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R0024-12650 · q-20261013-advance-20261026-r02-real-normed-vector-space-0025
Only the named real-coordinate formulas l1(v)=sum_i |v_i| and linfinity(v)=max_i |v_i| are supported here. Their universal algebraic certificates, not a finite sample, supply the norm axioms. An unsupported name is outside this protocol, not a claim that every other formula fails to be a norm. Integer vector=[12, 7, 7, 2]. Give (vector,norm_name,value).
G001 — Only the named real-coordinate formulas l1(v)=sum_i |v_i| and linfinity(v)=max_i |v_i| are supported here. Their universal algebraic certificates, not a finite sample, supply the norm axioms. An unsupported name is outside this protocol, not a claim that every other formula fails to be a norm. Integer vector=[12, 7, 7, 2]. Give (vector,norm_name,value).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
given vector:coordinate=0;signed value=12
After
absolute value=12
Conditions: none
Take the absolute value of each entire coordinate.Negative coordinates are not summed or maximized as signed values;retain the original signed vector.
Rule: named_norm_each_coordinate_absolute_value · Uses: G001
Before
given vector:coordinate=1;signed value=7
After
absolute value=7
Conditions: none
Take the absolute value of each entire coordinate.Negative coordinates are not summed or maximized as signed values;retain the original signed vector.
Rule: named_norm_each_coordinate_absolute_value · Uses: G001, S001
Before
given vector:coordinate=2;signed value=7
After
absolute value=7
Conditions: none
Take the absolute value of each entire coordinate.Negative coordinates are not summed or maximized as signed values;retain the original signed vector.
Rule: named_norm_each_coordinate_absolute_value · Uses: G001, S002
Before
given vector:coordinate=3;signed value=2
After
absolute value=2
Conditions: none
Take the absolute value of each entire coordinate.Negative coordinates are not summed or maximized as signed values;retain the original signed vector.
Rule: named_norm_each_coordinate_absolute_value · Uses: G001, S003
Before
given vector l1 sum := sum(12, 7, 7, 2)
After
given vector l1 sum = 28
Conditions: none
Compute exactly from the original roles and complete established operands,without changing pairings,order or replacing guards by approximation.
Rule: exact_rational_arithmetic · Uses: G001, S004
S005 · premise_and_result_audit — Recompute given vector l1 sum with exact rational arithmetic, not rounded decimals.S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.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.([12, 7, 7, 2], l1, 28)
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: bf46b3afa872d58fdd91bf4702be77c3123b4ec2ec0db60eb49dbfb598aba968candidate record SHA-256: 831e2e3133cf6b633efddf7242f795d3bf545828a3c08fc7785b5d3e96effcc8semantic review receipt SHA-256: 1c8f6c2c6c75852cb93c08235684ce9f32ebe86065c58c693a04257e772c2d35question-first witness SHA-256: 05fd764b5f9f7fff6185003efe576d87632f6daf40606ac3839a7feafe4f80d8Lean: NOT_RUN · human review: NOT_PERFORMED