Question 24211: One Convolution Degree Is Not the Whole Exponential Addition Proof

Original question and givens

Use the whole real series E(x)=sum over n≥0 of x^n/n!, with power-series coefficients1/n!. A finite sum is a separate object; whole-series identities require the declared convergence and rearrangement obligations. Use x=11/12, y=-12/13, declared degree=10. Give (x, y, degree, coefficient_terms, convolution_coefficient, sum_argument_coefficient, equal, certificate).

• G001 — Use the whole real series E(x)=sum over n≥0 of x^n/n!, with power-series coefficients1/n!. A finite sum is a separate object; whole-series identities require the declared convergence and rearrangement obligations. Use x=11/12, y=-12/13, declared degree=10. Give (x, y, degree, coefficient_terms, convolution_coefficient, sum_argument_coefficient, equal, certificate).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-real-exponential-function

Step-by-step derivation

source roles = [exp-addition-convolution]

derived = [[x, y, degree, coefficient_terms, convolution_coefficient, sum_argument_coefficient, equal, certificate]]

(11/12)^0

Exp convolution x power0 = 1

(-12/13)^10

Exp convolution y power10 = 61917364224/137858491849

Exp convolution numerator0 := mul(1, 61917364224/137858491849)

Exp convolution numerator0 = 61917364224/137858491849

source roles = [0]

derived = [1]

Exp convolution right0 factorial step1 := mul(1, 1)

Exp convolution right0 factorial step1 = 1

Exp convolution right0 factorial step2 := mul(1, 2)

Exp convolution right0 factorial step2 = 2

Exp convolution right0 factorial step3 := mul(2, 3)

Exp convolution right0 factorial step3 = 6

Exp convolution right0 factorial step4 := mul(6, 4)

Exp convolution right0 factorial step4 = 24

Exp convolution right0 factorial step5 := mul(24, 5)

Exp convolution right0 factorial step5 = 120

Exp convolution right0 factorial step6 := mul(120, 6)

Exp convolution right0 factorial step6 = 720

Exp convolution right0 factorial step7 := mul(720, 7)

Exp convolution right0 factorial step7 = 5040

Exp convolution right0 factorial step8 := mul(5040, 8)

Exp convolution right0 factorial step8 = 40320

Exp convolution right0 factorial step9 := mul(40320, 9)

Exp convolution right0 factorial step9 = 362880

Exp convolution right0 factorial step10 := mul(362880, 10)

Exp convolution right0 factorial step10 = 3628800

Exp convolution denominator0 := mul(1, 3628800)

Exp convolution denominator0 = 3628800

Exp convolution coefficient term0 := div(61917364224/137858491849, 3628800)

Exp convolution coefficient term0 = 2985984/24125236073575

(11/12)^1

Exp convolution x power1 = 11/12

(-12/13)^9

Exp convolution y power9 = -5159780352/10604499373

Exp convolution numerator1 := mul(11/12, -5159780352/10604499373)

Exp convolution numerator1 = -4729798656/10604499373

Exp convolution left1 factorial step1 := mul(1, 1)

Exp convolution left1 factorial step1 = 1

Exp convolution right1 factorial step1 := mul(1, 1)

Exp convolution right1 factorial step1 = 1

Exp convolution right1 factorial step2 := mul(1, 2)

Exp convolution right1 factorial step2 = 2

Exp convolution right1 factorial step3 := mul(2, 3)

Exp convolution right1 factorial step3 = 6

Exp convolution right1 factorial step4 := mul(6, 4)

Exp convolution right1 factorial step4 = 24

Exp convolution right1 factorial step5 := mul(24, 5)

Exp convolution right1 factorial step5 = 120

Exp convolution right1 factorial step6 := mul(120, 6)

Exp convolution right1 factorial step6 = 720

Exp convolution right1 factorial step7 := mul(720, 7)

Exp convolution right1 factorial step7 = 5040

Exp convolution right1 factorial step8 := mul(5040, 8)

Exp convolution right1 factorial step8 = 40320

Exp convolution right1 factorial step9 := mul(40320, 9)

Exp convolution right1 factorial step9 = 362880

Exp convolution denominator1 := mul(1, 362880)

Exp convolution denominator1 = 362880

Exp convolution coefficient term1 := div(-4729798656/10604499373, 362880)

Exp convolution coefficient term1 = -456192/371157478055

(11/12)^2

Exp convolution x power2 = 121/144

(-12/13)^8

Exp convolution y power8 = 429981696/815730721

Exp convolution numerator2 := mul(121/144, 429981696/815730721)

Exp convolution numerator2 = 361304064/815730721

Exp convolution left2 factorial step1 := mul(1, 1)

Exp convolution left2 factorial step1 = 1

Exp convolution left2 factorial step2 := mul(1, 2)

Exp convolution left2 factorial step2 = 2

Exp convolution right2 factorial step1 := mul(1, 1)

