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R0004-02560 · q-20261013-advance-20261021-r03-orbit-fixed-periodic-0085
Use the complete finite self-map on Fin(8)={0,…,7}, T(x)=(a*x+b) mod 8, a=-1, b=1. Take least nonnegative residues even for negative a*x+b. Fixed points, return times and least positive periods are different notions; the conclusion concerns this finite model only. Positive period bound=4. Give (modulus,a,b,bound,every [point,least period or nonperiodic-point] row in point order,points whose least positive period is at most the bound).
G001 — Use the complete finite self-map on Fin(8)={0,…,7}, T(x)=(a*x+b) mod 8, a=-1, b=1. Take least nonnegative residues even for negative a*x+b. Fixed points, return times and least positive periods are different notions; the conclusion concerns this finite model only. Positive period bound=4. Give (modulus,a,b,bound,every [point,least period or nonperiodic-point] row in point order,points whose least positive period is at most the bound).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
n=8; a=-1; b=1
After
S={0,...,7}; T(z)=(a·z+b) mod nConditions: none
Remainders lie in0,...,n−1,so every state has one successor in the same finite set;negative dividends do not produce negative canonical remainders.
Rule: finite_self_map · Uses: G001
Before
start=0
After
record each state before its first successor calculation
Conditions: none
Start with the specified point itself,not its first successor.
Rule: orbit_initial_state · Uses: G001, S001
Before
point0 step1 product := mul(-1, 0)
After
point0 step1 product = 0
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
point0 step1 affine value := sum(0, 1)
After
point0 step1 affine value = 1
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
Euclidean division of 1 by 8
After
1=0·8+1
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S004
Before
point0 step2 product := mul(-1, 1)
After
point0 step2 product = -1
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S005
Before
point0 step2 affine value := sum(-1, 1)
After
point0 step2 affine value = 0
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S006
Before
Euclidean division of 0 by 8
After
0=0·8+0
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S007
Before
distinct trace=[0, 1]; first repeated state=0
After
cycle_start=0; starting-point least period=2
Conditions: none
The first repeated state locates the cycle entry.If it is the initial point,the preceding states are distinct,so the first return is the least positive period.If entry is later,the initial point lies outside the cycle and never returns.
Rule: finite_orbit_certificate · Uses: G001, S008
Before
start=1
After
record each state before its first successor calculation
Conditions: none
Start with the specified point itself,not its first successor.
Rule: orbit_initial_state · Uses: G001, S009
Before
point1 step1 product := mul(-1, 1)
After
point1 step1 product = -1
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S010
Before
point1 step1 affine value := sum(-1, 1)
After
point1 step1 affine value = 0
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S011
Before
Euclidean division of 0 by 8
After
0=0·8+0
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S012
Before
point1 step2 product := mul(-1, 0)
After
point1 step2 product = 0
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S013
Before
point1 step2 affine value := sum(0, 1)
After
point1 step2 affine value = 1
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S014
Before
Euclidean division of 1 by 8
After
1=0·8+1
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S015
Before
distinct trace=[1, 0]; first repeated state=1
After
cycle_start=0; starting-point least period=2
Conditions: none
The first repeated state locates the cycle entry.If it is the initial point,the preceding states are distinct,so the first return is the least positive period.If entry is later,the initial point lies outside the cycle and never returns.
Rule: finite_orbit_certificate · Uses: G001, S016
Before
start=2
After
record each state before its first successor calculation
Conditions: none
Start with the specified point itself,not its first successor.
Rule: orbit_initial_state · Uses: G001, S017
Before
point2 step1 product := mul(-1, 2)
After
point2 step1 product = -2
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S018
Before
point2 step1 affine value := sum(-2, 1)
After
point2 step1 affine value = -1
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S019
Before
Euclidean division of -1 by 8
After
-1=-1·8+7
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S020
Before
point2 step2 product := mul(-1, 7)
After
point2 step2 product = -7
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S021
Before
point2 step2 affine value := sum(-7, 1)
After
point2 step2 affine value = -6
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S022
Before
Euclidean division of -6 by 8
After
-6=-1·8+2
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S023
Before
distinct trace=[2, 7]; first repeated state=2
After
cycle_start=0; starting-point least period=2
Conditions: none
The first repeated state locates the cycle entry.If it is the initial point,the preceding states are distinct,so the first return is the least positive period.If entry is later,the initial point lies outside the cycle and never returns.
