technicolor
217 |                | gauge mediation | anomaly mediation | <properqft>
218 |                | <dynadjective> mechanics | <dynadjective> dynamics | hydrodynamics
219 |                | thermodynamics | unparticle physics
220 | 
221 | dynadjective ::= quantum | <physicist> | <physadj>
222 | 
223 | ######## Adjectives ########
224 | 
225 | physadj ::= <physadj> <physadj> | non-<physadj> 
226 |           | <nondescriptivephysadj> | <descriptivephysadj>
227 |           | <nondescriptivephysadj> | <descriptivephysadj>
228 |           | <nondescriptivephysadj> | <descriptivephysadj>
229 |           | <nondescriptivephysadj> | <descriptivephysadj>
230 |           | <nondescriptivephysadj> | <descriptivephysadj>
231 |           | <nondescriptivephysadj> | <descriptivephysadj>
232 |           | <nondescriptivephysadj> | <descriptivephysadj>
233 | 
234 | nondescriptivephysadj ::=
235 |              seesaw | curvaton | hybrid | quantum | loop | cosmon
236 |            | scalar | <particle> | <physsubject> | isocurvature | <branetype> brane
237 |            | condensate | three-fluid | multi-field | variable mass
238 |            | particle | matrix | lattice | inflaton | bulk | boundary | halo
239 |            | braneworld | GUT | <liegroup> | scalar field | RS 
240 |            | flavor | Landau-Ginzburg | Planck | <physicist> | left-right
241 |            | large-N | parent | QCD | QED | BPS | unparticle | high-scale | low-scale
242 |            | large mass | <limittype> | <limittype> | first-order | second-order
243 | 
244 | descriptivephysadj ::=
245 |              non-gaussian | simple | inflationary | <inflationadj> inflationary
246 |            | exactly-soluble | unified | minimal | quantum | linear | nonlinear
247 |            | gravitational | quantum gravitational | cosmological | supersymmetric
248 |            | holographic | entropic | alternative | nonstandard | multidimensional
249 |            | nonlocal | chiral | phenomenological | nonperturbative | perturbative
250 |            | warped | <n>-dimensional | conformal | modified | supergravity mediated
251 |            | gauge mediated | anomaly mediated | superconformal | extra-ordinary
252 |            | general | anthropic | nilpotent | asymmetric | <symmetry> symmetric
253 |            | <symmetry> invariant | spontaneous | thermodynamic | planar | inertial
254 |            | metastable | unstable | stable | tachyonic | transverse | longitudinal
255 |            | momentum-dependent | exclusive | diffractive | dynamical | effective
256 |            | acoustic | primordial | possible | impossible | calculable | predictive
257 |            | unconventional | macroscopic | microscopic | holomorphic
258 |            | consistent | inconsistent | anomalous | hadronic | leptonic
259 |            | ferromagnetic | singular | nonsingular | leading | subleading
260 |            | higher-order | novel | next-to-leading
261 | 
262 | inflationadj ::= <inflationadj> <inflationadj> | <inflationadj> <inflationadj>
263 |                | <inflationadj> <inflationadj> | <inflationadj> <inflationadj>
264 |                | $D$-Term | anisotropic | asymptotic | brane | braneworld chaotic
265 |                | Brans-Dicke | chaotic | cosmological | de Sitter | double
266 |                | dynamical | elastic | extended | extranatural | F-term | hybrid | false vacuum
267 |                | first-order | general | generalized assisted | higher-curvature | hyper
268 |                | inflatonless | inspired | inverted | K | large-scale | late-time
269 |                | mild | low scale | modular invariant | multi-component | multi-field stochastic
270 |                | multi-field | mutated | natural | new | $\Omega<1$ | assisted | brane-assisted
271 |                | tachyonic | liouville | open | Cobe-Dmr-normalized | D-term | dissipative
272 |                | supersymmetric | eternal | extended | extreme | facilitated | warm
273 |                | generalized | gravitoelectromagnetic | holographic | induced | inhomogeneous
274 |                | intermediate | kinetic | local | mass | moduli | slow-roll | multi-scalar
275 |                | supergravity | natural | boundary | cosmic | dominated | early
276 |                | exact | fake | field line | fresh | gravity driven | induced-gravity
277 |                | intermediate scale | Jordan-Brans-Dicke | large field | locked
278 |                | massive | monopole | multiple | multiple-stage | supergravity
279 |                | non-slow-roll | old | particle physics | pole-like | power-law mass
280 |                | precise | pseudonatural | quasi-open | racetrack | running-mass
281 |                | simple | single scalar | single-bubble | spacetime | noncommutative
282 |                | standard | steady-state | successful | sunergistic | tensor field
283 |                | thermal brane | tilted ghost | topological | tsunami | unified | weak scale
284 |                | noise-induced | one-bubble | open-universe | patch | polynomial | primary
285 |                | quadratic | quintessential | rapid | asymmetric | scalar-tensor
286 |                | non-canonical | smooth | spin-driven | Starobinsky | stochastic
287 |                | string-forming | TeV-scale | three form | topological defect | viable
288 |                | weak-dissipative | nonminimal | oscillating | phantom | power law
289 |                | pre-big-bang | primordial | quantum | R-invariant | running
290 |                | shear-free | rotating | slinky | spinodal | thermal | tidal | tree-level
291 |                | two-stage | anthropic
292 | 
293 | ######## Physicist ########
294 | 
295 | physicist ::= <physicistname> | <physicistname> | <physicistname>-<physicistname> 
296 | physicistname ::=
297 |               Weinberg | Feynman | Witten | Seiberg | Polchinski | Intrilligator
298 |             | Vafa | Randall | Sundrum | Strominger | Georgi | Glashow | Coleman
299 |             | Bohr | Fermi | Heisenberg | Maldacena | Einstein | Kachru | Arkani-Hamed
300 |             | Schwinger | Higgs | Hitchin | Hawking | Stueckelberg | Unruh | Aranov-Bohm
301 |             | 't Hooft | Silverstein | Horava | Lifschitz | Beckenstein | Planck
302 |             | Euler | Lagrange | Maxwell | Boltzmann | Lorentz | Poincare | Susskind
303 |             | Polyakov | Gell-Mann | Penrose | Dyson | Dirac | Argyres | Douglass
304 |             | Gross | Politzer | Cabibo | Kobayashi | Denef | Shenker | Moore
305 |             | Nekrosov | Gaiotto | Motl | Strassler | Klebanov | Nelson | Gubser
306 |             | Verlinde | Bogoliubov | Schwartz
307 | 
308 | ######## Concepts ########
309 | 
310 | mathconcept ::= <singmathconcept> | <pluralmathconcept>
311 | 
312 | singmathconcept ::= integrability | perturbation theory | localization
313 |                   | duality | chaos | <mathadj> structure
314 |                   | dimensionality | <dualtype>-duality | unitarity
315 |                   | representation theory | Clebsch-Gordon decomposition
316 |                   | sheaf cohomology | anomaly matching | semidefinite programming
317 |                   | harmonic analysis | causality
318 | 
