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R0058-29513 · q-20261013-advance-20261022-r02-present-value-discounting-0088
Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=136/1, periods=0, nonnegative candidate=137/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
G001 — Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=136/1, periods=0, nonnegative candidate=137/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).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.
Before
source roles = [qf-str22-presentvalue-candidate-audit, presentvalue-candidate-audit]
After
derived = [[future, rate, periods, present, candidate, matches]]
Conditions: none
Follow THIS bank exact keys,domain/frame,operation and answer role.STR22/App20 tuples differ from legacy scalars;retain or omit/1 by the ORIGINAL contract,not a generic visual convention.
Rule: R58_EXACT_source_interface_and_answer_ROLE · Uses: G001
Before
source roles = [Present value rate, [0, 1]]
After
derived = [0]
Conditions: none
Check BOTH raw pair components within1e6 and nonzero denominator BEFORE sign/gcd normalization.This STR22 profile must not be imposed on legacy SAFE/BigInt tasks.
Rule: STR22_input_RAW_pair1e6_before_sign_gcd_normalization · Uses: G001, S001
Before
Present value ORIGINAL positive accumulation factor := sum(1, 0)
After
Present value ORIGINAL positive accumulation factor = 1
Conditions: none
Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
source roles = [Present value ORIGINAL positive accumulation factor, sum, [1, 0]]
After
derived = [[1], [1, 1], 1]
Conditions: none
SOURCE addition first uses denominator gcd,and multiplication cross-cancels.Check BOTH resulting raw components within1e6 BEFORE final reduction.Division qualifies the nonzero reciprocal.Do not substitute another bank profile or loosen a source hold.
Rule: STR22_SOURCE_gcd_crosscancel_THEN_raw1e6_BEFORE_final_reduction · Uses: G001, S003
Before
source roles = [0, 1]
After
derived = [Yes]
Conditions: none
Use the SAME fixed per-period rate/period convention without cash flows,fees,taxes or rounding.Require1+rate>0;the rate may be negative.This is not a market forecast or investment advice.
Rule: Present_value_FIXED_model_same_rate_period_NOcashflows · Uses: G001, S004
Before
source roles = [1, 0]
After
derived = [1, 1, 0, out*base^exp=factor^n]
Conditions: none
Initialize out=1,base=factor,exp=n with invariant out*base^exp=factor^n.At n=0 return the empty product1,but STILL qualify the original factor.
Rule: Present_value_BINARY_power_initial_emptyproduct_invariant · Uses: G001, S005
Before
source roles = [Present value future, [136, 1]]
After
derived = [136]
Conditions: none
Check BOTH raw pair components within1e6 and nonzero denominator BEFORE sign/gcd normalization.This STR22 profile must not be imposed on legacy SAFE/BigInt tasks.
Rule: STR22_input_RAW_pair1e6_before_sign_gcd_normalization · Uses: G001, S006
Before
Present value ORIGINAL future over actual binary accumulation := div(136, 1)
After
Present value ORIGINAL future over actual binary accumulation = 136
Conditions: none
Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.
Rule: exact_rational_arithmetic · Uses: G001, S007
Before
source roles = [Present value ORIGINAL future over actual binary accumulation, div, [136, 1]]
After
derived = [[1, 1], [136, 1], 136]
Conditions: none
SOURCE addition first uses denominator gcd,and multiplication cross-cancels.Check BOTH resulting raw components within1e6 BEFORE final reduction.Division qualifies the nonzero reciprocal.Do not substitute another bank profile or loosen a source hold.
Rule: STR22_SOURCE_gcd_crosscancel_THEN_raw1e6_BEFORE_final_reduction · Uses: G001, S008
Before
source roles = [136, 0, 0, 1]
After
derived = [136]
Conditions: none
The accumulation is n copies of the SAME factor;divide future by its positive value.At n=0 preserve the amount.Do not add unspecified cash flows or charges.
Rule: Present_value_Nperiod_exact_discount_NOT_unlisted_adjustments · Uses: G001, S009
Before
source roles = [Present value candidate, [137, 1]]
After
derived = [137]
Conditions: none
Check BOTH raw pair components within1e6 and nonzero denominator BEFORE sign/gcd normalization.This STR22 profile must not be imposed on legacy SAFE/BigInt tasks.
Rule: STR22_input_RAW_pair1e6_before_sign_gcd_normalization · Uses: G001, S010
Before
source roles = [136, 137]
After
derived = [No]
Conditions: none
Compare the NORMALIZED exact rational values,not raw pair spelling.Do not repair a mismatch by changing future,rate or period.
Rule: Present_value_candidate_NORMALIZED_exact_equality · Uses: G001, S011
S012 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S011 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S010 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S009 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S008 · premise_and_result_audit — Recompute Present value ORIGINAL future over actual binary accumulation with exact rational arithmetic, not rounded decimals.S007 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S006 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S005 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S004 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S003 · premise_and_result_audit — Recompute Present value ORIGINAL positive accumulation factor with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.S001 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.(136, 0, 0, 136, 137, No)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 74dd158120143224345374cb7522b303186dc8ccedaa0adefd08d8e64fdbca2fcandidate record SHA-256: 3147ff2ea51fc98d10419a5417429c650eb1554940b6b2a06bd38f87e0515e39semantic review receipt SHA-256: 66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05dfquestion-first witness SHA-256: b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7Lean: NOT_RUN · human review: NOT_PERFORMED