evolution_verdict tool v0.1 (STEP 1514)

evolution_verdict tool v0.1

STEP: 1514 / 公開日: 2026-08-28 / Test: 22/22 PASS / Lean 4: 5 theorem zero sorry / Type: STEP 1501 生物学 arc candidate #1 実装 (biology domain 未着手 first)

❶ Population 系列 → 進化 verdict: 絶滅 → ZERO / 定常 → SELF⟲ (★ 自己複製 fixpoint) / 減少 → FALSE / 指数増加 → INFINITY / adaptive 増加 → TRUE / 揺動 → NEITHER。

❷ SELF⟲ 生物学的実現: pop_next = pop_curr = 自己複製 fixpoint、 D-FUMT₈ SELF⟲ 領域 8 統一 (Lawvere/Tang Nano/Halting/feedback/Nash/**進化**/metacognition/Liar) の生物領域実装。

❸ 9 姉妹 verdict tool 目 (biology domain 未着手 first)。

決定表 (8 case)

#	Condition	Verdict	Reason
1	empty or length < 2	NEITHER	insufficient_series
2	negative value	NEITHER	negative_population
3	final = 0	ZERO	extinction_completed
4	all equal non-zero	SELF ★	evolution_stationary
5	strictly decreasing	FALSE	decline_extinction_progressing
6	any step ≥ 2× (default)	INFINITY	population_explosion
7	monotone increasing (非指数)	TRUE	adaptive_growth
8	mixed/oscillating	NEITHER	fluctuating_population

Condition

Verdict

Reason

empty or length < 2

NEITHER

insufficient_series

negative value

NEITHER

negative_population

final = 0

ZERO

extinction_completed

all equal non-zero

SELF ★

evolution_stationary

strictly decreasing

FALSE

decline_extinction_progressing

any step ≥ 2× (default)

INFINITY

population_explosion

monotone increasing (非指数)

TRUE

adaptive_growth

mixed/oscillating

NEITHER

fluctuating_population

使用例

evolutionVerdict({ populations: [100, 50, 20, 0] }) // { verdict: 'ZERO', reason: 'extinction_completed' } evolutionVerdict({ populations: [50, 50, 50, 50] }) // { verdict: 'SELF', reason: 'evolution_stationary' } ★ 自己複製 fixpoint evolutionVerdict({ populations: [10, 20, 40, 80] }) // { verdict: 'INFINITY', reason: 'population_explosion', maxRatio: 2 } evolutionVerdict({ populations: [10, 12, 14, 16] }) // { verdict: 'TRUE', reason: 'adaptive_growth' } evolutionVerdict({ populations: [10, 15, 45], explosionRatio: 3 }) // { verdict: 'INFINITY', reason: 'population_explosion' }

Lean 4 (5 theorem zero sorry)

evo_extinction_gives_zero : curr=0 → ZERO evo_stationary_gives_self : curr=prev>0 → SELF ★ evo_decline_gives_false : curr

Test coverage (22/22 PASS)

Guard 4 + ZERO 3 + SELF 3 + FALSE 3 + INFINITY 5 + TRUE 2 + NEITHER 1 + Determinism 1

Honest scope

❶ 実数 population dynamics (logistic dP/dt = rP(1-P/K)) 未 embed。 Nat 上離散時間系列のみ。

❷ Fisher's fundamental theorem / fitness landscape 未 embed。 size 変化のみ判定。

❸ 「世界初」なし = Darwin 1859 / Malthus 指数増加既知構造の D-FUMT₈ 再表現。

❹ 累計 defer 43 → 42 (本 tool 実装)。