319 | pluralmathconcept ::= gerbs | path integrals | Feynman diagrams | <mathadj> structures
320 |               | <physicist>'s equations | conformal blocks
321 |               | <optype> operators | <dualtype>-dualities | <physicist> points | <group> characters
322 |               | central charges | charges | currents | representations | <physicist> conditions
323 |               | symplectic quotients | hyperkahler quotients | Nahm's equations | vortices
324 |               | vortex equations | Hilbert schemes | integration cycles | divisors | line bundles
325 |               | index theorems | flow equations | metrics | Gromov-Witten invariants
326 |               | Gopakumar-Vafa invariants | Donaldson polynomials | type-1 factors
327 |               | Donaldson-Witten invariants | automorphic forms | modular forms | quasimodular forms
328 |               | integrable hierarchies | Kloosterman sums
329 | 
330 | physconcept ::= <pluralphysconcept> | <singphysconcept> | <singphysconcept>
331 | 
332 | pluralphysconcept ::=
333 |                 examples of <physconcept> | equations of <theory> | <n>-point correlators
334 |               | correlators of <optype> operators
335 |               | <symmetry> algebras | fragmentation functions | decay constants | anomaly constraints
336 |               | anomalous dimensions | PDFs | observables | effects of <physconcept> | partition functions
337 |               | <particle> collisions | <physadj> effects | <physadj> parameters | <physadj> hierarchies
338 |               | <physconceptnoun> | <physadj> <physconceptnoun> | amplitudes | scattering amplitudes
339 |               | geometric transitions | <optype> operators | bounds on <physconcept>
340 |               | <physadj> processes | <physadj> events | large logarithms
341 |               | Sudakov logs | soft theorems | quasinormal modes | anomalies | event shapes
342 |               | random tensors | melonic diagrams | BMS supertranslations
343 |               | causality constraints | gravitational waves | constraints on <physconcept>
344 |               | scattering equations | spinning <pluralphysconcept> | fast scramblers
345 |               | crunches | firewalls
346 | 
347 | physconceptnoun ::= sectors | vacua | solutions | states | geometries | currents
348 |                   | backgrounds | wavefunctions | excitations | branching ratios | amplitudes
349 |                   | decays | exotics | corrections | interactions | inhomogeneities
350 |                   | correlation functions | form factors | S-matrix elements | matix elements
351 |                   | remnants
352 |               
353 | singphysconcept ::= <symmviol> <symmetry> invariance | <symmviol> <symmetry> symmetry
354 |                   | <symmetry> symmetry breaking | <mechanism> | confinement | the <physadj> limit
355 |                   | the <physadj> law | the <symmetry> algebra | the beta function
356 |                   | the Wilsonian effective action | the <n>PI effective action
357 |                   | the partition function | <particle> production | black hole evaporation
358 |                   | the effective potential | Hawking radiation
359 |                   | renormalization | regularization | backreaction | AdS/CFT | the partition function
360 |                   | a <physadj> hierarchy | the <physicist> formalism | the <physadj> formalism
361 |                   | <physadj> regularization | the 't Hooft anomaly matching condition
362 |                   | the S-matrix | the <particle> S-matrix | the Hamiltonian | the Lagrangian | the omega deformation
363 |                   | the <physadj> Hilbert space | the Hilbert space | "<singphysconcept>"
364 |                   | <effect> | the OPE | IR behavior | UV behavior | a warped throat
365 |                   | a holographic superconductor | the <particle> charge | the <particle> gyromagnetic ratio
366 |                   | the HRT surface | the <formulaname> formula | a <extended> <formulaname> formula
367 |                   | the <boundname> bound | a <extended> <boundname> bound
368 |                   | bit threads | Tomita-Takesaki theory | the <physicist> equation
369 |                   | the <energycondition> | the <bootstraptype> bootstrap
370 |                   | the entangling surface | the <limittype> limit | analyticity in spin
371 |                   | the crossing equation | <entropytype> | the <entropytype> of <singspace>
372 |                   | complexity | data from <experiment> | the BV formalism | the shadow formalism
373 |                   | the space of <optype> operators | the OPE of <optype> operators
374 |                   | the equivalence principle | gravitational birefringence
375 |                   | a bound on <physconcept> | chaos | the <horizontype> horizon
376 |                   | <moonshinetype> moonshine | <particle> physics | soft radiation
377 |                   | <particle> mixing | <optype> operator mixing | the <physicist> instanton
378 |                   | the Weyl anomaly | p-adic AdS/CFT | <letter>
379 |                   | cosmic censorship | the code subspace | the Hayden-Preskill protocol
380 |                   | the thermofield double | bulk locality | locality
381 |                   | an anomaly | a <soladj> anomaly | a Lifshitz point | a holographic superconductor
382 |                   | a hologram | a double copy of <qft> | the double copy construction
383 |                   | the butterfly effect | black hole complementarity | complementarity
384 | 
385 | entropytype ::= holographic <entropytype> | entropy | von-Neumann entropy | mutual information
386 |               | relative entropy | complexity | entanglement
387 |               | entanglement entropy | entanglement negativity 
388 |               | modular hamiltonian | entanglement of purification | entropy cone
389 | 
390 | extended ::= extended | improved | less-useful | more-useful | modified | generalized | defect | boundary
391 | 
392 | formulaname ::= Ryu-Takayanagi | CHY | Duistermaat-Heckman | Cardy | Lorentzian inversion | Froissart-Gribov
393 | boundname ::= Beckenstein | HKS | Froissart | chaos 
394 | 
395 | bootstraptype ::= conformal | numerical | analytic | lightcone | Regge | modular | sphere-packing
396 |                 | S-matrix | cosmological | hexagon | pentagon | amplitudes | holographic
397 | 
398 | energycondition ::= Average Null Energy Condition | ANEC | Quantum Null Energy Condition | QNEC
399 |                   | Quantum Focusing Conjecture | Null Energy Condition | Dominant Energy Condition
400 |                   | Generalized Second Law 
401 | 
402 | moonshinetype ::= monstrous | umbral | Mathieu | <group>
403 | 
404 | limittype ::= lightcone | Regge | OPE | second-sheet lightcone | multi-Regge | high-energy | low-energy
405 |             | small-angle | long-distance
406 |                   
407 | dualtype ::=T|U|S|magnetic|electric|gravitational|boundary|Seiberg|Geometric Langlands|N=<n>|holographic
408 | 
409 | symmviol ::= | violation of | <physadj> violation of | breaking of
410 | symmetry ::= dilation | translation | rotation | Lorentz | conformal | superconformal
411 |            | super | Poincare | worldsheet | diffeomorphism | superdiffeomorphism | <liegroup>
