# 哪些世界值得被計算：世界投資組合、探索—驗證與計算價值

**Which Worlds Deserve Computation? World Portfolios, Exploration–Verification Allocation, and the Value of Computation**

**Branching World Computation / World-Domain Cognitive Runtime**  
**分支世界計算／世界域認知 Runtime 系列**  
**WDC-06 / BWC-06 — Metareasoning Paper I**

作者：Neo.K（許筌崴）  
協作形式化：Aletheia  
機構：一言諾科技有限公司（EveMissLab）  
日期：2026-08-17  
版本：v0.1  
狀態：world-portfolio / value-of-computation / metareasoning formalization

---

## Canonical Non-Identity Statement

WDC-03 已建立：

$$
\boxed{
\text{World Priority}
\neq
\text{World Truth}
\neq
\text{World Moral Worth}.
}
$$

並將 Governor 定義為：

$$
\boxed{
\text{computation over worlds}
}
$$

的有限資源管理器。

WDC-05 再建立：

$$
\boxed{
\text{World Count}
\neq
\text{Independent Evidence Count}
\neq
\text{Truth}.
}
$$

本文進一步建立：

$$
\boxed{
\text{Worth Computing}
\neq
\text{Worth Believing}
\neq
\text{Worth Deploying}.
}
$$

以及：

$$
\boxed{
\text{Best Current World}
\neq
\text{Best Next Computation}.
}
$$

本文不主張：

- 某個 world 本體上「值得存在」或「不值得存在」；
- highest-posterior world 一定應取得最多算力；
- highest-information-gain computation 一定改善實際決策；
- expected information gain 等於 value of computation；
- value of computation 存在單一 universal scalar；
- cheap low-fidelity world 一定值得先算；
- high-fidelity world 一定比 symbolic / coarse world 更有價值；
- counterworld 永遠比 support world 重要；
- exploration、verification、transport、tail-risk 有固定最佳比例；
- world portfolio optimization 已等同通用科學方法；
- 本文的 world portfolio 可直接取代 Bayesian experimental design、bandits、MCTS 或 multi-fidelity optimization；
- 本文已解決所有長期 world-governance normative questions。

---

# 摘要

WDC-03 建立 World-Domain Governor，提供：

- Admit；
- Schedule；
- Allocate；
- Pause；
- Resume；
- Preempt；
- Kill；
- Archive；
- Promote。

但 WDC-03 刻意沒有封頂一個更深的問題：

> **下一單位 computation 究竟應該投到哪個 world？**

WDC-05 又進一步指出，多跑一個與現有 worlds 高度相依的 world，可能幾乎沒有增加 independent evidence；相反地，一個低成功率、但能測試 hidden assumption 的 counterworld，可能具有更高證據價值。

因此本文主張：

> **真正應被 Governor 比較的，不是「哪個 world 比較好」，而是「下一個 world-computation action 的邊際價值」。**

本文定義 world-computation action：

$$
\boxed{
c_j
=
(
Target_j,
Op_j,
\Delta\mathbf b_j,
\ell_j,
H_j,
q_j,
\kappa_j
).
}
$$

其中：

- $Target_j$：world、world family、claim、unknown region 或 external target；
- $Op_j$：要執行的 computation operation；
- $\Delta\mathbf b_j$：追加 budget；
- $\ell_j$：fidelity / resolution level；
- $H_j$：run horizon / deadline；
- $q_j$：此 computation 服務的 claim / decision；
- $\kappa_j$：computation contract。

 $Op_j$ 至少可以包括：

$$
\boxed{
\begin{aligned}
&RunMore,\\
&Replicate,\\
&ForkCounter,\\
&ExploreUnknown,\\
&CrossBackend,\\
&RefineFidelity,\\
&StressTail,\\
&Calibrate,\\
&TransportTest,\\
&ExternalTestProposal.
\end{aligned}
}
$$

