History of Roots of the $k$-XORSAT threshold equation

     of random $k$-XORSAT]   relation: thresholds obtained from these roots by the formula for $\alpha_k$-- table: HREF{T274}[Cuckoo hashing thresholds of random $k$-uniform hypergraphs]-  relation: the auxiliary roots $\xi_{k,\ell}$ used to compute those thresholds reduce-    to $\xi_k$ at bucket capacity $\ell=1$+- table: HREF{T288}[Roots of the cuckoo hashing threshold equation]+  relation: the same roots in the rows with bucket capacity $\ell=1$ and $k\geq3$ Links:   WikiXORSAT:

   - CITE{PittelSorkin}   complete: 'no'-  complete-note: it holds $\xi_k$ for every $k$ with $3\leq k\leq12$, matching the-    companion satisfiability-threshold table+  complete-note: it holds $\xi_k$ for every $k$ with $3\leq k\leq12$, the range of+    HREF{Satisfiability_thresholds_of_random_k-XORSAT}[the satisfiability thresholds+    $\alpha_k$]; at the end of this range, $0<12-\xi_{12}<10^{-3}$   rigour details: Each entry is computed in ball arithmetic with 64 guard bits beyond     the 100 digits written. The root $\xi_k$ is enclosed by bisection on the sign

   number-header: $\xi_k$ Numbers:-  '3':-    number: '2.149125799907062542079080149425149925528828496714285459034660801183768221524370129087681616217046728'-    comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#3}[$\alpha_{3}$].-  '4':-    number: '3.593511969447426082272169884555315798860946340951301392760865045230967927293167350976509334752600022'-    comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#4}[$\alpha_{4}$].-  '5':-    number: '4.801007549722517843402554184936876206309580045670987737307642940448096932959992199826971793616174495'-    comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#5}[$\alpha_{5}$].-  '6':-    number: '5.903000058948943810458175385422799724242893481515842146827627134583507853576375177519654679441566068'-    comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#6}[$\alpha_{6}$].-  '7':-    number: '6.953455713353474571757750459668776777157703675694193843415968941936946472738479953900380174362202268'-    comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#7}[$\alpha_{7}$].-  '8':-    number: '7.978107736977070325801043211904953879262698393828180241246253405412112875926606187603354958634672340'-    comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#8}[$\alpha_{8}$].-  '9':-    number: '8.989912519269479737859486962678439859820876867181214191191759058921700750894868987723157685967200046'-    comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#9}[$\alpha_{9}$].-  '10':-    number: '9.995441133814842741400932592133052045659869599058257396947103091116896080275781481170753765750751443'-    comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#10}[$\alpha_{10}$].-  '11':-    number: '10.99797533724523459964809795243574469075450093882819090308597431902540854000078754311674399450335085'-    comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#11}[$\alpha_{11}$].-  '12':-    number: '11.99911450952184187994188030867116719218749935503081985334373686869595954724308587188802621404555431'-    comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#12}[$\alpha_{12}$].+- params:+    k: '3'+  number: '2.149125799907062542079080149425149925528828496714285459034660801183768221524370129087681616217046728'+  comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#3}[$\alpha_{3}$].+- params:+    k: '4'+  number: '3.593511969447426082272169884555315798860946340951301392760865045230967927293167350976509334752600022'+  comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#4}[$\alpha_{4}$].+- params:+    k: '5'+  number: '4.801007549722517843402554184936876206309580045670987737307642940448096932959992199826971793616174495'+  comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#5}[$\alpha_{5}$].+- params:+    k: '6'+  number: '5.903000058948943810458175385422799724242893481515842146827627134583507853576375177519654679441566068'+  comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#6}[$\alpha_{6}$].+- params:+    k: '7'+  number: '6.953455713353474571757750459668776777157703675694193843415968941936946472738479953900380174362202268'+  comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#7}[$\alpha_{7}$].+- params:+    k: '8'+  number: '7.978107736977070325801043211904953879262698393828180241246253405412112875926606187603354958634672340'+  comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#8}[$\alpha_{8}$].+- params:+    k: '9'+  number: '8.989912519269479737859486962678439859820876867181214191191759058921700750894868987723157685967200046'+  comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#9}[$\alpha_{9}$].+- params:+    k: '10'+  number: '9.995441133814842741400932592133052045659869599058257396947103091116896080275781481170753765750751443'+  comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#10}[$\alpha_{10}$].+- params:+    k: '11'+  number: '10.99797533724523459964809795243574469075450093882819090308597431902540854000078754311674399450335085'+  comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#11}[$\alpha_{11}$].+- params:+    k: '12'+  number: '11.99911450952184187994188030867116719218749935503081985334373686869595954724308587188802621404555431'+  comment: The associated satisfiability threshold is HREF{Satisfiability_thresholds_of_random_k-XORSAT#12}[$\alpha_{12}$].