412 |            | dual-superconformal | Yangian | Virosoro | <nzdigit>-form | higher-form
413 |            | broken <symmetry> | unbroken <symmetry> | spontaneously-broken <symmetry>
414 | 
415 | mechanism ::= the <mechanismadj> mechanism | the <physadj> <mechanismadj> mechanism
416 | mechanismadj ::= Higgs | seesaw | <physicist> | attractor | anomaly inflow | reheating
417 |                | SuperHiggs | confinement
418 | 
419 | effect ::= the <effectadj> effect | the <physadj> <effectadj> effect | <physadj> effects
420 | effectadj ::= <physicist> | quantum Hall | Unruh | Stark | Casimir
421 | 
422 | ######## Subject ########
423 | 
424 | physsubject ::= <singphyssubject> | <pluralphyssubject>
425 | singphyssubject ::=
426 |             quintessence | <inflationadj> inflation | inflation | dark matter | dark energy
427 |           | spacetime foam | instanton gas | <entropytype> | flavor | bubble nucleation
428 | 
429 | pluralphyssubject ::=
430 |             condensates | <branetype> branes | cosmic rays | instanton liquids
431 |           | <physadj> fluctuations | bubbles | tensor networks
432 | 
433 | particle ::= hadron| lepton| quark| neutrino| electron| positron| WIMP|
434 |              slepton| squark| kk graviton| gluon| W-boson| Z-boson| neutralino|
435 |              chargino| ghost| axion| monopole| soliton| dion| kaon| B-meson| pion|
436 |              heavy-ion| Higgs| <particleadj> <particle>| <particleadj> <particle>|
437 |              <particleadj> particle| anyon| magnon| hexaquark
438 | 
439 | particleadj ::= high-energy | soft | prompt | heavy | light | higher-spin | long-lived
440 |               | unstable | stable | relativistic
441 | 
442 | subject ::= <singsubject> | <pluralsubject>
443 | 
444 | pluralsubject ::= <pluralmodel> | <pluraltheoryobj> | <particle>s
445 |           | <pluralphysconcept> in <modeltheory>
446 |           | <pluralmathconcept> in <theory> | <mathadj> <pluralmathconcept>
447 |           | <pluralphysconcept> | <pluraltheory> | <pluralphyssubject> <objectplace>
448 |           | <pluraltheoryobj> <objectplace> | some <specific> <examples> of <subject>
449 |           | <pluralmathconcept> on <space>
450 | 
451 | specific ::= specific | general | little-known | novel
452 | examples ::= cases | examples | investigations | computations | frameworks | paradigms
453 | 
454 | singsubject ::= <singmodel> | <singtheory> | <singtheoryobj> | <problem>
455 |               | <solution> | <studyingverb> <modeltheory>
456 |               | <article> <physadj> <actiondone> of <modeltheory> | <singphysconcept> in <modeltheory>
457 |               | <singmathconcept> in <theory> | <mathadj> <singmathconcept>
458 |               | <singphysconcept> | the <actiondone> of <modeltheory>
459 |               | <article> <actiondone> of <mathconcept> in <modeltheory>
460 |               | the <correspondent>/<correspondent> correspondence
461 |               | <article> <dualtype>-dual of <modeltheory> | <dualtype>-duality in <modeltheory>
462 |               | <singtheoryobj> <objectplace> | <singphyssubject> <objectplace>
463 |               | <singsubject> (<including> <subject>) | <singmathconcept> on <space>
464 |               | <singmathconcept> | a certain notion of <singmathconcept>
465 |               | a <test> of <singsubject> | a <test> of <singsubject> <via> <subject>
466 | 
467 | modeltheory ::= <model> | <theory>
468 | 
469 | including ::= including | excluding | involving | taking into account
470 | 
471 | correspondent ::= <generalmodel> | <propermodel> | <properqft> | <genericqft> | <mathspace>
472 | 
473 | solution ::= <article> solution <solved> | <article> <soladj> solution <solved>
474 |            | <article> solution <solved> <via> <subject>
475 |            | <article> <soladj> solution <solved> <via> <subject>
476 |            | a resolution of <problem> | a <soladj> resolution of <problem>
477 |            | a <soladj> approach to <problem>
478 | solved ::= to <problem> | of <theory>
479 | via ::= via | from | using
480 | soladj ::= better | new | beautiful | quantum | physical | old | clever
481 |          | minimal | non-minimal | <physadj> | anthropic | entropic | possible
482 |          | probable | partial | novel | unexpected
483 | 
484 | problem ::= the <problemtype> problem 
485 | problemtype ::= hierarchy | flavor | cosmological constant | lithium | mu
486 |               | strong CP | naturalness | little hierarchy | SUSY CP | LHC inverse
487 |               | cosmic coincidence | U(1) | fine-tuning | mu/B_mu | confinement
488 |               | black-hole information | typical state
489 | 
490 | ######## Verbs ########
491 | 
492 | verb ::= derive | obtain | deduce | discover | find
493 |        | conjecture | check | calculate | predict | implement
494 | verbed ::= derived | obtained | deduced | discovered | found | conjectured
495 |          | realized | checked | calculated | predicted | implemented
496 | verbs ::= extremizes | maximizes | minimizes | realizes | implements
497 |         | predicts
498 | 
499 | studyverb ::= study | solve | investigate | demystify | bound
500 |             | classify | obtain | derive | generalize | explore
501 |             | examine | consider | analyze | evaluate | review
502 |             | survey | explain | clarify | shed light on
503 |             | extend | construct | reconstruct | calculate | discuss
504 |             | formulate | reformulate | understand
505 | 
506 | studyingverb ::= studying | solving | investigating | demystifying | bounding
507 |                | classifying | obtaining | deriving | generalizing | exploring
508 |                | examining | considering | analyzing | evaluating | reviewing
509 |                | surveying | explaining | clarifying | formulating | reformulating
510 |                | extending | constructing | reconstructing | discussing | understanding
511 | 
512 | studiedverb ::= studied | solved | investigated | demystified | bounded
513 |               | classified | obtained | derived | generalized | explored
514 |               | examined | considered | analyzed | evaluated | reviewed
515 |               | surveyed | recalled | explained | clarified | extended | constructed
516 |               | reconstructed | discussed | understood
517 | 
518 | singbeingverb ::= exists | is present | must be there | must be present | does not exist
519 | 
520 | revealed ::= revealed | produced | led to | led us to | exposed | uncovered
521 | 
522 | singstatementverb ::= is | is equivalent to | is related to | derives from
523 |                       | reduces to | follows from | lets us <studyverb>
524 |                       | can be interpreted as | can be <verbed> from | turns out to be equivalent to
525 |                       | relates to | depends on | <adverb> <singstatementverb>
526 |                       | can be incorporated into | can be brought to bear in <studyingverb>
527 |                       | is useful for <studyingverb> | is the final component in <studyingverb>
528 | 
529 | pluralstatementverb ::= are the same as | are equivalent to | are related to
530 |                       | let us <studyverb> | can compute | follow from | can be interpreted as
