Content-Type: multipart/mixed; boundary="-------------0409020854391" This is a multi-part message in MIME format. ---------------0409020854391 Content-Type: text/plain; name="04-272.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-272.comments" Later versions of this paper may be obtained from http://www.ma.utexas.edu/users/radin/papers.html ---------------0409020854391 Content-Type: text/plain; name="04-272.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-272.keywords" hard sphere gas, densest packing, sphere packing ---------------0409020854391 Content-Type: application/postscript; name="text13.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="text13.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: text13.dvi %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMBX10 CMR10 CMMI10 CMSY10 MSBM10 CMR7 CMMI7 CMEX10 %%+ 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 56 /bracelefttp put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 62 /braceex put dup 90 /integraldisplay put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 113 /radicalBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0 ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{ pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type /nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[ exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if} forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def end %%EndProcSet %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F C0962EAC6E3EBFB8AD256A3C654EAAF9A50C51BC6FA90B61B60401C235AFAB7B B078D20B4B8A6D7F0300CF694E6956FF9C29C84FCC5C9E8890AA56B1BC60E868 DA8488AC4435E6B5CE34EA88E904D5C978514D7E476BF8971D419363125D4811 4D886EDDDCDDA8A6B0FDA5CF0603EA9FA5D4393BEBB26E1AB11C2D74FFA6FEE3 FAFBC6F05B801C1C3276B11080F5023902B56593F3F6B1F37997038F36B9E3AB 76C2E97E1F492D27A8E99F3E947A47166D0D0D063E4E6A9B535DC9F1BED129C5 123775D5D68787A58C93009FD5DA55B19511B95168C83429BD2D878207C39770 012318EA7AA39900C97B9D3859E3D0B04750B8390BF1F1BC29DC22BCAD50ECC6 A3C633D0937A59E859E5185AF9F56704708D5F1C50F78F43DFAC43C4E7DC9413 44CEFE43279AFD3C167C942889A352F2FF806C2FF8B3EB4908D50778AA58CFFC 4D1B14597A06A994ED8414BBE8B26E74D49F6CF54176B7297CDA112A69518050 01337CBA5478EB984CDD22020DAED9CA8311C33FBCC84177F5CE870E709FC608 D28B3A7208EFF72988C136142CE79B4E9C7B3FE588E9824ABC6F04D141E589B3 914A73A42801305439862414F893D5B6C327A7EE2730DEDE6A1597B09C258F05 261BC634F64C9F8477CD51634BA648FC70F659C90DC042C0D6B68CD1DF36D615 24F362B85A58D65A8E6DFD583EF9A79A428F2390A0B5398EEB78F4B5A89D9AD2 A517E0361749554ABD6547072398FFDD863E40501C316F28FDDF8B550FF8D663 9843D0BEA42289F85BD844891DB42EC7C51229D33EE7E83B1290404C799B8E8C 889787CDC194F782420BB447DE705EAE7963391B36646500230A4D818B2F649D 775E07F189F805EDAE3A866E68C96EBDD976A7002D4001BC5F88B6E81BBDABEA 10E2A15412E997BC14204A492AB6D00544D4F2C9FF8FA2294D8F6C67D3A259ED 9B824F51E86565443C9F7866AF9B50FFBCB342063DAD42972069CC6926D92341 4A495C8849486563D3B2E6C69B8CB0577E2B529FBE5099D97ED20A8B9EA990BD F83EC6A531E1DDBE7BD7129AC5F5558433C24F2233E4EEF897E1A4ECE91FAA65 CE37056B3B8F13B14579340937CDF5FB3349F853FC17FAB0DC0F89F7C1A15E9F F3F327E9987E0923D29B3F02A190F08FF368907F3F9DB8F066707FA411FC0F23 7D8352158F7ED750CF0BC6EAE21B366EADD586517E82138B165434D99DB7429E 3947CC3AAA64D15D8FC913A57CBF922A1EC61CD8BDCDB28C98A0972C17BBDB3D 6F462ACBFBA98A6AD1688AAAEF38EBAF4290F2B1120A12CFFCA84D68872BE1D6 7D993BF215F5CA2E65DBFBA53BA6D00B53FF4CC6D4024D525C7B959BD306A29A A8AE621F414C6FA546C91EF52BE12214 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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y(6)p eop end %%Page: 7 8 TeXDict begin 7 7 bop 150 100 a Fk(p)s(erturbations)27 b(obtained)h(b)m(y)f(lo)s(osening)f(isolated)h(pairs)g(of)g(neigh)m(b)s (oring)g(spheres)i(from)e(their)150 219 y(lattice)k(p)s(ositions.)43 b(Clearly)31 b(the)h(latter)e(is)i(our)g(only)f(non)m(trivial)f (assumption.)45 b(Our)32 b(result)g(is)150 339 y(that)h(p)s (erturbations)i(of)f(the)g(HCP)f(structure)i(ha)m(v)m(e)f(the)g (largest)f(en)m(trop)m(y)-8 b(,)34 b(in)g(con)m(tradiction)150 458 y(with)c([9])g(in)h(whic)m(h)h(it)e(is)h(claimed)f(that)h(the)g (con)m(tributions)g(from)g(nearest)h(neigh)m(b)s(or)f(spheres)150 578 y(alone)i(yields)g(a)g(preference)j(for)d(F)m(CC.)150 817 y Fl(IV.)38 b(References)194 1057 y Fk([1])49 b(J.A.)31 b(Bark)m(er,)h Fb(L)-5 b(attic)g(e)34 b(The)-5 b(ories)33 b(of)h(the)h(Liquid)f(State)p Fk(,)e(Macmillan,)f(New)h(Y)-8 b(ork,)31 b(1963.)194 1176 y([2])49 b(H.N.V.)44 b(T)-8 b(emp)s(erley)g(,)49 b(J.S.)d(Ro)m(wlinson)g(and)h(G.S.)f(Rush)m(bro)s (ok)m(e,)k 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