Rule: finite_orbit_certificate · Uses: G001, S024
Before
start=3
After
record each state before its first successor calculation
Conditions: none
Start with the specified point itself,not its first successor.
Rule: orbit_initial_state · Uses: G001, S025
Before
point3 step1 product := mul(-1, 3)
After
point3 step1 product = -3
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S026
Before
point3 step1 affine value := sum(-3, 1)
After
point3 step1 affine value = -2
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S027
Before
Euclidean division of -2 by 8
After
-2=-1·8+6
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S028
Before
point3 step2 product := mul(-1, 6)
After
point3 step2 product = -6
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S029
Before
point3 step2 affine value := sum(-6, 1)
After
point3 step2 affine value = -5
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S030
Before
Euclidean division of -5 by 8
After
-5=-1·8+3
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S031
Before
distinct trace=[3, 6]; first repeated state=3
After
cycle_start=0; starting-point least period=2
Conditions: none
The first repeated state locates the cycle entry.If it is the initial point,the preceding states are distinct,so the first return is the least positive period.If entry is later,the initial point lies outside the cycle and never returns.
Rule: finite_orbit_certificate · Uses: G001, S032
Before
start=4
After
record each state before its first successor calculation
Conditions: none
Start with the specified point itself,not its first successor.
Rule: orbit_initial_state · Uses: G001, S033
Before
point4 step1 product := mul(-1, 4)
After
point4 step1 product = -4
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S034
Before
point4 step1 affine value := sum(-4, 1)
After
point4 step1 affine value = -3
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S035
Before
Euclidean division of -3 by 8
After
-3=-1·8+5
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S036
Before
point4 step2 product := mul(-1, 5)
After
point4 step2 product = -5
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S037
Before
point4 step2 affine value := sum(-5, 1)
After
point4 step2 affine value = -4
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S038
Before
Euclidean division of -4 by 8
After
-4=-1·8+4
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S039
Before
distinct trace=[4, 5]; first repeated state=4
After
cycle_start=0; starting-point least period=2
Conditions: none
The first repeated state locates the cycle entry.If it is the initial point,the preceding states are distinct,so the first return is the least positive period.If entry is later,the initial point lies outside the cycle and never returns.
Rule: finite_orbit_certificate · Uses: G001, S040
Before
start=5
After
record each state before its first successor calculation
Conditions: none
Start with the specified point itself,not its first successor.
Rule: orbit_initial_state · Uses: G001, S041
Before
point5 step1 product := mul(-1, 5)
After
point5 step1 product = -5
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S042
Before
point5 step1 affine value := sum(-5, 1)
After
point5 step1 affine value = -4
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S043
Before
Euclidean division of -4 by 8
After
-4=-1·8+4
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S044
Before
point5 step2 product := mul(-1, 4)
After
point5 step2 product = -4
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S045
Before
point5 step2 affine value := sum(-4, 1)
After
point5 step2 affine value = -3
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S046
Before
Euclidean division of -3 by 8
After
-3=-1·8+5
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S047
Before
distinct trace=[5, 4]; first repeated state=5
After
cycle_start=0; starting-point least period=2
Conditions: none
The first repeated state locates the cycle entry.If it is the initial point,the preceding states are distinct,so the first return is the least positive period.If entry is later,the initial point lies outside the cycle and never returns.
Rule: finite_orbit_certificate · Uses: G001, S048
Before
start=6
After
record each state before its first successor calculation
Conditions: none
Start with the specified point itself,not its first successor.