531 |                       | can be <verbed> from | turn out to be equivalent to | relate to | depend on
532 |                       | derive from | reduce to | <adverb> <pluralstatementverb>
533 |                       | can be incorporated into | can be brought to bear in <studyingverb>
534 |                       | are useful for <studyingverb> | relate <subject> to
535 | 
536 | yields ::= yields | gives | provides | produces | gives rise to
537 | prove ::= prove | show | demonstrate | establish | illustrate | determine | confirm | verify
538 | 
539 | contradict ::= contradict | disagree with | agree with | find inconsistencies with | argue against
540 |              | run counter to | cannot corroborate | cannot support | challenge | fail to <prove>
541 | 
542 | ######## Language ########
543 | 
544 | capital ::= A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z
545 | 
546 | article ::= a | the
547 | 
548 | adverb ::= remarkably | actually | interestingly | however | moreover | therefore | thus
549 |          | consequently | curiously | fortunately | unfortunately | surprisingly | unsurprisingly
550 |          | quite simply | in short 
551 | 
552 | recently ::= recently | in recent years | in recent papers | over the last decade
553 |            | in the 20th century | among particle physicists | among mathematicians
554 | 
555 | thereby ::= <thereby> <thereby> | thereby | completely | conclusively | wholly
556 |           | thoroughly | fully | ultimately | unambiguously
557 | 
558 | motivated ::= motivated by this | inspired by this | continuing in this vein
559 |             | continuing with this program
560 | 
561 | assuming ::= if | whenever | provided that | supposing that | assuming | assuming that
562 |            | as long as | given that
563 | 
564 | preposition ::= after | before | while | when
565 | whenphrase ::= <preposition> <studyingverb> <subject> 
566 | 
567 | actiondone ::= reduction | compactification | formulation | extension | solution | analytic continuation
568 | 
569 | qualifier ::= at least in the context of <subject> | without regard to <subject>
570 |             | in the approximation that <statement> | in the limit that <statement>
571 |             | as realized in <subject> | as hinted at by <physicist>
572 |             | as revealed by <mathconcept> | by <symmetry> symmetry | by symmetry
573 |             | whenever <statement> | as we will see in this paper | with the help of <subject>
574 |             | as will be made clear | as will be <studiedverb> shortly | in the <singmathconcept> case
575 | 
576 | inorderto ::= to <prove> that <statement> | in order to <prove> that <statement>
577 |             | in order to avoid <studyingverb> <subject> | to best <studyverb> <subject>
578 |             | to <studyverb> <subject> | to <studyverb> recent results linking <subject> and <subject>
579 |             | in a way that <yields> <subject> | to explore questions such as the <singmathconcept> conjecture
580 | 
581 | was ::= has been | was
582 | muchwork ::= much work <was> done | interesting progress <was> made
583 |            | substantial progress has been made | minimal progress <was> made
584 |            | some work <was> done | little work <was> done | a fair amount of work <was> done
585 |            | partial progress <was> made
586 | 
587 | test ::= <computation> | test | probe | measurement | check
588 | computation ::= computation | calculation | determination | prediction | analytical <test> | numerical <test>
589 | correspondence ::= correspondence | conjecture | theorem | result
590 | fact ::= fact | truth | principle | law | theorem | rule | pattern
591 |        | structure | framework | edifice
592 | 
593 | thesame ::= the same | the very same | our very same | our | the exact same | a previously studied
594 | 
595 | beautiful ::= beautiful | surprising | elegant | pretty | arresting | charming
596 |             | simple | ingenious | sophisticated | intricate | elaborate | detailed
597 |             | confusing | bewildering | perplexing | elaborate | involved | complicated
598 |             | startling | unforseen | amazing | extraordinary | remarkable
599 |             | shocking | unexpected | deep | mysterious | profound | unsurprising
600 |             | essential | fundamental | crucial | critical | key | important
601 | 
602 | ######## Statements & Sentences ########
603 | 
604 | statement ::= <singsubject> <singstatementverb> <singsubject> | <pluralsubject> <pluralstatementverb> <subject>
605 |             | <singsubject> is <descriptivephysadj> | <pluralsubject> are <descriptivephysadj>
606 | 
607 | asentence ::= 
608 |     <asentence>, <qualifier>
609 |   | <recently>, <muchwork> on <model>
610 |   | <recently>, <muchwork> <studyingverb> <theory>
611 |   | <recently>, <muchwork> on <model> <inorderto>
612 |   | <recently>, <muchwork> <studyingverb> <theory> <inorderto>
613 |   | <muchwork> <recently> on <model>
614 |   | <muchwork> <recently> <studyingverb> <theory>
615 |   | <recently>, work on <model> has opened up a <descriptivephysadj> class of <physadj> models
616 |   | <recently>, <physicistname> <studiedverb> <subject>
617 |   | <recently>, <physicistname> <verbed> that <statement>
618 |   | <asentence>. we take a <descriptivephysadj> approach
619 |   | <asentence>. <motivated>, <bsentence>
620 |   | <singsubject> offers the possibility of <studyingverb> <subject>
621 |   | <singsubject> <yields> a <beautiful> framework for <studyingverb> <subject>
622 |   | <singsubject> is usually <verbed> <via> <subject>
623 |   | <pluralsubject> are usually <verbed> <via> <subject>
624 | 
625 | bsentence ::=
626 |     <bsentence>, <qualifier>
627 |   | <inorderto>, <bsentence>
628 |   | we <studyverb> <subject>
629 |   | we solve <problem>
630 |   | we take a <descriptivephysadj> approach to <subject>
631 |   | we <prove> that <statement>
632 |   | we <prove> a <beautiful> correspondence between <subject> and <subject>
633 |   | <bsentence>, and <studyverb> <subject>
634 |   | <bsentence>, and <verb> that <statement>
635 |   | <bsentence>, and <verb> that, <qualifier>, <statement>
636 |   | <bsentence>, <thereby> <studyingverb> that <statement>
637 |   | <via> <studyingverb> <pluralmathconcept>, we <studyverb> <subject>
638 |   | <via> <studyingverb> <physconcept>, we <studyverb> <subject>
639 |   | we <verb> evidence for <subject>
640 |   | using the behavior of <singsubject>, we <studyverb> <subject>
641 |   | we present a criterion for <subject>
642 |   | we make contact with <subject>, <adverb> <studyingverb> <subject>
643 |   | we make contact between <subject> and <subject>
644 |   | we <studyverb> why <statement>
645 |   | we use <subject> to <studyverb> <subject>
646 |   | we use <subject>, together with <subject> to <studyverb> <subject>
647 |   | in this paper, <bsentence>
648 | 
649 | csentence ::=
650 |     <csentence>, <qualifier>
651 |   | <motivated>, <bsentence>
652 |   | we take a <descriptivephysadj> approach
653 |   | <adverb>, <statement>
654 |   | next, <bsentence>
655 |   | <singtheory> is also <studiedverb>
656 |   | <pluraltheory> are also <studiedverb>
657 |   | <singmodel> is also <studiedverb>
