Question derivations
All 36000 derivations have bilingual display, basic symbol and structural checks, and questions 1–36000 all have second-context mathematical and bilingual review; no display/symbol-checked candidates remain.
This cohort has 36000 questions. 36000 derivations are published: 36000 mathematically reviewed and 0 display/symbol-checked candidates. 0 are not published here.
- Question 11801: An Affine Jensen Identity on a Qualified Interval ·
R0022-11801· Mathematically reviewed - Question 11802: An Affine Jensen Identity on a Qualified Interval ·
R0022-11802· Mathematically reviewed - Question 11803: An Affine Jensen Identity on a Qualified Interval ·
R0022-11803· Mathematically reviewed - Question 11804: An Affine Jensen Identity on a Qualified Interval ·
R0022-11804· Mathematically reviewed - Question 11805: An Affine Jensen Identity on a Qualified Interval ·
R0022-11805· Mathematically reviewed - Question 11806: An Affine Jensen Identity on a Qualified Interval ·
R0022-11806· Mathematically reviewed - Question 11807: An Affine Jensen Identity on a Qualified Interval ·
R0022-11807· Mathematically reviewed - Question 11808: An Affine Jensen Identity on a Qualified Interval ·
R0022-11808· Mathematically reviewed - Question 11809: An Affine Jensen Identity on a Qualified Interval ·
R0022-11809· Mathematically reviewed - Question 11810: An Affine Jensen Identity on a Qualified Interval ·
R0022-11810· Mathematically reviewed - Question 11811: An Affine Jensen Identity on a Qualified Interval ·
R0022-11811· Mathematically reviewed - Question 11812: An Affine Jensen Identity on a Qualified Interval ·
R0022-11812· Mathematically reviewed - Question 11813: An Affine Jensen Identity on a Qualified Interval ·
R0022-11813· Mathematically reviewed - Question 11814: An Affine Jensen Identity on a Qualified Interval ·
R0022-11814· Mathematically reviewed - Question 11815: An Affine Jensen Identity on a Qualified Interval ·
R0022-11815· Mathematically reviewed - Question 11816: An Affine Jensen Identity on a Qualified Interval ·
R0022-11816· Mathematically reviewed - Question 11817: An Affine Jensen Identity on a Qualified Interval ·
R0022-11817· Mathematically reviewed - Question 11818: An Affine Jensen Identity on a Qualified Interval ·
R0022-11818· Mathematically reviewed - Question 11819: An Affine Jensen Identity on a Qualified Interval ·
R0022-11819· Mathematically reviewed - Question 11820: An Affine Jensen Identity on a Qualified Interval ·
R0022-11820· Mathematically reviewed - Question 11821: An Affine Jensen Identity on a Qualified Interval ·
R0022-11821· Mathematically reviewed - Question 11822: An Affine Jensen Identity on a Qualified Interval ·
R0022-11822· Mathematically reviewed - Question 11823: An Affine Jensen Identity on a Qualified Interval ·
R0022-11823· Mathematically reviewed - Question 11824: An Affine Jensen Identity on a Qualified Interval ·
R0022-11824· Mathematically reviewed - Question 11825: An Affine Jensen Identity on a Qualified Interval ·
R0022-11825· Mathematically reviewed - Question 11826: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11826· Mathematically reviewed - Question 11827: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11827· Mathematically reviewed - Question 11828: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11828· Mathematically reviewed - Question 11829: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11829· Mathematically reviewed - Question 11830: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11830· Mathematically reviewed - Question 11831: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11831· Mathematically reviewed - Question 11832: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11832· Mathematically reviewed - Question 11833: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11833· Mathematically reviewed - Question 11834: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11834· Mathematically reviewed - Question 11835: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11835· Mathematically reviewed - Question 11836: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11836· Mathematically reviewed - Question 11837: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11837· Mathematically reviewed - Question 11838: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11838· Mathematically reviewed - Question 11839: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11839· Mathematically reviewed - Question 11840: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11840· Mathematically reviewed - Question 11841: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11841· Mathematically reviewed - Question 11842: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11842· Mathematically reviewed - Question 11843: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11843· Mathematically reviewed - Question 11844: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11844· Mathematically reviewed - Question 11845: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11845· Mathematically reviewed - Question 11846: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11846· Mathematically reviewed - Question 11847: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11847· Mathematically reviewed - Question 11848: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11848· Mathematically reviewed - Question 11849: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11849· Mathematically reviewed - Question 11850: Qualify a Declared Nonempty Interval before Using Jensen Semantics ·
R0022-11850· Mathematically reviewed - Question 11851: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11851· Mathematically reviewed - Question 11852: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11852· Mathematically reviewed - Question 11853: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11853· Mathematically reviewed - Question 11854: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11854· Mathematically reviewed - Question 11855: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11855· Mathematically reviewed - Question 11856: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11856· Mathematically reviewed - Question 11857: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11857· Mathematically reviewed - Question 11858: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11858· Mathematically reviewed - Question 11859: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11859· Mathematically reviewed - Question 11860: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11860· Mathematically reviewed - Question 11861: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11861· Mathematically reviewed - Question 11862: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11862· Mathematically reviewed - Question 11863: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11863· Mathematically reviewed - Question 11864: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11864· Mathematically