Exp convolution right2 factorial step1 = 1

Exp convolution right2 factorial step2 := mul(1, 2)

Exp convolution right2 factorial step2 = 2

Exp convolution right2 factorial step3 := mul(2, 3)

Exp convolution right2 factorial step3 = 6

Exp convolution right2 factorial step4 := mul(6, 4)

Exp convolution right2 factorial step4 = 24

Exp convolution right2 factorial step5 := mul(24, 5)

Exp convolution right2 factorial step5 = 120

Exp convolution right2 factorial step6 := mul(120, 6)

Exp convolution right2 factorial step6 = 720

Exp convolution right2 factorial step7 := mul(720, 7)

Exp convolution right2 factorial step7 = 5040

Exp convolution right2 factorial step8 := mul(5040, 8)

Exp convolution right2 factorial step8 = 40320

Exp convolution denominator2 := mul(2, 40320)

Exp convolution denominator2 = 80640

Exp convolution coefficient term2 := div(361304064/815730721, 80640)

Exp convolution coefficient term2 = 156816/28550575235

(11/12)^3

Exp convolution x power3 = 1331/1728

(-12/13)^7

Exp convolution y power7 = -35831808/62748517

Exp convolution numerator3 := mul(1331/1728, -35831808/62748517)

Exp convolution numerator3 = -27599616/62748517

Exp convolution left3 factorial step1 := mul(1, 1)

Exp convolution left3 factorial step1 = 1

Exp convolution left3 factorial step2 := mul(1, 2)

Exp convolution left3 factorial step2 = 2

Exp convolution left3 factorial step3 := mul(2, 3)

Exp convolution left3 factorial step3 = 6

Exp convolution right3 factorial step1 := mul(1, 1)

Exp convolution right3 factorial step1 = 1

Exp convolution right3 factorial step2 := mul(1, 2)

Exp convolution right3 factorial step2 = 2

Exp convolution right3 factorial step3 := mul(2, 3)

Exp convolution right3 factorial step3 = 6

Exp convolution right3 factorial step4 := mul(6, 4)

Exp convolution right3 factorial step4 = 24

Exp convolution right3 factorial step5 := mul(24, 5)

Exp convolution right3 factorial step5 = 120

Exp convolution right3 factorial step6 := mul(120, 6)

Exp convolution right3 factorial step6 = 720

Exp convolution right3 factorial step7 := mul(720, 7)

Exp convolution right3 factorial step7 = 5040

Exp convolution denominator3 := mul(6, 5040)

Exp convolution denominator3 = 30240

Exp convolution coefficient term3 := div(-27599616/62748517, 30240)

Exp convolution coefficient term3 = -31944/2196198095

(11/12)^4

Exp convolution x power4 = 14641/20736

(-12/13)^6

Exp convolution y power6 = 2985984/4826809

Exp convolution numerator4 := mul(14641/20736, 2985984/4826809)

Exp convolution numerator4 = 2108304/4826809

Exp convolution left4 factorial step1 := mul(1, 1)

Exp convolution left4 factorial step1 = 1

Exp convolution left4 factorial step2 := mul(1, 2)

Exp convolution left4 factorial step2 = 2

Exp convolution left4 factorial step3 := mul(2, 3)

Exp convolution left4 factorial step3 = 6

Exp convolution left4 factorial step4 := mul(6, 4)

Exp convolution left4 factorial step4 = 24

Exp convolution right4 factorial step1 := mul(1, 1)

Exp convolution right4 factorial step1 = 1

Exp convolution right4 factorial step2 := mul(1, 2)

Exp convolution right4 factorial step2 = 2

Exp convolution right4 factorial step3 := mul(2, 3)

Exp convolution right4 factorial step3 = 6

Exp convolution right4 factorial step4 := mul(6, 4)

Exp convolution right4 factorial step4 = 24

Exp convolution right4 factorial step5 := mul(24, 5)

Exp convolution right4 factorial step5 = 120

Exp convolution right4 factorial step6 := mul(120, 6)

Exp convolution right4 factorial step6 = 720

Exp convolution denominator4 := mul(24, 720)

Exp convolution denominator4 = 17280

Exp convolution coefficient term4 := div(2108304/4826809, 17280)

Exp convolution coefficient term4 = 14641/579217080

(11/12)^5

Exp convolution x power5 = 161051/248832

(-12/13)^5

Exp convolution y power5 = -248832/371293

Exp convolution numerator5 := mul(161051/248832, -248832/371293)

Exp convolution numerator5 = -161051/371293

Exp convolution left5 factorial step1 := mul(1, 1)

Exp convolution left5 factorial step1 = 1

Exp convolution left5 factorial step2 := mul(1, 2)

Exp convolution left5 factorial step2 = 2

Exp convolution left5 factorial step3 := mul(2, 3)

Exp convolution left5 factorial step3 = 6

Exp convolution left5 factorial step4 := mul(6, 4)