658 |   | <pluralmodel> are also <studiedverb>
659 |   | <singphysconcept> is also <studiedverb>
660 |   | <pluralphysconcept> are also <studiedverb>
661 |   | we <thereby> <prove> a <beautiful> correspondence between <subject> and <subject>
662 |   | we also <verb> agreement with <subject>
663 |   | the <computation> of <physconcept> localizes to <space>
664 |   | <statement> <assuming> <statement>
665 |   | <subject> <revealed> a <beautiful> <fact>: <statement>
666 |   | <studyingverb> is made easier by <studyingverb> <subject>
667 |   | our <computation> of <subject> <yields> <subject>
668 |   | as an interesting outcome of this work for <subject>, <bsentence>
669 |   | <csentence>, <studyingverb> <subject>
670 |   | <adverb>, <singsubject> <singstatementverb> <thesame> <singmathconcept>
671 |   | we therefore <contradict> a result of <physicistname> that <statement>
672 |   | this probably <singstatementverb> <subject>, though we've been unable to <prove> a <correspondence>
673 |   | this is most likely a result of <physsubject>, an observation first mentioned in work on <subject>
674 |   | this <yields> an extremely precise <test> of <singphysconcept>
675 |   | the <singmathconcept> depends, <adverb>, on whether <statement>
676 |   | a <beautiful> part of this analysis <singstatementverb> <subject>
677 |   | in this <correspondence>, <singsubject> makes a <beautiful> appearance
678 |   | why this happens can be <studiedverb> by <studyingverb> <subject>
679 |   | the title of this article refers to <subject>
680 |   | we <verb> that <singtheoryobj> <singbeingverb> <qualifier>
681 |   | this <correspondence> has long been understood in terms of <subject>
682 | 
683 | dsentence ::=
684 |     <dsentence>, <qualifier>
685 |   | <whenphrase>, we <verb> that <statement> | <statement>
686 |   | <whenphrase>, we <verb> that, <qualifier>, <statement>
687 |   | <dsentence>. <adverb>, <dsentence> | our results <prove> that <statement>
688 | 
689 | closing ::= finally, <bsentence>
690 |           | <adverb>, there is much to be done
691 |           | we hope this paper provides a good starting point for <studyingverb> <subject>
692 |           | we leave the rest for future study
693 |           | <adverb>, <singsubject> is beyond the scope of this paper
694 |           | we will provide more details in a future paper
695 |           | our results are similar to work done by <physicistname>
696 |           | we believe this is indicative of a <beautiful> <fact>
697 |           | given this, our work may seem quite <beautiful>
698 |              
699 | abstract ::= 
700 |     <asentence>. <bsentence>. <csentence>. <dsentence>.
701 |   | <asentence>. <adverb>, <asentence>. <bsentence>. <csentence>. <dsentence>.
702 |   | <asentence>. <bsentence>. <csentence>. <dsentence>. <closing>.
703 |   | <asentence>. <adverb>, <asentence>. <bsentence>. <csentence>. <dsentence>. <closing>.
704 |   | <statement>. <csentence>. <csentence>. <dsentence>.
705 |   | <statement>. <adverb>, <asentence>. <csentence>. <csentence>. <dsentence>.
706 |   | <statement>. <adverb>, <asentence>. <csentence>. <csentence>. <dsentence>. <closing>.
707 |   | <bsentence>. <csentence>. <adverb>, <asentence>. <csentence>. <csentence>. <dsentence>.
708 |   | <bsentence>. <csentence>. <dsentence>. <adverb>, <asentence>. <csentence>. <closing>.
709 | 
710 | title ::= <subject> | <fancytitle> | <fancytitle>
711 | fancytitle ::= <subject> and <subject>
712 |              | <subject> and <subject>
713 |              | <subject> and <subject>
714 |              | <subject>, <subject>, and <subject>
715 |              | from <subject> to <subject>
716 |              | <subject> <verbed> <via> <pluralmathconcept>
717 |              | towards <subject>
718 |              | <subject> <via> <subject>
719 |              | <subject> as <subject>
720 |              | <studyingverb> <subject>
721 |              | <studyingverb> <subject>: <subject>
722 |              | <soladj> approaches to <problem>
723 |              | <pluralsubject> are <descriptivephysadj>
724 |              | <singsubject> <verbs> <singsubject>
725 |              | <studyingverb> <subject>: a <descriptivephysadj> <approach>
726 |              | on <subject>
727 |              | progress in <subject>
728 |              | <subject> <revisited>
729 |              | <remarks> on <subject>
730 |              | <subject> in <subject>
731 |              | <school> lectures on <subject>
732 |              | <subject> vs <subject>
733 |              | <goofytitle>
734 | 
735 | school ::= PIPT | TASI | Cargese | Strings School | CERN Winter School | Jerusalem | Mathematica School
736 | 
737 | goofytitle ::= <nzdigit><zdigit> years of debate with <physicist>
738 |              | reading between the lines of <subject>
739 |              | <physicist> and me
740 |              | the world as <singphysconcept>
741 |              | cool horizons for <pluralphysconcept>
742 |              | <singphysconcept> is not enough
743 |              | the <nzdigit> faces of <singphysconcept>
744 |              | disturbing implications of <singphysconcept>
745 |              | how <physicist> tamed <singphysconcept> from <singspace>
746 |              | invasion of <singphysconcept> from <singspace>
747 |              | trouble for <pluralphysconcept>
748 |              | comment on a proposal by <physicist>
749 |              | some speculations about <physconcept>
750 |              | <singphysconcept> catastrophe
751 | 
752 | approach ::= approach | formalism | method | technique | procedure | conjecture
753 | remarks ::= remarks | comments
754 | revisited ::= revisited | reexamined | reconsidered
755 | 
756 | author ::= <capital>. <physicistname> | <capital>. <capital>. <physicistname>
757 | authors ::= <author> | <author>, <authors>
758 | 
759 | morecomments ::= <smallinteger> figures | JHEP style | Latex file | no figures | BibTeX
760 |                | JHEP3 | typos corrected | <nzdigit> tables | added refs | minor changes
761 |                | minor corrections | published in PRD | reference added | pdflatex
762 |                | based on a talk given on <physicistname>'s <nzdigit>0th birthday
763 |                | talk presented at the international <pluralphysconcept> workshop
764 | comments ::= <smallinteger> pages | <comments>, <morecomments>
765 | 
766 | primarysubj ::= High Energy Physics - Theory (hep-th)| High Energy Physics - Phenomenology (hep-ph)
767 | secondarysubj ::= Nuclear Theory (nucl-th)| Cosmology and Extragalactic Astrophysics (astro-ph.CO)|
768 |              General Relativity and Quantum Cosmology (gr-qc)| Statistical Mechanics (cond-mat.stat-mech)
769 | papersubjects ::= <primarysubj> | <papersubjects>; <secondarysubj>
770 | 
771 | paper ::= <title> \\ <authors> \\ <comments> \\ <papersubjects> \\ <abstract>
772 | 
773 | tweetpaper ::= <authors>: <title>
774 | 


--------------------------------------------------------------------------------
/thm.gram:
--------------------------------------------------------------------------------
  1 | top ::= <theorem> | <theorem> | <theorem> | <theorem>
  2 | #    | <lemma> <theorem> | <theorem> <cor>
  3 | 
  4 | theorem ::= \begin{theorem}[<thname>]<thmstatement>.