reviewed - Question 11865: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11865· Mathematically reviewed - Question 11866: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11866· Mathematically reviewed - Question 11867: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11867· Mathematically reviewed - Question 11868: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11868· Mathematically reviewed - Question 11869: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11869· Mathematically reviewed - Question 11870: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11870· Mathematically reviewed - Question 11871: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11871· Mathematically reviewed - Question 11872: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11872· Mathematically reviewed - Question 11873: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11873· Mathematically reviewed - Question 11874: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11874· Mathematically reviewed - Question 11875: One Exact Jensen Instance: a Counterexample or Only an Example ·
R0022-11875· Mathematically reviewed - Question 11876: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11876· Mathematically reviewed - Question 11877: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11877· Mathematically reviewed - Question 11878: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11878· Mathematically reviewed - Question 11879: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11879· Mathematically reviewed - Question 11880: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11880· Mathematically reviewed - Question 11881: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11881· Mathematically reviewed - Question 11882: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11882· Mathematically reviewed - Question 11883: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11883· Mathematically reviewed - Question 11884: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11884· Mathematically reviewed - Question 11885: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11885· Mathematically reviewed - Question 11886: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11886· Mathematically reviewed - Question 11887: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11887· Mathematically reviewed - Question 11888: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11888· Mathematically reviewed - Question 11889: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11889· Mathematically reviewed - Question 11890: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11890· Mathematically reviewed - Question 11891: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11891· Mathematically reviewed - Question 11892: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11892· Mathematically reviewed - Question 11893: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11893· Mathematically reviewed - Question 11894: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11894· Mathematically reviewed - Question 11895: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11895· Mathematically reviewed - Question 11896: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11896· Mathematically reviewed - Question 11897: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11897· Mathematically reviewed - Question 11898: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11898· Mathematically reviewed - Question 11899: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11899· Mathematically reviewed - Question 11900: A Nondegenerate-Interval Quadratic Jensen-Gap Certificate ·
R0022-11900· Mathematically reviewed - Question 11901: Feasibility Alone Supplies No Optimum ·
R0022-11901· Mathematically reviewed - Question 11902: Feasibility Alone Supplies No Optimum ·
R0022-11902· Mathematically reviewed - Question 11903: Feasibility Alone Supplies No Optimum ·
R0022-11903· Mathematically reviewed - Question 11904: Feasibility Alone Supplies No Optimum ·
R0022-11904· Mathematically reviewed - Question 11905: Feasibility Alone Supplies No Optimum ·
R0022-11905· Mathematically reviewed - Question 11906: Feasibility Alone Supplies No Optimum ·
R0022-11906· Mathematically reviewed - Question 11907: Feasibility Alone Supplies No Optimum ·
R0022-11907· Mathematically reviewed - Question 11908: Feasibility Alone Supplies No Optimum ·
R0022-11908· Mathematically reviewed - Question 11909: Feasibility Alone Supplies No Optimum ·
R0022-11909· Mathematically reviewed - Question 11910: Feasibility Alone Supplies No Optimum ·
R0022-11910· Mathematically reviewed - Question 11911: Feasibility Alone Supplies No Optimum ·
R0022-11911· Mathematically reviewed - Question 11912: Feasibility Alone Supplies No Optimum ·
R0022-11912· Mathematically reviewed - Question 11913: Feasibility Alone Supplies No Optimum ·
R0022-11913· Mathematically reviewed - Question 11914: Feasibility Alone Supplies No Optimum ·
R0022-11914· Mathematically reviewed - Question 11915: Feasibility Alone Supplies No Optimum ·
R0022-11915· Mathematically reviewed - Question 11916: Feasibility Alone Supplies No Optimum ·
R0022-11916· Mathematically reviewed - Question 11917: Feasibility Alone Supplies No Optimum ·
R0022-11917· Mathematically reviewed - Question 11918: Feasibility Alone Supplies No Optimum ·
R0022-11918· Mathematically reviewed - Question 11919: Feasibility Alone Supplies No Optimum ·
R0022-11919· Mathematically reviewed - Question 11920: Feasibility Alone Supplies No Optimum ·
R0022-11920· Mathematically reviewed - Question 11921: Feasibility Alone Supplies No Optimum ·
R0022-11921· Mathematically reviewed - Question 11922: Feasibility Alone Supplies No Optimum ·
R0022-11922· Mathematically reviewed - Question 11923: Feasibility Alone Supplies No Optimum ·
R0022-11923· Mathematically reviewed - Question 11924: Feasibility Alone Supplies No Optimum ·
R0022-11924· Mathematically reviewed - Question 11925: Feasibility Alone Supplies No Optimum ·