Exp convolution left5 factorial step4 = 24

Exp convolution left5 factorial step5 := mul(24, 5)

Exp convolution left5 factorial step5 = 120

Exp convolution right5 factorial step1 := mul(1, 1)

Exp convolution right5 factorial step1 = 1

Exp convolution right5 factorial step2 := mul(1, 2)

Exp convolution right5 factorial step2 = 2

Exp convolution right5 factorial step3 := mul(2, 3)

Exp convolution right5 factorial step3 = 6

Exp convolution right5 factorial step4 := mul(6, 4)

Exp convolution right5 factorial step4 = 24

Exp convolution right5 factorial step5 := mul(24, 5)

Exp convolution right5 factorial step5 = 120

Exp convolution denominator5 := mul(120, 120)

Exp convolution denominator5 = 14400

Exp convolution coefficient term5 := div(-161051/371293, 14400)

Exp convolution coefficient term5 = -161051/5346619200

(11/12)^6

Exp convolution x power6 = 1771561/2985984

(-12/13)^4

Exp convolution y power4 = 20736/28561

Exp convolution numerator6 := mul(1771561/2985984, 20736/28561)

Exp convolution numerator6 = 1771561/4112784

Exp convolution left6 factorial step1 := mul(1, 1)

Exp convolution left6 factorial step1 = 1

Exp convolution left6 factorial step2 := mul(1, 2)

Exp convolution left6 factorial step2 = 2

Exp convolution left6 factorial step3 := mul(2, 3)

Exp convolution left6 factorial step3 = 6

Exp convolution left6 factorial step4 := mul(6, 4)

Exp convolution left6 factorial step4 = 24

Exp convolution left6 factorial step5 := mul(24, 5)

Exp convolution left6 factorial step5 = 120

Exp convolution left6 factorial step6 := mul(120, 6)

Exp convolution left6 factorial step6 = 720

Exp convolution right6 factorial step1 := mul(1, 1)

Exp convolution right6 factorial step1 = 1

Exp convolution right6 factorial step2 := mul(1, 2)

Exp convolution right6 factorial step2 = 2

Exp convolution right6 factorial step3 := mul(2, 3)

Exp convolution right6 factorial step3 = 6

Exp convolution right6 factorial step4 := mul(6, 4)

Exp convolution right6 factorial step4 = 24

Exp convolution denominator6 := mul(720, 24)

Exp convolution denominator6 = 17280

Exp convolution coefficient term6 := div(1771561/4112784, 17280)

Exp convolution coefficient term6 = 1771561/71068907520

(11/12)^7

Exp convolution x power7 = 19487171/35831808

(-12/13)^3

Exp convolution y power3 = -1728/2197

Exp convolution numerator7 := mul(19487171/35831808, -1728/2197)

Exp convolution numerator7 = -19487171/45556992

Exp convolution left7 factorial step1 := mul(1, 1)

Exp convolution left7 factorial step1 = 1

Exp convolution left7 factorial step2 := mul(1, 2)

Exp convolution left7 factorial step2 = 2

Exp convolution left7 factorial step3 := mul(2, 3)

Exp convolution left7 factorial step3 = 6

Exp convolution left7 factorial step4 := mul(6, 4)

Exp convolution left7 factorial step4 = 24

Exp convolution left7 factorial step5 := mul(24, 5)

Exp convolution left7 factorial step5 = 120

Exp convolution left7 factorial step6 := mul(120, 6)

Exp convolution left7 factorial step6 = 720

Exp convolution left7 factorial step7 := mul(720, 7)

Exp convolution left7 factorial step7 = 5040

Exp convolution right7 factorial step1 := mul(1, 1)

Exp convolution right7 factorial step1 = 1

Exp convolution right7 factorial step2 := mul(1, 2)

Exp convolution right7 factorial step2 = 2

Exp convolution right7 factorial step3 := mul(2, 3)

Exp convolution right7 factorial step3 = 6

Exp convolution denominator7 := mul(5040, 6)

Exp convolution denominator7 = 30240

Exp convolution coefficient term7 := div(-19487171/45556992, 30240)

Exp convolution coefficient term7 = -19487171/1377643438080

(11/12)^8

Exp convolution x power8 = 214358881/429981696

(-12/13)^2

Exp convolution y power2 = 144/169

Exp convolution numerator8 := mul(214358881/429981696, 144/169)

Exp convolution numerator8 = 214358881/504631296

Exp convolution left8 factorial step1 := mul(1, 1)

Exp convolution left8 factorial step1 = 1

Exp convolution left8 factorial step2 := mul(1, 2)

Exp convolution left8 factorial step2 = 2

Exp convolution left8 factorial step3 := mul(2, 3)

Exp convolution left8 factorial step3 = 6

Exp convolution left8 factorial step4 := mul(6, 4)

Exp convolution left8 factorial step4 = 24

Exp convolution left8 factorial step5 := mul(24, 5)