  5 |           \end{theorem} \begin{proof} <proof>
  6 |           \end{proof}
  7 | 
  8 | # these don't seem that convincing at the moment
  9 | # lemma ::= \begin{lemma}<thmstatement>.
 10 | #          \end{lemma} \begin{proof} <proof>
 11 | #          \end{proof}
 12 | #
 13 | # cor ::= \begin{cor}<thmstatement>.\end{cor}
 14 | 
 15 | proof ::= <statement>. <conclusion>. | See <citation>.
 16 |     | <statement>. <conclusion>. | <statement>. <conclusion>.
 17 | 
 18 | conclusion ::= 
 19 |     The result follows by d\'evissage | The theorem follows trivially
 20 |     | The conclusion is self-evident | Clearly, the theorem holds
 21 |     | We leave the rest as an exercise | This is the desired result
 22 |     | The rest follows from <citation> | QED
 23 |     | A simple application of <famoustheorem> completes the proof
 24 | 
 25 | famoustheorem ::=
 26 |     <mathguy>'s theorem
 27 |     | Hilbert's problem <nzdigit><zdigit>
 28 |     | the Riemann Hypothesis
 29 |     | Perelman's theorem (formerly the Poincar\'e Conjecture)
 30 |     | horizontal Iwasawa theory | Kummer theory | the different
 31 |     | Dynkin diagrams | Gegenbauer polynomials
 32 |     | trichotomy
 33 | 
 34 | thmstatement ::=
 35 |     <subject> <connection> <claim>
 36 |     | If <claim> then <claim>
 37 | 
 38 | thname ::=
 39 |     The <mathguypart> <mathnoun> <theoremtype>
 40 |     | <mathguy>'s <modifier> <mathnoun> <theoremtype>
 41 |     | The <modifier> <mathnoun> <theoremtype>
 42 | 
 43 | mathguypart ::= <mathguy> | <mathguy>-<mathguypart>
 44 | 
 45 | mathguy ::=
 46 |     Weierstrass | Thurston | K\"och | Kronecker | Lagrange | Cramer
 47 |     | Gauss | Euler | Euclid | Mazur | Elkies | Zorn | Bowditch
 48 |     | Russell | Cantor | Godel | de Moivre | Galois | Schwarz | Erd\H{o}s
 49 |     | Laplace | Boltzmann | Kantorovich | Abel | Poincar\'e | Peano
 50 |     | Riemann | Stokes | Lebesgue | Lipschitz | Bunyakovsky | Fermat
 51 |     | Urys\"ohn | Arzela | Ascoli | Ramanujan | Wiles | Lobachevsky
 52 |     | Sokhotskii | Bertrand | Fubini | Frobenius | Dynkin | Bieberbach
 53 |     | Gegenbauer | Swinnerton-Dyer | Stone | Pythagoras
 54 | 
 55 | bookadj ::=
 56 |     Algebraic | Geometric | Complex | Metrizable | Analytic | Non-Standard
 57 |     | <bookadj> <bookadj> | Advanced <bookadj> | Non-Metrizable
 58 | 
 59 | booksubj ::=
 60 |     Number Theory | Topology | Analysis | Algebra | Manifolds | K-Theory
 61 |     | Constructions
 62 | 
 63 | booktitle ::=
 64 |     <mathguy>'s {\it <bookadj> <booksubj>}
 65 |     | <mathguy>'s {\it <bookadj> <booksubj>}, <ordinal> Edition
 66 |     | <mathguy> and <mathguy>'s {\it <bookadj> <booksubj>}   
 67 |     | [<nzdigit>] | [<mathguy>]
 68 |     | {\it <bookadj> <booksubj> Revisited}
 69 |     | <mathguy>'s {\it <booksubj> Revisited}
 70 |     
 71 | citation ::= <booktitle> | <booktitle>, page <biginteger> |
 72 |     <booktitle>, <bookthmtype> <smallinteger>
 73 |     | <booktitle>, <bookthmtype> <nzdigit>.<nzdigit>.<nzdigit>
 74 | 
 75 | modifier ::=
 76 |     first | second | third | implicit | inverse | normalizable | last
 77 |     | mean | average
 78 | 
 79 | ordinal ::= 1st | 2nd | 3rd | 4th
 80 | 
 81 | mathnoun ::=
 82 |     openness | completeness | function | isomorphism | diffeomorphism
 83 |     | homeomorphism | linearity | orthogonality | dimensionality 
 84 |     | diagonalizability | symmetry | discreteness | asymmetry | boundary
 85 |     | value | covering | inequality | category | compactness | mapping 
 86 |     | contraction | metrization | quantization | multiplier
 87 | 
 88 | bookthmtype ::=
 89 |     Theorem | Lemma | Corollary | Proposition | Definition | Exercise
 90 | 
 91 | theoremtype ::=
 92 |     theorem | lemma | conjecture | hypothesis
 93 | 			    
 94 | subject ::=
 95 |     <prefix> <vobject>, | <prefix> <cobject>, | <statement>. then
 96 |     | <prefix> <variable> <comparison> <constant>,
 97 | 
 98 | statement ::=
 99 |     let <variable> be a <cobject>
100 |     | let <variable> be an <vobject>
101 |     | suppose <variable> is a <cobject>
102 |     | suppose <variable> is an <vobject>
103 |     | suppose <variable> is a <cobject> and <statement>
104 |     | suppose <variable> is an <vobject> and <statement>
105 | 
106 | thing ::=
107 |     a <cobject> | an <vobject> | <variable> <comparison> <constant>
108 |     | <thing> and <thing> | a unique <cobject> | a unique <vobject>
109 | 
110 | ergo ::= therefore | now | hence | consequently | thus | ergo
111 | 
112 | connection ::= 
113 |     there exists <thing> such that | if <claim> then
114 | 
115 | prefix ::=
116 |     given some | given any | for any | for every | for an arbitrary
117 | 
118 | cobject ::= 
119 |     vector <variable> | tensor <variable> | <cspacemodifier> <setbit>
120 |     | <csequencemodifier> <seriesbit> | <cfunctionmodifier> <afunction>
121 |     | <afunction> <funname> of <variable>
122 | 
123 | funname ::= $<texfun>$
124 | 