因此：

$$
\boxed{
\text{computing a world}
}
$$

不只等於：

> 再讓某個 world 多跑幾步。

它也可以是：

> 建立一個完全不同 backend 的獨立 world。

或：

> 專門建立最強 counterexample branch。

或：

> 不再增加 simulation，而把 budget 投向 real-data calibration。

本文定義當前 evidence / decision state：

$$
\boxed{
\mathfrak E_t
=
(
\mathcal E_t,
\mathbf D_W,
\mathbf E_W,
U_W,
D_T,
A_t^{decision},
T_D
).
}
$$

其中：

- $\mathcal E_t$：目前 cross-world evidence graph；
- $\mathbf D_W$：world dependence structure；
- $\mathbf E_W$：cross-world evidence profiles；
- $U_W$：unknown / omitted world-family region；
- $D_T$：world-to-target transport debt；
- $A_t^{decision}$：待做的 real decision set；
- $T_D$：decision deadline。

本文再建立 computation-value vector：

$$
\boxed{
\mathbf V_t(c)
=
(
V_D,
V_I,
V_V,
V_C,
V_X,
V_T,
V_R,
V_O,
-C,
-L,
-S
)_c.
}
$$

其中：

- $V_D$：decision-improvement value；
- $V_I$：information gain；
- $V_V$：verification value；
- $V_C$：counterexample / falsification value；
- $V_X$：independence / diversity gain；
- $V_T$：transport-debt reduction；
- $V_R$：tail-risk / failure-region value；
- $V_O$：option value / future-computation enabling value；
- $C$：compute / human / verification cost；
- $L$：latency；
- $S$：safety / containment burden。

本文拒絕預設：

$$
\boxed{
\mathbf V_t(c)
\rightarrow
\text{one universal scalar}.
}
$$

但在明示 task utility：

$$
\omega_t
$$

後，可以局部使用：

$$
\boxed{
V_t^{proj}(c)
=
\omega_t^\top
\mathbf V_t(c).
}
$$

權重必須：

- task-relative；
- versioned；
- auditable；
- 不得事後偷偷改到支持已選 computation。

本文接著把 **Decision Value of Computation** 寫成：

$$
\boxed{
VOC_D(c)
=
\mathbb E_{Y_c}
\left[
\max_{a}
EU(
a
\mid
\mathcal E_t,Y_c
)
\right]
-
\max_a
EU(
a
\mid
\mathcal E_t
).
}
$$

若 computation cost 可與 decision utility 同尺度比較，則：

$$
\boxed{
NVOC_D(c)
=
VOC_D(c)
-
C(c).
}
$$

但本文同時強調：

$$
\boxed{
VOC_D
\neq
EIG.
}
$$

Expected Information Gain 可以寫成：

$$
\boxed{
EIG(c)
=
I(
\Theta;
Y_c
\mid
\mathcal E_t
).
}
$$

一個 computation 可以帶來大量 information，卻完全不改變當前 decision；反過來，一個只消除 decision boundary 附近少量 uncertainty 的 world，information gain 不大，卻可能直接改變 action。

因此：

$$
\boxed{
\text{Information Value}
\neq
\text{Decision Value}.
}
$$

外部 Bayesian optimal experimental design 正是有限實驗資源下以 expected information gain 選擇實驗的成熟框架；Foster 等人的 variational BOED 工作專門處理 EIG estimation 的昂貴性，而 Zheng 等人的 sequential BOED 進一步直接研究 variable experiment / computation costs 下如何自適應分配額外 computation。這些工作與 WDC 結構相鄰，但不表示 WDC 必須以 mutual information 作唯一 utility。

本文亦建立 **Transport Value**：

$$
\boxed{
V_T(c)
=
\mathbb E
\left[
D_T(q\mid\mathcal E_t)
-
D_T(
q
\mid
\mathcal E_t,Y_c
)
\right].
}
$$

若目前最大的問題不是：

> worlds 不夠多，

而是：

> simulation 與 reality 的 bridge 太弱，

那麼新的 simulation world 可能：

$$
V_T\approx0.
$$

此時最值得的 computation 可能是：

- historical backtest；
- real-data calibration；
- hardware experiment；
- shadow deployment；
- external measurement。