Exp convolution left8 factorial step5 = 120

Exp convolution left8 factorial step6 := mul(120, 6)

Exp convolution left8 factorial step6 = 720

Exp convolution left8 factorial step7 := mul(720, 7)

Exp convolution left8 factorial step7 = 5040

Exp convolution left8 factorial step8 := mul(5040, 8)

Exp convolution left8 factorial step8 = 40320

Exp convolution right8 factorial step1 := mul(1, 1)

Exp convolution right8 factorial step1 = 1

Exp convolution right8 factorial step2 := mul(1, 2)

Exp convolution right8 factorial step2 = 2

Exp convolution denominator8 := mul(40320, 2)

Exp convolution denominator8 = 80640

Exp convolution coefficient term8 := div(214358881/504631296, 80640)

Exp convolution coefficient term8 = 214358881/40693467709440

(11/12)^9

Exp convolution x power9 = 2357947691/5159780352

(-12/13)^1

Exp convolution y power1 = -12/13

Exp convolution numerator9 := mul(2357947691/5159780352, -12/13)

Exp convolution numerator9 = -2357947691/5589762048

Exp convolution left9 factorial step1 := mul(1, 1)

Exp convolution left9 factorial step1 = 1

Exp convolution left9 factorial step2 := mul(1, 2)

Exp convolution left9 factorial step2 = 2

Exp convolution left9 factorial step3 := mul(2, 3)

Exp convolution left9 factorial step3 = 6

Exp convolution left9 factorial step4 := mul(6, 4)

Exp convolution left9 factorial step4 = 24

Exp convolution left9 factorial step5 := mul(24, 5)

Exp convolution left9 factorial step5 = 120

Exp convolution left9 factorial step6 := mul(120, 6)

Exp convolution left9 factorial step6 = 720

Exp convolution left9 factorial step7 := mul(720, 7)

Exp convolution left9 factorial step7 = 5040

Exp convolution left9 factorial step8 := mul(5040, 8)

Exp convolution left9 factorial step8 = 40320

Exp convolution left9 factorial step9 := mul(40320, 9)

Exp convolution left9 factorial step9 = 362880

Exp convolution right9 factorial step1 := mul(1, 1)

Exp convolution right9 factorial step1 = 1

Exp convolution denominator9 := mul(362880, 1)

Exp convolution denominator9 = 362880

Exp convolution coefficient term9 := div(-2357947691/5589762048, 362880)

Exp convolution coefficient term9 = -2357947691/2028412851978240

(11/12)^10

Exp convolution x power10 = 25937424601/61917364224

(-12/13)^0

Exp convolution y power0 = 1

Exp convolution numerator10 := mul(25937424601/61917364224, 1)

Exp convolution numerator10 = 25937424601/61917364224

Exp convolution left10 factorial step1 := mul(1, 1)

Exp convolution left10 factorial step1 = 1

Exp convolution left10 factorial step2 := mul(1, 2)

Exp convolution left10 factorial step2 = 2

Exp convolution left10 factorial step3 := mul(2, 3)

Exp convolution left10 factorial step3 = 6

Exp convolution left10 factorial step4 := mul(6, 4)

Exp convolution left10 factorial step4 = 24

Exp convolution left10 factorial step5 := mul(24, 5)

Exp convolution left10 factorial step5 = 120

Exp convolution left10 factorial step6 := mul(120, 6)

Exp convolution left10 factorial step6 = 720

Exp convolution left10 factorial step7 := mul(720, 7)

Exp convolution left10 factorial step7 = 5040

Exp convolution left10 factorial step8 := mul(5040, 8)

Exp convolution left10 factorial step8 = 40320

Exp convolution left10 factorial step9 := mul(40320, 9)

Exp convolution left10 factorial step9 = 362880

Exp convolution left10 factorial step10 := mul(362880, 10)

Exp convolution left10 factorial step10 = 3628800

source roles = [0]

derived = [1]

Exp convolution denominator10 := mul(3628800, 1)

Exp convolution denominator10 = 3628800

Exp convolution coefficient term10 := div(25937424601/61917364224, 3628800)

Exp convolution coefficient term10 = 25937424601/224685731296051200

Exp complete declared-degree convolution := sum(2985984/24125236073575, -456192/371157478055, 156816/28550575235, -31944/2196198095, 14641/579217080, -161051/5346619200, 1771561/71068907520, -19487171/1377643438080, 214358881/40693467709440, -2357947691/2028412851978240, 25937424601/224685731296051200)

Exp complete declared-degree convolution = 1/30974836056463278561086668800

Exp ORIGINAL arguments sum := sum(11/12, -12/13)

Exp ORIGINAL arguments sum = -1/156

(-1/156)^10

Exp sum argument declared power = 1/8535834451185868210176

Exp sum argument factorial step1 := mul(1, 1)

Exp sum argument factorial step1 = 1

Exp sum argument factorial step2 := mul(1, 2)