125 | texfun ::= \zeta | \Gamma | p | f | g | y | h | y' | f' | \xi | f^{-1}
126 |     | \phi | \psi
127 | 
128 | vobject ::=
129 |     <vspacemodifier> <setbit> | <vsequencemodifier> <seriesbit>
130 |     | <vfunctionmodifier> <afunction>
131 |     
132 | setbit ::= 
133 |     subspace of <field> | vector space over <field> | subset of <field>
134 |     | group in <field> | manifold locally resembling <field>
135 |     | polytope in <field> | tangent space of <field> at <variable>
136 |     | irreducible representation of <field>
137 |     | <nzdigit>-dimensional Riemann surface
138 | 
139 | seriesbit ::=
140 |     series in <field> | series | sequence in <field> | sequence
141 | 
142 | cspacemodifier ::=
143 |     bounded | non-empty | closed | compact | trivial | non-trivial
144 |     | connected | disjoint | finite | discrete | Euclidean
145 | 
146 | vspacemodifier ::= 
147 |     open | unbounded | infinite | isotropic
148 | 
149 | csequencemodifier ::= 
150 |     convergent | divergent | bounded | finite | Cauchy | square-summable
151 | 
152 | vsequencemodifier ::= 
153 |     infinite | alternating | unbounded | absolutely convergent
154 | 
155 | vfunctionmodifier ::= 
156 |     even | odd | antisymmetric | integrable
157 | 
158 | cfunctionmodifier ::= 
159 |     continuous | smooth | differentiable | positive | negative
160 |     | non-degenerate | skew-symmetric | linear | multilinear | nonlinear
161 |     | differential | quadratic | symmetric | positive-definite | bilinear
162 |     | sesquilinear | piecewise <cfunctionmodifier>
163 | 
164 | variable ::= 
165 |     $\lambda$ | $\alpha$ | $\beta$ | $\gamma$ | $\epsilon$ | $\delta$
166 |     | $\mu$ | $\rho$ | $\nu$ | $\psi$ | $a_n$ | $x_n$ | $x_i$ | $\theta$
167 |     | $v$ | $u$ | $w$ | $x$ | $y$ | $z$ | $b$ | $\omega$ | $\phi$
168 | 
169 | nzdigit ::= 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
170 | zdigit ::=  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
171 | 
172 | smallinteger ::= <nzdigit> | <nzdigit> | <nzdigit><zdigit>
173 | biginteger ::= <zdigit> | <nzdigit><biginteger>
174 | pninteger ::= 0 | <smallinteger> | $-<smallinteger>$
175 | 
176 | constant ::= 
177 |      $\pi$ | $e$ | $\kappa$ | $0$ | $1$ | $\epsilon$ | $\delta$ | <pninteger>
178 | 
179 | texfield ::=
180 |     \Z | \Q | \R | \C | \Q_p | \Z/p\Z | \mathbb{H}
181 | 
182 | texgroup ::=
183 |    <texfield> | <texfield>^<n> | H | G
184 | 
185 | n ::=
186 |     n | n | <nzdigit> | m
187 | 
188 | field ::= 
189 |     $<texfield>$ | $<texgroup>$ | $<texgroup>$
190 |     | $\mathcal{C}(<texfield>)$ | $<texfield>[x]$
191 |     | $\mathrm{GL}_<n>(<texfield>)$
192 |     | $\mathrm{SU}(<nzdigit>)$
193 |     | $\mathrm{M}_n(<texfield>)$
194 |     | $\mathrm{Hom}(<texgroup>,<texgroup>)$
195 |     | $\mathrm{Ker}(T)$
196 |     | $H^<n>(<texgroup>,<texgroup>)$
197 |     | $<texgroup> \otimes <texgroup>$
198 |     | the $p$-adics | $\mathrm{Im}(T)$ | $\mathrm{Ker}(\phi)$
199 | 
200 | comparison ::= $\lt$ | $\gt$ | $\geq$ | $\leq$
201 | 
202 | claim ::= 
203 |     <claimstart> an <vspacemodifier> <setbit> <spaceaction>
204 |     | <claimstart> a <cspacemodifier> <setbit> <spaceaction>
205 |     | <claimstart> a <cfunctionmodifier> <afunction> <funcaction>
206 |     | <claimstart> an <vfunctionmodifier> <afunction> <funcaction>
207 |     | <claimstart> a <csequencemodifier> <seriesbit> <seriesaction>
208 |     | <claimstart> an <vsequencemodifier> <seriesbit> <seriesaction>
209 |     | <claimstart> some vector <variable> <vecaction>
210 |     | <funname> is a well-defined <mapping> from <field> to <field>
211 |     | the following diagram commutes: <commdiagram>
212 |     | the sequence \begin{eqnarray}<texexactsequence>\end{eqnarray} is exact
213 | 
214 | commdiagram ::= 
215 |     \begin{eqnarray}<heightonediagram>\end{eqnarray}
216 |     | \begin{eqnarray}<heightonediagram>\end{eqnarray}
217 |     | \begin{eqnarray}<heighttwodiagram>\end{eqnarray}
218 | 
219 | heightonediagram ::= <onediagleft><onediagmiddle><onediagright>
220 |     
221 | onediagleft ::= \onebyone<fourgroups><fourfuns> | \onebyone<fourgroups><fourfuns>
222 |     | \oneldots\rightaddone{<texfun>}{<texgroup>}{<texfun>}{<texfun>}{<texgroup>}
223 | 
224 | onediagright ::=
225 |     \nothing
226 |     | \rightaddone{<texfun>}{<texgroup>}{<texfun>}{<texfun>}{<texgroup>}
227 |     | \rightaddonedots{<texfun>}{<texfun>}
228 | 
229 | onediagmiddle ::=
230 |     \rightaddone{<texfun>}{<texgroup>}{<texfun>}{<texfun>}{<texgroup>}
231 |     | \nothing
232 |     | \rightaddone{<texfun>}{<texgroup>}{<texfun>}{<texfun>}{<texgroup>}<onediagmiddle>
233 | 
234 | heighttwodiagram ::= <twodiagleft><twodiagmiddle><twodiagright>
235 | 
236 | twodiagleft ::=
237 |      \begin{diagram}
238 |        \squarecode<fourgroups><fourfuns>
239 |        \bottomadd{<texfun>}{<texfun>}{<texgroup>}{<texfun>}{<texgroup>}
240 |      \end{diagram}
241 |     | \begin{diagram}
242 |        \squarecode<fourgroups><fourfuns>
