History of Satisfiability thresholds of random $k$-XORSAT

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2026-09-16 12:25 zeta3 table-repair@1.108+e1dcbafe repair critique: keep threshold definition concise current reviewed
2026-09-16 12:24 zeta3 table-repair@1.108+e1dcbafe repair critique: shorten definition after audit
2026-09-16 12:23 zeta3 table-repair@1.108+e1dcbafe repair critique: clarify threshold prose and comments
2026-09-16 12:11 zeta3 table-build@1.125+52322b0c address audit findings on definition and tags
2026-09-16 12:10 zeta3 table-build@1.125+52322b0c address audit findings on definition and tags
2026-09-16 12:09 zeta3 table-build@1.125+52322b0c address audit findings on definition and tags
2026-09-16 12:07 zeta3 with codex-cli table-build@1.125+52322b0c random k-XORSAT satisfiability thresholds alpha_k for 3 <= k <= 12, with the defining root enclosed in ball arithmetic
2026-09-16 12:03 zeta3 table-build@1.125+52322b0c created this table

What changed between 2026-09-16 12:03 and 2026-09-16 12:07

from line 98 (53 lines, 51 more than before) @@ -98,2 +98,53 @@
 Display properties:   number-header: $\alpha_k$+Numbers:+- params:+    k: '3'+  number: '0.9179352766580860135154412282330241295566462813786741119388567679432894341028061252100137350717952174'+  comment: The root is $\xi_{3}=2.14912579991$; Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this threshold as $0.9179352767$ to ten decimal+    places CITE{DGMMPR}.+- params:+    k: '4'+  number: '0.9767701648780461315596453315801681767089324117092366344477820171954417168938976107089484319269740715'+  comment: The root is $\xi_{4}=3.59351196945$; Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this threshold as $0.9767701649$ to ten decimal+    places CITE{DGMMPR}.+- params:+    k: '5'+  number: '0.9924383912621006266589799793323504474696379410861973127564646960469684573473547755463108213196347197'+  comment: The root is $\xi_{5}=4.80100754972$; Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this threshold as $0.9924383913$ to ten decimal+    places CITE{DGMMPR}.+- params:+    k: '6'+  number: '0.9973795527786723480335298422727171806947578778455543989561183255629649006299375198226788332339351435'+  comment: The root is $\xi_{6}=5.90300005895$; Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this threshold as $0.9973795528$ to ten decimal+    places CITE{DGMMPR}.+- params:+    k: '7'+  number: '0.9990637587536802554886204642246230679289335411670661479087836641414840208770255075157509128677423698'+  comment: The root is $\xi_{7}=6.95345571335$; Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this threshold as $0.9990637588$ to ten decimal+    places CITE{DGMMPR}.+- params:+    k: '8'+  number: '0.9996603987428638243814171691235945492361531052227223433740666229649241363721042964687963886298818589'+  comment: The root is $\xi_{8}=7.97810773698$.+- params:+    k: '9'+  number: '0.9998758980601650313509133871165240775778498642763184195380306052968600407828001914487458328743244041'+  comment: The root is $\xi_{9}=8.98991251927$.+- params:+    k: '10'+  number: '0.9999544861999791689002330696779352200131085165458282053982667948233340350833028799898216722898518400'+  comment: The root is $\xi_{10}=9.99544113381$.+- params:+    k: '11'+  number: '0.9999832798521640659649313526046903579198515250526178277676080828819870320558190962324726668561837885'+  comment: The root is $\xi_{11}=10.9979753372$.+- params:+    k: '12'+  number: '0.9999938528404832018983826756900406615708068784861080583270032085169228297637417460919200515828429412'+  comment: The root is $\xi_{12}=11.9991145095$. 

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