Exp sum argument factorial step2 = 2

Exp sum argument factorial step3 := mul(2, 3)

Exp sum argument factorial step3 = 6

Exp sum argument factorial step4 := mul(6, 4)

Exp sum argument factorial step4 = 24

Exp sum argument factorial step5 := mul(24, 5)

Exp sum argument factorial step5 = 120

Exp sum argument factorial step6 := mul(120, 6)

Exp sum argument factorial step6 = 720

Exp sum argument factorial step7 := mul(720, 7)

Exp sum argument factorial step7 = 5040

Exp sum argument factorial step8 := mul(5040, 8)

Exp sum argument factorial step8 = 40320

Exp sum argument factorial step9 := mul(40320, 9)

Exp sum argument factorial step9 = 362880

Exp sum argument factorial step10 := mul(362880, 10)

Exp sum argument factorial step10 = 3628800

Exp sum argument coefficient := div(1/8535834451185868210176, 3628800)

Exp sum argument coefficient = 1/30974836056463278561086668800

source roles = [[11/12, -12/13], a_n=1/n! for EVERY n>=0]

derived = [coefficient ratio=1/(n+1), for EVERY fixed real z,term absolute ratio=|z|/(n+1)->0, absolute convergence and real-valued E(z)]

source roles = [[11/12, -12/13, 10], E(x),E(y) absolutely convergent]

derived = [for EVERY n,sum_k x^k*y^(n-k)/(k!*(n-k)!)=(x+y)^n/n!, E(x)E(y)=E(x+y)]

