History of Minimisers in the core threshold formula of random $k$-uniform hypergraphs

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2026-09-19 18:27 zeta3 shorten graph-case minimiser definition current reviewed
2026-09-19 18:26 zeta3 with codex-cli added graph-case minimisers lambda_{2,r} for 3 <= r <= 12
2026-09-19 18:25 zeta3 include graph-case minimisers
2026-09-17 03:28 zeta3 table-repair@1.109+64cc4f29 clarify the core-threshold minimiser prose
2026-09-17 03:15 zeta3 table-build@1.130+3450381c state minimiser uniqueness and graph-core check
2026-09-17 03:14 zeta3 table-build@1.130+3450381c state minimiser uniqueness and graph-core check
2026-09-17 03:12 zeta3 with Codex CLI, table-bu table-build@1.130+3450381c minimisers lambda_{k,r} of the random k-uniform hypergraph core threshold for 3 <= k <= 8 and 2 <= r <= 8
2026-09-17 03:08 zeta3 table-build@1.130+3450381c claim core-threshold minimisers draft

What changed between 2026-09-17 03:08 and 2026-09-17 03:12

from line 70 (213 lines, 210 more than before) @@ -70,3 +70,213 @@
 Display properties:   number-header: $\lambda_{k,r}$-Numbers: []+Numbers:+- params:+    k: '3'+    r: '2'+  number: '1.256431208626169676982737616609216326916416831701323711125894727048300478541051903533664750947250849'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,2}[$c_{3,2}$].+- params:+    k: '3'+    r: '3'+  number: '3.213563520216979243990721598628550332961016937266993935011570314990932508944562066900919080501639543'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,3}[$c_{3,3}$].+- params:+    k: '3'+    r: '4'+  number: '4.921981846772290888776752883024317186056436573439824091508273468468509196715986475449901324256178986'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,4}[$c_{3,4}$].+- params:+    k: '3'+    r: '5'+  number: '6.515591826097798170851877858293313883072308134824081056860046654688644744395191367617398426422648410'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,5}[$c_{3,5}$].+- params:+    k: '3'+    r: '6'+  number: '8.039263820146856092138856254339199422167993794012407995996779695584362939354934009423133546902118161'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,6}[$c_{3,6}$].+- params:+    k: '3'+    r: '7'+  number: '9.514469508880899030507393558450993274264377875660089436754383763320216720140867547689851121592635562'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,7}[$c_{3,7}$].+- params:+    k: '3'+    r: '8'+  number: '10.95346075985564844256143919627797293749795469545187124088935549568731785512016948741082119567842981'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,8}[$c_{3,8}$].+- params:+    k: '4'+    r: '2'+  number: '1.903813694440383484710140360828135127280364804561987445879389818281945875445251742935897221209070264'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,2}[$c_{4,2}$].+- params:+    k: '4'+    r: '3'+  number: '3.943432991608201993709553168630446799608703563709097909739285068630870979892017973839711377125004985'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,3}[$c_{4,3}$].+- params:+    k: '4'+    r: '4'+  number: '5.712655689793184261749113193644386168167982023993296659606920984267937821370298005601033912014038776'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,4}[$c_{4,4}$].+- params:+    k: '4'+    r: '5'+  number: '7.356238662572010428146260839034522811851758906746380894035040209606244738087812519651127293227178069'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,5}[$c_{4,5}$].+- params:+    k: '4'+    r: '6'+  number: '8.923133543937897404138547779823342524209920334968527807245157335182798107944509307833635497158032921'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,6}[$c_{4,6}$].+- params:+    k: '4'+    r: '7'+  number: '10.43685728939695192283051786477345424635359010958106227104559457532044084712440111362795839930312800'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,7}[$c_{4,7}$].+- params:+    k: '4'+    r: '8'+  number: '11.91085482297029987283273947363803164895241207451413619648971821871543101470988522101009737414578049'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,8}[$c_{4,8}$].+- params:+    k: '5'+    r: '2'+  number: '2.336662982263053881182850266714011154679504739557109039685225120116767568104385781543593285556392922'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,2}[$c_{5,2}$].+- params:+    k: '5'+    r: '3'+  number: '4.429961741174340595794299265887946343440849798841691898549878810448210800725524242240549510592604875'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,3}[$c_{5,3}$].+- params:+    k: '5'+    r: '4'+  number: '6.239233099841364699091761779242710268467766957008527239152171992449855251908655717861069860689669939'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,4}[$c_{5,4}$].+- params:+    k: '5'+    r: '5'+  number: '7.915932808932573244389888265459534420745939469008615284488694955445411352543868387413870342466396931'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,5}[$c_{5,5}$].+- params:+    k: '5'+    r: '6'+  number: '9.511581543348483155284054757333259972267475267373966015269183105044286077661111762509825055266705227'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,6}[$c_{5,6}$].