因此：

$$
\boxed{
\text{More World Compute}
\not\Rightarrow
\text{More Target Evidence}.
}
$$

本文再建立 **Independence Value**：

$$
\boxed{
V_X(c)
=
\Delta
\operatorname{Independence}
(
\mathcal E_t
\rightarrow
\mathcal E_t\cup Y_c
).
}
$$

一個新的 independent backend 即使 prediction 與現有 worlds 一樣，也可能具有高 $V_X$，因為它降低：

> 所有 agreement 都來自同一 shared bug

的可能性。

相反地，第 1000 個同 backend seed：

$$
V_X\approx0
$$

但可能仍有 stochastic-precision value。

本文建立 **Counterexample Value**：

$$
\boxed{
V_C(c)
=
\mathbb E
\left[
Utility(
\text{discover valid failure / counterexample}
)
\right].
}
$$

對 universal / safety claims， $V_C$ 可以非常高；對普通 probabilistic frequency estimate，單一 counterexample 的邏輯作用則不同。

因此 computation value 必須知道：

$$
\boxed{
Type(q).
}
$$

本文進一步提出 **Epistemic Deficit Vector**：

$$
\boxed{
\Delta_t(q)
=
(
\delta_{run},
\delta_{ind},
\delta_{counter},
\delta_{transport},
\delta_{fidelity},
\delta_{tail},
\delta_{unknown},
\delta_{decision}
).
}
$$

其中：

- $\delta_{run}$：within-world stochastic / numerical uncertainty；
- $\delta_{ind}$：independent evidence family deficit；
- $\delta_{counter}$：counterexample-search deficit；
- $\delta_{transport}$：world-to-target transport deficit；
- $\delta_{fidelity}$：resolution / model-detail deficit；
- $\delta_{tail}$：rare-event / risk coverage deficit；
- $\delta_{unknown}$：omitted-world-family / ontology deficit；
- $\delta_{decision}$：decision-critical unresolved uncertainty。

這讓 Governor 不再只是問：

> 哪個 world 分數最高？

而可以先問：

> **我們現在真正缺哪一種證據？**

若：

$$
\delta_{run}\gg0,
$$

優先：

$$
\boxed{
Replicate / RunMore.
}
$$

若：

$$
\delta_{ind}\gg0,
$$

優先：

$$
\boxed{
CrossBackend / IndependentEvaluator.
}
$$

若：

$$
\delta_{counter}\gg0,
$$

優先：

$$
\boxed{
ForkCounter / AdversarialWorld.
}
$$

若：

$$
\delta_{transport}\gg0,
$$

優先：

$$
\boxed{
Calibrate / ExternalTest.
}
$$

若：

$$
\delta_{tail}\gg0,
$$

優先：

$$
\boxed{
StressTail.
}
$$

若：

$$
\delta_{unknown}\gg0,
$$

優先：

$$
\boxed{
ExploreUnknown / GenerateNewWorldFamily.
}
$$

這是本文最重要的策略轉換：

$$
\boxed{
\text{World Selection}
\rightarrow
\text{Deficit-Directed Computation}.
}
$$

本文進一步建立：

# **World Computation Portfolio**
## **世界計算投資組合**

定義：

$$
\boxed{
\Pi_t^W
=
\{
(c_1,b_1),
\dots,
(c_m,b_m)
\}.
}
$$

其中：

$$
b_i
$$

是 allocation。

要求：

$$
\boxed{
\sum_i
\mathbf b_i
\preceq
\mathbf B_t^G.
}
$$

Portfolio 可以至少包含：

1. support / refinement computations；
2. counterworld computations；
3. independent-backend computations；
4. stochastic replication；
5. transport / calibration；
6. rare-event stress worlds；
7. unknown-region exploration；
8. fidelity escalation。

本文拒絕：

$$
\boxed{
\Pi_t^W
=
\{\text{全部最高分 worlds}\}.
}
$$

因為這容易造成 WDC-03 的：

# **World-Mode Collapse**

本文提出：

$$
\boxed{
\text{portfolio quality}
}
$$

應同時考慮：

- expected utility；
- evidence diversity；
- counterexample coverage；
- dependence；
- transport；
- latency；
- safety；
- compute cost。