Reverse checks

• S184 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S183 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S182 · premise_and_result_audit — Recompute Exp sum argument coefficient with exact rational arithmetic, not rounded decimals.
• S181 · premise_and_result_audit — Recompute Exp sum argument factorial step10 with exact rational arithmetic, not rounded decimals.
• S180 · premise_and_result_audit — Recompute Exp sum argument factorial step9 with exact rational arithmetic, not rounded decimals.
• S179 · premise_and_result_audit — Recompute Exp sum argument factorial step8 with exact rational arithmetic, not rounded decimals.
• S178 · premise_and_result_audit — Recompute Exp sum argument factorial step7 with exact rational arithmetic, not rounded decimals.
• S177 · premise_and_result_audit — Recompute Exp sum argument factorial step6 with exact rational arithmetic, not rounded decimals.
• S176 · premise_and_result_audit — Recompute Exp sum argument factorial step5 with exact rational arithmetic, not rounded decimals.
• S175 · premise_and_result_audit — Recompute Exp sum argument factorial step4 with exact rational arithmetic, not rounded decimals.
• S174 · premise_and_result_audit — Recompute Exp sum argument factorial step3 with exact rational arithmetic, not rounded decimals.
• S173 · premise_and_result_audit — Recompute Exp sum argument factorial step2 with exact rational arithmetic, not rounded decimals.
• S172 · premise_and_result_audit — Recompute Exp sum argument factorial step1 with exact rational arithmetic, not rounded decimals.
• S171 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S170 · premise_and_result_audit — Recompute Exp ORIGINAL arguments sum with exact rational arithmetic, not rounded decimals.
• S169 · premise_and_result_audit — Recompute Exp complete declared-degree convolution with exact rational arithmetic, not rounded decimals.
• S168 · premise_and_result_audit — Recompute Exp convolution coefficient term10 with exact rational arithmetic, not rounded decimals.
• S167 · premise_and_result_audit — Recompute Exp convolution denominator10 with exact rational arithmetic, not rounded decimals.
• S166 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S165 · premise_and_result_audit — Recompute Exp convolution left10 factorial step10 with exact rational arithmetic, not rounded decimals.
• S164 · premise_and_result_audit — Recompute Exp convolution left10 factorial step9 with exact rational arithmetic, not rounded decimals.
• S163 · premise_and_result_audit — Recompute Exp convolution left10 factorial step8 with exact rational arithmetic, not rounded decimals.
• S162 · premise_and_result_audit — Recompute Exp convolution left10 factorial step7 with exact rational arithmetic, not rounded decimals.
• S161 · premise_and_result_audit — Recompute Exp convolution left10 factorial step6 with exact rational arithmetic, not rounded decimals.
• S160 · premise_and_result_audit — Recompute Exp convolution left10 factorial step5 with exact rational arithmetic, not rounded decimals.
• S159 · premise_and_result_audit — Recompute Exp convolution left10 factorial step4 with exact rational arithmetic, not rounded decimals.
• S158 · premise_and_result_audit — Recompute Exp convolution left10 factorial step3 with exact rational arithmetic, not rounded decimals.
• S157 · premise_and_result_audit — Recompute Exp convolution left10 factorial step2 with exact rational arithmetic, not rounded decimals.
• S156 · premise_and_result_audit — Recompute Exp convolution left10 factorial step1 with exact rational arithmetic, not rounded decimals.
• S155 · premise_and_result_audit — Recompute Exp convolution numerator10 with exact rational arithmetic, not rounded decimals.
• S154 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S153 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S152 · premise_and_result_audit — Recompute Exp convolution coefficient term9 with exact rational arithmetic, not rounded decimals.
• S151 · premise_and_result_audit — Recompute Exp convolution denominator9 with exact rational arithmetic, not rounded decimals.
• S150 · premise_and_result_audit — Recompute Exp convolution right9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S149 · premise_and_result_audit — Recompute Exp convolution left9 factorial step9 with exact rational arithmetic, not rounded decimals.
• S148 · premise_and_result_audit — Recompute Exp convolution left9 factorial step8 with exact rational arithmetic, not rounded decimals.
• S147 · premise_and_result_audit — Recompute Exp convolution left9 factorial step7 with exact rational arithmetic, not rounded decimals.
• S146 · premise_and_result_audit — Recompute Exp convolution left9 factorial step6 with exact rational arithmetic, not rounded decimals.
• S145 · premise_and_result_audit — Recompute Exp convolution left9 factorial step5 with exact rational arithmetic, not rounded decimals.
• S144 · premise_and_result_audit — Recompute Exp convolution left9 factorial step4 with exact rational arithmetic, not rounded decimals.
• S143 · premise_and_result_audit — Recompute Exp convolution left9 factorial step3 with exact rational arithmetic, not rounded decimals.
• S142 · premise_and_result_audit — Recompute Exp convolution left9 factorial step2 with exact rational arithmetic, not rounded decimals.
• S141 · premise_and_result_audit — Recompute Exp convolution left9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S140 · premise_and_result_audit — Recompute Exp convolution numerator9 with exact rational arithmetic, not rounded decimals.
• S139 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S138 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S137 · premise_and_result_audit — Recompute Exp convolution coefficient term8 with exact rational arithmetic, not rounded decimals.
• S136 · premise_and_result_audit — Recompute Exp convolution denominator8 with exact rational arithmetic, not rounded decimals.
• S135 · premise_and_result_audit — Recompute Exp convolution right8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S134 · premise_and_result_audit — Recompute Exp convolution right8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S133 · premise_and_result_audit — Recompute Exp convolution left8 factorial step8 with exact rational arithmetic, not rounded decimals.
• S132 · premise_and_result_audit — Recompute Exp convolution left8 factorial step7 with exact rational arithmetic, not rounded decimals.
• S131 · premise_and_result_audit — Recompute Exp convolution left8 factorial step6 with exact rational arithmetic, not rounded decimals.
• S130 · premise_and_result_audit — Recompute Exp convolution left8 factorial step5 with exact rational arithmetic, not rounded decimals.
• S129 · premise_and_result_audit — Recompute Exp convolution left8 factorial step4 with exact rational arithmetic, not rounded decimals.
• S128 · premise_and_result_audit — Recompute Exp convolution left8 factorial step3 with exact rational arithmetic, not rounded decimals.
• S127 · premise_and_result_audit — Recompute Exp convolution left8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S126 · premise_and_result_audit — Recompute Exp convolution left8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S125 · premise_and_result_audit — Recompute Exp convolution numerator8 with exact rational arithmetic, not rounded decimals.