243 |        \bottomadd{<texfun>}{<texfun>}{<texgroup>}{<texfun>}{<texgroup>}
244 |       \end{diagram}
245 |     | \twoldots\rightaddtwo{<texfun>}{<texgroup>}{<texfun>}{<texfun>}{<texgroup>}
246 |                            {<texfun>}{<texfun>}{<texgroup>}
247 | 
248 | twodiagmiddle ::=
249 |     \nothing
250 |     | \rightaddtwo{<texfun>}{<texgroup>}{<texfun>}{<texfun>}{<texgroup>}
251 |                    {<texfun>}{<texfun>}{<texgroup>}
252 |     | \rightaddtwo{<texfun>}{<texgroup>}{<texfun>}{<texfun>}{<texgroup>}
253 |                    {<texfun>}{<texfun>}{<texgroup>}<twodiagmiddle>
254 | 
255 | twodiagright ::=
256 |     \nothing
257 |     | \rightaddtwo{<texfun>}{<texgroup>}{<texfun>}{<texfun>}{<texgroup>}
258 |                    {<texfun>}{<texfun>}{<texgroup>}
259 |     | \rightaddtwodots{<texfun>}{<texfun>}{<texfun>}
260 | 
261 | fourgroups ::= {<texgroup>}{<texgroup>}{<texgroup>}{<texgroup>}
262 | fourfuns ::= {<texfun>}{<texfun>}{<texfun>}{<texfun>}
263 | 
264 | texexactsequence ::= <texgroup> \rTo^{<texfun>} <texseqmid>
265 |     | 0 \rTo <texseqmid> | \dots \rTo <texgroup> \rTo^{<texfun>}
266 |      <texgroup> \rTo^{<texfun>} <texseqmid>
267 | 
268 | texseqmid ::= <texgroup> \rTo <texseqend>
269 | 	| <texgroup> \rTo^{<texfun>} <texseqend>
270 | 
271 | texseqend ::= <texgroup> | <texgroup> \rTo 0 
272 |     | <texgroup> \rTo^{<texfun>} <texgroup> \rTo \dots 
273 |     | <texgroup> \rTo^{<texfun>} <texseqend>
274 |     | <texgroup> \rTo^{<texfun>} <texseqend>
275 | 
276 | mapping ::=
277 |     function | mapping | homomorphism | homeomorphism | isomorphism
278 |     | surjective <mapping> | injective <mapping> | holomorphism
279 |     | biholomorphism | isometry
280 |   
281 | claimstart ::= there is | we can construct
282 | 
283 | spaceaction ::= 
284 |     isomorphic to <field> | contained within <field> | containing <thing>
285 |     | diffeomorphic to <field> | homeomorphic to a <setbit>
286 |     | in the <intersection> | not in the <intersection>
287 | 
288 | funcaction ::= 
289 |     that diverges | whose <alimit> is <constant> | that is Lipschitz
290 | 
291 | seriesaction ::= 
292 |     that diverges | that converges to <constant> | that contains <constant>
293 |     | whose terms are all <comparison> <constant> | containing <thing>
294 | 
295 | vecaction ::= 
296 |     contained within <field> | not in the <intersection>
297 |     | in the <intersection>
298 | 
299 | alimit ::= limit as <variable> approaches <constant>
300 | 
301 | intersection ::= 
302 |     intersection of <field> and <field> | union of <field> with <field>
303 |     | quotient of <field> and <field>
304 | 
305 | afunction ::= $k$-form | function | mapping | transformation | relation
306 | 	| form
307 | 


--------------------------------------------------------------------------------
/thmheader.tex:
--------------------------------------------------------------------------------
 1 | \documentclass{article}
 2 | \usepackage{amsthm}
 3 | \usepackage{amssymb}
 4 | \usepackage{diagrams}
 5 | \pagestyle{empty}
 6 | \setlength\textwidth{3.9in}
 7 | 
 8 | \newtheorem*{theorem}{Theorem}
 9 | \newcommand\Z{\mathbb{Z}}
10 | \newcommand\Q{\mathbb{Q}}
11 | \newcommand\R{\mathbb{R}}
12 | \newcommand\C{\mathbb{C}}
13 | \newcommand\lt{<}
14 | \newcommand\gt{>}
15 | \newcommand\squarecode[8]{
16 |       #1        & \rTo^{#5} & #2       \\
17 |       \dTo^{#6} &           & \dTo^{#7}\\
18 |       #3        & \rTo^{#8} & #4\\
19 | }
20 | \newcommand\bottomadd[5]{
21 | \dTo^{#1} & & \dTo^{#2}\\
22 | #3 & \rTo^{#4} & #5\\
23 | }
24 | \newcommand\onebyone[8]{
25 | \begin{diagram}
26 | \squarecode{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}
27 | \end{diagram}
28 | }
29 | \newcommand\nothing{}
30 | \newcommand\oneldots{
31 | \begin{diagram}
32 | \cdots\\
33 | \\
34 | \cdots\\
35 | \end{diagram}
36 | }
37 | \newcommand\twoldots{
38 | \begin{diagram}
39 | \cdots\\
40 | \\
41 | \cdots\\
42 | \\
43 | \cdots\\
44 | \end{diagram}
45 | }
46 | \newcommand\threeldots{
47 | \begin{diagram}
48 | \cdots\\
49 | \\
50 | \cdots\\
51 | \\
52 | \cdots\\
53 | \\
54 | \cdots\\
55 | \end{diagram}
56 | }
57 | \newcommand\rightonearrow[2]{
58 | &\rTo^{#1} & #2\\
59 | }
60 | \newcommand\bottomrightadd[3]{
61 | & & \dTo^{#1}\\
62 | & \rTo^{#2} & #3\\
63 | }
64 | \newcommand\rightaddone[5]{
65 | \begin{diagram}
66 | \rightonearrow{#1}{#2}
67 | \bottomrightadd{#3}{#4}{#5}
68 | \end{diagram}
69 | }
70 | \newcommand\rightaddtwo[8]{
71 | \begin{diagram}
72 | \rightonearrow{#1}{#2}
73 | \bottomrightadd{#3}{#4}{#5}
74 | \bottomrightadd{#6}{#7}{#8}
75 | \end{diagram}
76 | }
77 | \newcommand\rightaddonedots[2]{
78 | \begin{diagram}
79 | &\rTo^{#1}&\cdots\\
80 | & & &\\
81 | & \rTo^{#2} & \cdots\\
82 | \end{diagram}
83 | }
84 | \newcommand\rightaddtwodots[3]{
85 | \begin{diagram}
86 | &\rTo^{#1}&\cdots\\
87 | & & &\\
88 | & \rTo^{#2} & \cdots\\
89 | & & &\\
90 | & \rTo^{#3} & \cdots\\
91 | \end{diagram}
92 | }
93 | 


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