Rule: orbit_initial_state · Uses: G001, S049
Before
point6 step1 product := mul(-1, 6)
After
point6 step1 product = -6
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S050
Before
point6 step1 affine value := sum(-6, 1)
After
point6 step1 affine value = -5
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S051
Before
Euclidean division of -5 by 8
After
-5=-1·8+3
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S052
Before
point6 step2 product := mul(-1, 3)
After
point6 step2 product = -3
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S053
Before
point6 step2 affine value := sum(-3, 1)
After
point6 step2 affine value = -2
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S054
Before
Euclidean division of -2 by 8
After
-2=-1·8+6
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S055
Before
distinct trace=[6, 3]; first repeated state=6
After
cycle_start=0; starting-point least period=2
Conditions: none
The first repeated state locates the cycle entry.If it is the initial point,the preceding states are distinct,so the first return is the least positive period.If entry is later,the initial point lies outside the cycle and never returns.
Rule: finite_orbit_certificate · Uses: G001, S056
Before
start=7
After
record each state before its first successor calculation
Conditions: none
Start with the specified point itself,not its first successor.
Rule: orbit_initial_state · Uses: G001, S057
Before
point7 step1 product := mul(-1, 7)
After
point7 step1 product = -7
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S058
Before
point7 step1 affine value := sum(-7, 1)
After
point7 step1 affine value = -6
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S059
Before
Euclidean division of -6 by 8
After
-6=-1·8+2
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S060
Before
point7 step2 product := mul(-1, 2)
After
point7 step2 product = -2
Conditions: none
Multiply the current state by the original coefficient a,retaining its sign.
Rule: exact_rational_arithmetic · Uses: G001, S061
Before
point7 step2 affine value := sum(-2, 1)
After
point7 step2 affine value = -1
Conditions: none
Then add the original constant b;this integer is not yet the canonical state.
Rule: exact_rational_arithmetic · Uses: G001, S062
Before
Euclidean division of -1 by 8
After
-1=-1·8+7
Conditions: none
Check the transition using quotient and nonnegative remainder;n>0 and0≤remainder<n ensure uniqueness.
Rule: orbit_successor · Uses: G001, S063
Before
distinct trace=[7, 2]; first repeated state=7
After
cycle_start=0; starting-point least period=2
Conditions: none
The first repeated state locates the cycle entry.If it is the initial point,the preceding states are distinct,so the first return is the least positive period.If entry is later,the initial point lies outside the cycle and never returns.
Rule: finite_orbit_certificate · Uses: G001, S064
Before
[[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2]]
After
least positive period≤4: [0, 1, 2, 3, 4, 5, 6, 7]
Conditions: none
Cover all n states;select only periodic points whose least positive period is at most the bound,not transient points that merely enter a cycle.
Rule: least_period_bound_filter · Uses: G001, S065
S066 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S065 · premise_and_result_audit — Replay the cycle of this fixed self-map;return or nonreturn is certified only for this complete finite model,not an unspecified system.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 — Recompute point7 step2 affine value with exact rational arithmetic, not rounded decimals.S062 · premise_and_result_audit — Recompute point7 step2 product with exact rational arithmetic, not rounded decimals.S061 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S060 · premise_and_result_audit — Recompute point7 step1 affine value with exact rational arithmetic, not rounded decimals.S059 · premise_and_result_audit — Recompute point7 step1 product with exact rational arithmetic, not rounded decimals.S058 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S057 · premise_and_result_audit — Replay the cycle of this fixed self-map;return or nonreturn is certified only for this complete finite model,not an unspecified system.S056 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S055 · premise_and_result_audit — Recompute point6 step2 affine value with exact rational arithmetic, not rounded decimals.S054 · premise_and_result_audit — Recompute point6 step2 product with exact rational arithmetic, not rounded decimals.S053 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S052 · premise_and_result_audit — Recompute point6 step1 affine value with exact rational arithmetic, not rounded decimals.S051 · premise_and_result_audit — Recompute point6 step1 product with exact rational arithmetic, not rounded decimals.S050 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S049 · premise_and_result_audit — Replay the cycle of this fixed self-map;return or nonreturn is certified only for this complete finite model,not an unspecified system.