• S124 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S123 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S122 · premise_and_result_audit — Recompute Exp convolution coefficient term7 with exact rational arithmetic, not rounded decimals.
• S121 · premise_and_result_audit — Recompute Exp convolution denominator7 with exact rational arithmetic, not rounded decimals.
• S120 · premise_and_result_audit — Recompute Exp convolution right7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S119 · premise_and_result_audit — Recompute Exp convolution right7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S118 · premise_and_result_audit — Recompute Exp convolution right7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S117 · premise_and_result_audit — Recompute Exp convolution left7 factorial step7 with exact rational arithmetic, not rounded decimals.
• S116 · premise_and_result_audit — Recompute Exp convolution left7 factorial step6 with exact rational arithmetic, not rounded decimals.
• S115 · premise_and_result_audit — Recompute Exp convolution left7 factorial step5 with exact rational arithmetic, not rounded decimals.
• S114 · premise_and_result_audit — Recompute Exp convolution left7 factorial step4 with exact rational arithmetic, not rounded decimals.
• S113 · premise_and_result_audit — Recompute Exp convolution left7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S112 · premise_and_result_audit — Recompute Exp convolution left7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S111 · premise_and_result_audit — Recompute Exp convolution left7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S110 · premise_and_result_audit — Recompute Exp convolution numerator7 with exact rational arithmetic, not rounded decimals.
• S109 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S108 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S107 · premise_and_result_audit — Recompute Exp convolution coefficient term6 with exact rational arithmetic, not rounded decimals.
• S106 · premise_and_result_audit — Recompute Exp convolution denominator6 with exact rational arithmetic, not rounded decimals.
• S105 · premise_and_result_audit — Recompute Exp convolution right6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S104 · premise_and_result_audit — Recompute Exp convolution right6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S103 · premise_and_result_audit — Recompute Exp convolution right6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S102 · premise_and_result_audit — Recompute Exp convolution right6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S101 · premise_and_result_audit — Recompute Exp convolution left6 factorial step6 with exact rational arithmetic, not rounded decimals.
• S100 · premise_and_result_audit — Recompute Exp convolution left6 factorial step5 with exact rational arithmetic, not rounded decimals.
• S099 · premise_and_result_audit — Recompute Exp convolution left6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S098 · premise_and_result_audit — Recompute Exp convolution left6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S097 · premise_and_result_audit — Recompute Exp convolution left6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S096 · premise_and_result_audit — Recompute Exp convolution left6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S095 · premise_and_result_audit — Recompute Exp convolution numerator6 with exact rational arithmetic, not rounded decimals.
• S094 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S093 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S092 · premise_and_result_audit — Recompute Exp convolution coefficient term5 with exact rational arithmetic, not rounded decimals.
• S091 · premise_and_result_audit — Recompute Exp convolution denominator5 with exact rational arithmetic, not rounded decimals.
• S090 · premise_and_result_audit — Recompute Exp convolution right5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S089 · premise_and_result_audit — Recompute Exp convolution right5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S088 · premise_and_result_audit — Recompute Exp convolution right5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S087 · premise_and_result_audit — Recompute Exp convolution right5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S086 · premise_and_result_audit — Recompute Exp convolution right5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S085 · premise_and_result_audit — Recompute Exp convolution left5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S084 · premise_and_result_audit — Recompute Exp convolution left5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S083 · premise_and_result_audit — Recompute Exp convolution left5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S082 · premise_and_result_audit — Recompute Exp convolution left5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S081 · premise_and_result_audit — Recompute Exp convolution left5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S080 · premise_and_result_audit — Recompute Exp convolution numerator5 with exact rational arithmetic, not rounded decimals.
• S079 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S078 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S077 · premise_and_result_audit — Recompute Exp convolution coefficient term4 with exact rational arithmetic, not rounded decimals.
• S076 · premise_and_result_audit — Recompute Exp convolution denominator4 with exact rational arithmetic, not rounded decimals.
• S075 · premise_and_result_audit — Recompute Exp convolution right4 factorial step6 with exact rational arithmetic, not rounded decimals.
• S074 · premise_and_result_audit — Recompute Exp convolution right4 factorial step5 with exact rational arithmetic, not rounded decimals.
• S073 · premise_and_result_audit — Recompute Exp convolution right4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S072 · premise_and_result_audit — Recompute Exp convolution right4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S071 · premise_and_result_audit — Recompute Exp convolution right4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S070 · premise_and_result_audit — Recompute Exp convolution right4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S069 · premise_and_result_audit — Recompute Exp convolution left4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S068 · premise_and_result_audit — Recompute Exp convolution left4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S067 · premise_and_result_audit — Recompute Exp convolution left4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S066 · premise_and_result_audit — Recompute Exp convolution left4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S065 · premise_and_result_audit — Recompute Exp convolution numerator4 with exact rational arithmetic, not rounded decimals.
• S064 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S063 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S062 · premise_and_result_audit — Recompute Exp convolution coefficient term3 with exact rational arithmetic, not rounded decimals.
• S061 · premise_and_result_audit — Recompute Exp convolution denominator3 with exact rational arithmetic, not rounded decimals.
• S060 · premise_and_result_audit — Recompute Exp convolution right3 factorial step7 with exact rational arithmetic, not rounded decimals.