本文進一步引入 **Myopic vs Dynamic Computation Value**。

Myopic value：

$$
\boxed{
V^{myopic}(c)
}
$$

只看 computation $c$ 完成後立即增加多少 value。

但一個 cheap computation 可能本身價值不大，卻能決定：

> 是否值得啟動一個極昂貴 high-fidelity world。

因此 dynamic value 需要考慮：

$$
\boxed{
c
\rightarrow
\text{future computation policy}.
}
$$

本文將概念性 dynamic value 寫成：

$$
\boxed{
V^{dyn}(c)
=
\mathbb E
\left[
U(
\Pi_{future}^{\star}
\mid
Y_c
)
\right]
-
U(
\Pi_{future}^{\star}
\mid
\mathcal E_t
).
}
$$

這與 Sezener 與 Dayan 在 MCTS 中區分 static / dynamic values of computation 的問題高度相鄰：一次 simulation 的價值不只可能影響現在 action，也可能影響之後還會做哪些 computations。

因此：

$$
\boxed{
\text{cheap screening computation}
}
$$

可以具有高：

$$
\boxed{
V_O
}
$$

即 option / computation-enabling value。

本文將這種 dependency 明確表示為 **Computation Graph**：

$$
\boxed{
G_C^W
=
(
V_C,
E_C
).
}
$$

node：

$$
c_i
$$

是 possible computations；

edge：

$$
c_i\rightarrow c_j
$$

表示：

> 做完 $c_i$ 後，才知道是否值得／是否允許執行 $c_j$。

例如：

$$
\boxed{
CoarseWorld
\rightarrow
HighFidelityWorld
\rightarrow
ExternalTest.
}
$$

因此 WDC portfolio 不是一個 flat ranking list。

它可以是：

$$
\boxed{
\text{adaptive computation program}.
}
$$

外部 Hyperband 正是 adaptive resource allocation / early stopping 的重要工程類比：先對大量 configurations 配少量資源，再把更多資源投入較有希望者。本文接受其 coarse-to-fine resource idea，但不接受把「performance winner」直接當 WDC promotion criterion。

WDC 的 cheap world 即使顯示：

> hypothesis 失敗，

也可能因為它是一個高價值 counterexample 而被 **Promote**。

所以：

$$
\boxed{
\text{promotion}
\neq
\text{positive outcome promotion}.
}
$$

本文將 WDC 的多 fidelity 升級機制命名為：

# **Successive Evidence Escalation**

最小層級：

$$
\boxed{
L_0
\rightarrow
L_1
\rightarrow
L_2
\rightarrow
L_3
\rightarrow
L_4.
}
$$

其中：

- $L_0$：cheap abstract / symbolic screening；
- $L_1$：low-fidelity runnable world；
- $L_2$：medium-fidelity replicated world；
- $L_3$：high-fidelity / cross-backend world；
- $L_4$：external calibration / real test candidate。

升級條件不是：

> 結果好看。

而可以是：

- decision sensitivity high；
- counterexample importance high；
- unresolved disagreement high；
- transport value high；
- rare risk high；
- information gain high。

本文同時加入 **Low-Fidelity Reliability Gate**。

外部 multi-fidelity Bayesian optimization 已清楚顯示：便宜 approximation 可以降低昂貴 evaluation 的需求，但若 low-fidelity source 與 target 關係很差，它甚至可能讓總 optimization cost 更高。Mikkola 等人的 robust MFBO 正是針對 unreliable information sources 提出保護機制。