R0022-11925· Mathematically reviewed - Question 11926: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11926· Mathematically reviewed - Question 11927: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11927· Mathematically reviewed - Question 11928: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11928· Mathematically reviewed - Question 11929: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11929· Mathematically reviewed - Question 11930: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11930· Mathematically reviewed - Question 11931: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11931· Mathematically reviewed - Question 11932: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11932· Mathematically reviewed - Question 11933: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11933· Mathematically reviewed - Question 11934: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11934· Mathematically reviewed - Question 11935: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11935· Mathematically reviewed - Question 11936: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11936· Mathematically reviewed - Question 11937: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11937· Mathematically reviewed - Question 11938: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11938· Mathematically reviewed - Question 11939: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11939· Mathematically reviewed - Question 11940: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11940· Mathematically reviewed - Question 11941: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11941· Mathematically reviewed - Question 11942: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11942· Mathematically reviewed - Question 11943: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11943· Mathematically reviewed - Question 11944: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11944· Mathematically reviewed - Question 11945: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11945· Mathematically reviewed - Question 11946: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11946· Mathematically reviewed - Question 11947: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11947· Mathematically reviewed - Question 11948: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11948· Mathematically reviewed - Question 11949: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11949· Mathematically reviewed - Question 11950: Evaluate the Polynomial while Separately Reporting Feasibility ·
R0022-11950· Mathematically reviewed - Question 11951: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11951· Mathematically reviewed - Question 11952: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11952· Mathematically reviewed - Question 11953: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11953· Mathematically reviewed - Question 11954: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11954· Mathematically reviewed - Question 11955: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11955· Mathematically reviewed - Question 11956: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11956· Mathematically reviewed - Question 11957: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11957· Mathematically reviewed - Question 11958: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11958· Mathematically reviewed - Question 11959: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11959· Mathematically reviewed - Question 11960: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11960· Mathematically reviewed - Question 11961: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11961· Mathematically reviewed - Question 11962: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11962· Mathematically reviewed - Question 11963: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11963· Mathematically reviewed - Question 11964: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11964· Mathematically reviewed - Question 11965: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11965· Mathematically reviewed - Question 11966: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11966· Mathematically reviewed - Question 11967: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11967· Mathematically reviewed - Question 11968: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11968· Mathematically reviewed - Question 11969: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11969· Mathematically reviewed - Question 11970: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11970· Mathematically reviewed - Question 11971: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11971· Mathematically reviewed - Question 11972: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11972· Mathematically reviewed - Question 11973: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11973· Mathematically reviewed - Question 11974: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11974· Mathematically reviewed - Question 11975: Compare Only Two Eligible Candidates, Not the Whole Problem ·
R0022-11975· Mathematically reviewed - Question 11976: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11976· Mathematically reviewed - Question 11977: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11977· Mathematically reviewed - Question 11978: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11978· Mathematically reviewed - Question 11979: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11979· Mathematically reviewed - Question 11980: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11980· Mathematically reviewed - Question 11981: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11981· Mathematically reviewed - Question 11982: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11982· Mathematically reviewed - Question 11983: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11983· Mathematically reviewed - Question 11984: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11984· Mathematically reviewed - Question 11985: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11985· Mathematically reviewed - Question 11986: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11986· Mathematically reviewed - Question 11987: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11987· Mathematically reviewed - Question 11988: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11988· Mathematically reviewed - Question 11989: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11989· Mathematically reviewed - Question 11990: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11990· Mathematically reviewed - Question 11991: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11991· Mathematically reviewed - Question 11992: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11992· Mathematically reviewed - Question 11993: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11993· Mathematically reviewed - Question 11994: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11994· Mathematically reviewed - Question 11995: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11995· Mathematically reviewed - Question 11996: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11996· Mathematically reviewed - Question 11997: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11997· Mathematically reviewed - Question 11998: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11998· Mathematically reviewed - Question 11999: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-11999· Mathematically reviewed - Question 12000: Separate a Quadratic Objective Certificate from Feasible-Interval Qualification ·
R0022-12000· Mathematically reviewed
The source bank retains its original candidate and verification labels. Display and symbol checks are not recorded as mathematical review or independent recomputation.
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