• S059 · premise_and_result_audit — Recompute Exp convolution right3 factorial step6 with exact rational arithmetic, not rounded decimals.
• S058 · premise_and_result_audit — Recompute Exp convolution right3 factorial step5 with exact rational arithmetic, not rounded decimals.
• S057 · premise_and_result_audit — Recompute Exp convolution right3 factorial step4 with exact rational arithmetic, not rounded decimals.
• S056 · premise_and_result_audit — Recompute Exp convolution right3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S055 · premise_and_result_audit — Recompute Exp convolution right3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S054 · premise_and_result_audit — Recompute Exp convolution right3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S053 · premise_and_result_audit — Recompute Exp convolution left3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S052 · premise_and_result_audit — Recompute Exp convolution left3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S051 · premise_and_result_audit — Recompute Exp convolution left3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S050 · premise_and_result_audit — Recompute Exp convolution numerator3 with exact rational arithmetic, not rounded decimals.
• S049 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S048 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S047 · premise_and_result_audit — Recompute Exp convolution coefficient term2 with exact rational arithmetic, not rounded decimals.
• S046 · premise_and_result_audit — Recompute Exp convolution denominator2 with exact rational arithmetic, not rounded decimals.
• S045 · premise_and_result_audit — Recompute Exp convolution right2 factorial step8 with exact rational arithmetic, not rounded decimals.
• S044 · premise_and_result_audit — Recompute Exp convolution right2 factorial step7 with exact rational arithmetic, not rounded decimals.
• S043 · premise_and_result_audit — Recompute Exp convolution right2 factorial step6 with exact rational arithmetic, not rounded decimals.
• S042 · premise_and_result_audit — Recompute Exp convolution right2 factorial step5 with exact rational arithmetic, not rounded decimals.
• S041 · premise_and_result_audit — Recompute Exp convolution right2 factorial step4 with exact rational arithmetic, not rounded decimals.
• S040 · premise_and_result_audit — Recompute Exp convolution right2 factorial step3 with exact rational arithmetic, not rounded decimals.
• S039 · premise_and_result_audit — Recompute Exp convolution right2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S038 · premise_and_result_audit — Recompute Exp convolution right2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S037 · premise_and_result_audit — Recompute Exp convolution left2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S036 · premise_and_result_audit — Recompute Exp convolution left2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S035 · premise_and_result_audit — Recompute Exp convolution numerator2 with exact rational arithmetic, not rounded decimals.
• S034 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S033 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S032 · premise_and_result_audit — Recompute Exp convolution coefficient term1 with exact rational arithmetic, not rounded decimals.
• S031 · premise_and_result_audit — Recompute Exp convolution denominator1 with exact rational arithmetic, not rounded decimals.
• S030 · premise_and_result_audit — Recompute Exp convolution right1 factorial step9 with exact rational arithmetic, not rounded decimals.
• S029 · premise_and_result_audit — Recompute Exp convolution right1 factorial step8 with exact rational arithmetic, not rounded decimals.
• S028 · premise_and_result_audit — Recompute Exp convolution right1 factorial step7 with exact rational arithmetic, not rounded decimals.
• S027 · premise_and_result_audit — Recompute Exp convolution right1 factorial step6 with exact rational arithmetic, not rounded decimals.
• S026 · premise_and_result_audit — Recompute Exp convolution right1 factorial step5 with exact rational arithmetic, not rounded decimals.
• S025 · premise_and_result_audit — Recompute Exp convolution right1 factorial step4 with exact rational arithmetic, not rounded decimals.
• S024 · premise_and_result_audit — Recompute Exp convolution right1 factorial step3 with exact rational arithmetic, not rounded decimals.
• S023 · premise_and_result_audit — Recompute Exp convolution right1 factorial step2 with exact rational arithmetic, not rounded decimals.
• S022 · premise_and_result_audit — Recompute Exp convolution right1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S021 · premise_and_result_audit — Recompute Exp convolution left1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S020 · premise_and_result_audit — Recompute Exp convolution numerator1 with exact rational arithmetic, not rounded decimals.
• S019 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S018 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S017 · premise_and_result_audit — Recompute Exp convolution coefficient term0 with exact rational arithmetic, not rounded decimals.
• S016 · premise_and_result_audit — Recompute Exp convolution denominator0 with exact rational arithmetic, not rounded decimals.
• S015 · premise_and_result_audit — Recompute Exp convolution right0 factorial step10 with exact rational arithmetic, not rounded decimals.
• S014 · premise_and_result_audit — Recompute Exp convolution right0 factorial step9 with exact rational arithmetic, not rounded decimals.
• S013 · premise_and_result_audit — Recompute Exp convolution right0 factorial step8 with exact rational arithmetic, not rounded decimals.
• S012 · premise_and_result_audit — Recompute Exp convolution right0 factorial step7 with exact rational arithmetic, not rounded decimals.
• S011 · premise_and_result_audit — Recompute Exp convolution right0 factorial step6 with exact rational arithmetic, not rounded decimals.
• S010 · premise_and_result_audit — Recompute Exp convolution right0 factorial step5 with exact rational arithmetic, not rounded decimals.
• S009 · premise_and_result_audit — Recompute Exp convolution right0 factorial step4 with exact rational arithmetic, not rounded decimals.
• S008 · premise_and_result_audit — Recompute Exp convolution right0 factorial step3 with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Recompute Exp convolution right0 factorial step2 with exact rational arithmetic, not rounded decimals.
• S006 · premise_and_result_audit — Recompute Exp convolution right0 factorial step1 with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S004 · premise_and_result_audit — Recompute Exp convolution numerator0 with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(11/12, -12/13, 10, [[0, 2985984/24125236073575], [1, -456192/371157478055], [2, 156816/28550575235], [3, -31944/2196198095], [4, 14641/579217080], [5, -161051/5346619200], [6, 1771561/71068907520], [7, -19487171/1377643438080], [8, 214358881/40693467709440], [9, -2357947691/2028412851978240], [10, 25937424601/224685731296051200]], 1/30974836056463278561086668800, 1/30974836056463278561086668800, Yes, binomial_convolution_matches_the_declared_degree;the_general_addition_law_requires_all_degrees_plus_absolute_convergence_for_Cauchy_product_rearrangement)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.