+- params:+    k: '5'+    r: '7'+  number: '11.05099850311515789634766292263302508532769550742277390402251011897664690455990175411305835670362303'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,7}[$c_{5,7}$].+- params:+    k: '5'+    r: '8'+  number: '12.54839414688261437023640741484170199310321861483385964228059641879490595267312347778684332551874187'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,8}[$c_{5,8}$].+- params:+    k: '6'+    r: '2'+  number: '2.660399058463684990432673112693838761316192793557399779133621108141380344526679670369701126317582048'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,2}[$c_{6,2}$].+- params:+    k: '6'+    r: '3'+  number: '4.792922350729458389393836269395977881768808104455610404765378350938009353293442180198297113646891715'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,3}[$c_{6,3}$].+- params:+    k: '6'+    r: '4'+  number: '6.631692044980859859695457087456113562828943559209647679904601932328360504449403525078647056405154631'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,4}[$c_{6,4}$].+- params:+    k: '6'+    r: '5'+  number: '8.332885060545474643453038367357276844362292641194579907242869038284539339311870952451145000236630570'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,5}[$c_{6,5}$].+- params:+    k: '6'+    r: '6'+  number: '9.949856035279598965993281101298144352595406559863380482666470886487477439749560118793565830379607461'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,6}[$c_{6,6}$].+- params:+    k: '6'+    r: '7'+  number: '11.50836092309161955292977618826790777947661320182321955172192652659584731470204336130700207829174634'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,7}[$c_{6,7}$].+- params:+    k: '6'+    r: '8'+  number: '13.02316374017669072156336769629112584326498148263216486482457051849391131216069892990076318148638379'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,8}[$c_{6,8}$].+- params:+    k: '7'+    r: '2'+  number: '2.918300475783052591304221719797499459970061873861584609944495208244877889764383735414949103879265396'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,2}[$c_{7,2}$].+- params:+    k: '7'+    r: '3'+  number: '5.081459160901541280072984052767384364834705608549266804400302362457469786927329892961576241670256255'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,3}[$c_{7,3}$].+- params:+    k: '7'+    r: '4'+  number: '6.943403149510170669582130838854226834674871175506322769216454740852507523491016500409957336861346672'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,4}[$c_{7,4}$].+- params:+    k: '7'+    r: '5'+  number: '8.663897435137174519899583577567728252667605281255596605005591025135471805928532424709794084516994332'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,5}[$c_{7,5}$].+- params:+    k: '7'+    r: '6'+  number: '10.29770370948003437532796512255737443462847796934890923922314195797931097072888681130447394638516963'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,6}[$c_{7,6}$].+- params:+    k: '7'+    r: '7'+  number: '11.87130070214323957227718493587230991764172191009718801979638624429793118363290687748586153232250824'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,7}[$c_{7,7}$].+- params:+    k: '7'+    r: '8'+  number: '13.39988120401632761753924670661057126272293378422422449028809204749315606537864394912727852237790303'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,8}[$c_{7,8}$].+- params:+    k: '8'+    r: '2'+  number: '3.132265450540420106833422460869303332477500804253648991520139627783433414358227583586491785309904738'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,2}[$c_{8,2}$].+- params:+    k: '8'+    r: '3'+  number: '5.320410398592856390274399571423194057429031818068357224721914044015662800282969722273689295179037782'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,3}[$c_{8,3}$].+- params:+    k: '8'+    r: '4'+  number: '7.201342167086465465995230954511332137013680863221225905126416091272120474693659568328505902778556493'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,4}[$c_{8,4}$].+- params:+    k: '8'+    r: '5'+  number: '8.937689058821257897847473075778498054363562033589717691202034236556493355565920677841425777848131716'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,5}[$c_{8,5}$].+- params:+    k: '8'+    r: '6'+  number: '10.58534398664845734750878149290269445326079627643095634678228319037799585247784783513560945584997527'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,6}[$c_{8,6}$].+- params:+    k: '8'+    r: '7'+  number: '12.17136936664993198917735237904287147986248521678215131664326659268714127192768870112217956585325223'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,7}[$c_{8,7}$].+- params:+    k: '8'+    r: '8'+  number: '13.71130531896385558662755379683587375766125942222105380706720345280147382907814364034891657375807970'+  comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,8}[$c_{8,8}$]. 

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