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 point5 step2 affine value with exact rational arithmetic, not rounded decimals.S046 · premise_and_result_audit — Recompute point5 step2 product with exact rational arithmetic, not rounded decimals.S045 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S044 · premise_and_result_audit — Recompute point5 step1 affine value with exact rational arithmetic, not rounded decimals.S043 · premise_and_result_audit — Recompute point5 step1 product with exact rational arithmetic, not rounded decimals.S042 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S041 · premise_and_result_audit — Replay the cycle of this fixed self-map;return or nonreturn is certified only for this complete finite model,not an unspecified system.S040 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S039 · premise_and_result_audit — Recompute point4 step2 affine value with exact rational arithmetic, not rounded decimals.S038 · premise_and_result_audit — Recompute point4 step2 product with exact rational arithmetic, not rounded decimals.S037 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S036 · premise_and_result_audit — Recompute point4 step1 affine value with exact rational arithmetic, not rounded decimals.S035 · premise_and_result_audit — Recompute point4 step1 product 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 — Replay the cycle of this fixed self-map;return or nonreturn is certified only for this complete finite model,not an unspecified system.S032 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S031 · premise_and_result_audit — Recompute point3 step2 affine value with exact rational arithmetic, not rounded decimals.S030 · premise_and_result_audit — Recompute point3 step2 product with exact rational arithmetic, not rounded decimals.S029 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S028 · premise_and_result_audit — Recompute point3 step1 affine value with exact rational arithmetic, not rounded decimals.S027 · premise_and_result_audit — Recompute point3 step1 product with exact rational arithmetic, not rounded decimals.S026 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S025 · premise_and_result_audit — Replay the cycle of this fixed self-map;return or nonreturn is certified only for this complete finite model,not an unspecified system.S024 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S023 · premise_and_result_audit — Recompute point2 step2 affine value with exact rational arithmetic, not rounded decimals.S022 · premise_and_result_audit — Recompute point2 step2 product with exact rational arithmetic, not rounded decimals.S021 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S020 · premise_and_result_audit — Recompute point2 step1 affine value with exact rational arithmetic, not rounded decimals.S019 · premise_and_result_audit — Recompute point2 step1 product with exact rational arithmetic, not rounded decimals.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 — Replay the cycle of this fixed self-map;return or nonreturn is certified only for this complete finite model,not an unspecified system.S016 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S015 · premise_and_result_audit — Recompute point1 step2 affine value with exact rational arithmetic, not rounded decimals.S014 · premise_and_result_audit — Recompute point1 step2 product with exact rational arithmetic, not rounded decimals.S013 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S012 · premise_and_result_audit — Recompute point1 step1 affine value with exact rational arithmetic, not rounded decimals.S011 · premise_and_result_audit — Recompute point1 step1 product with exact rational arithmetic, not rounded decimals.S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S009 · premise_and_result_audit — Replay the cycle of this fixed self-map;return or nonreturn is certified only for this complete finite model,not an unspecified system.S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S007 · premise_and_result_audit — Recompute point0 step2 affine value with exact rational arithmetic, not rounded decimals.S006 · premise_and_result_audit — Recompute point0 step2 product 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 point0 step1 affine value with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Recompute point0 step1 product with exact rational arithmetic, not rounded decimals.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.(8, -1, 1, 4, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2]], [0, 1, 2, 3, 4, 5, 6, 7])
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: 0a9799b2341005ebb14d03986bb20fb5dd056c22cdc45dec07a72878ba443491candidate record SHA-256: 87868d8961494a212911275ebfc110bd6dde66fa5f85b38769733a9fa35df779semantic review receipt SHA-256: 312ae86315346b8955842a547cb2d09246e1f826755f72c2a51f042e5c7d5c56question-first witness SHA-256: 831f449ed41ff9144a290e534aa32adf7252d15b81c16ed5886a7dfd65dee70cLean: NOT_RUN · human review: NOT_PERFORMED