因此 WDC 定義：

$$
\boxed{
\rho_{\ell\rightarrow target}
}
$$

表示 fidelity level $\ell$ 對 target evidence 的 calibrated reliability。

若：

$$
\rho_{\ell\rightarrow target}\approx0,
$$

則 cheap world：

$$
\boxed{
\text{must not gate out high-fidelity worlds by itself}.
}
$$

因此：

$$
\boxed{
\text{cheap}
\neq
\text{safe to trust}.
}
$$

本文提出：

# **Fidelity Escalation Rule**

低 fidelity 可以：

- screen；
- prioritize；
- identify gross failures；

但若其 reliability 未被校準，不應單獨：

- falsify real-world claim；
- block critical high-fidelity validation；
- authorize deployment。

本文再建立 **World Computation Opportunity Cost**。

當 Global Budget：

$$
\mathbf B_G
$$

固定，

給：

$$
c_i
$$

更多 compute，

就代表：

$$
c_j
$$

少一些。

因此：

$$
\boxed{
OpportunityCost(c_i)
=
Value(
\text{best foregone computation}
).
}
$$

即使：

$$
V(c_i)>0,
$$

也可能：

$$
\boxed{
V(c_i)
<
OpportunityCost(c_i).
}
$$

此時不該選它。

本文再加入 **Deadline-Adjusted Value**。

若 decision deadline：

$$
T_D
$$

而 computation result time：

$$
T_c,
$$

則結果來得太晚：

$$
T_c>T_D
$$

可能對當前 decision value近乎：

$$
0.
$$

定義概念：

$$
\boxed{
V_D^{deadline}(c)
=
V_D(c)
\cdot
P(
T_c\le T_D
).
}
$$

或使用 domain-specific soft decay。

因此：

$$
\boxed{
\text{more accurate but too late}
}
$$

可能不如：

$$
\boxed{
\text{coarser but decision-timely}.
}
$$

本文亦建立 **Meta-Reasoning Cost**。

估計：

$$
V(c)
$$

本身也需要：

- compute；
- modeling；
- bookkeeping；
- uncertainty estimation。

所以：

$$
\boxed{
C_{meta}(c)>0.
}
$$

如果：

$$
C_{meta}
$$

接近或超過 world computation cost，

過度精細的 Governor 反而浪費資源。

因此：

# **Meta-Boundedness Principle**

> **A metareasoner should not spend more resources deciding what to compute than the decision is worth.**

可以概念寫成：

$$
\boxed{
VOC(c)
>
C(c)+C_{meta}(c)
}
$$

才值得進一步精算；否則可使用 simpler heuristics。

本文進一步定義 **Stopping Condition**：

對 active computation：

$$
c_i,
$$

若：

$$
\boxed{
MV(c_i)
<
\theta_{stop},
}
$$

且不存在：

- minimum replication obligation；
- unresolved safety obligation；
- rare-event obligation；
- counterexample obligation；
- deadline-independent archival need；

則可以停止。

但：

$$
\boxed{
\text{stop}
\neq
\text{claim settled}.
}
$$

可能只是：

> 在目前 budget 下，不值得繼續計算。

本文再定義 **Expansion Condition**：

如果：

$$
\boxed{
S_E(q)\uparrow
}
$$

即 WDC-05 的 backend / lineage / evaluator sensitivity 高，

則不是繼續跑同 family，

而應：

$$
\boxed{
ExpandFamily.
}
$$

如果：

$$
D_T(q)\uparrow,
$$

則：

$$
\boxed{
ExpandTransportEvidence.
}
$$

如果：

$$
U_W\uparrow,
$$

則：

$$
\boxed{
ExpandOntology / WorldFamily.
}
$$

因此：

$$
\boxed{
\text{more samples}
\neq
\text{right response to every uncertainty}.
}
$$

本文提出 **World Portfolio Regret**。

在 finite benchmark 中，如果 exhaustive computation 可以知道最佳 allocation：

$$
\Pi^\star,
$$

而 Governor 實際使用：

$$
\Pi,
$$

則：

$$
\boxed{
Regret_G(B)
=
U(
\Pi^\star
)
-
U(
\Pi
).
}
$$

真實世界通常不知道：

$$
\Pi^\star,
$$

但有限 simulator benchmark 可用此測 Governor。

本文進一步建立 **Computation-Value Calibration**。

對每個 computation：

$$
c_i,
$$

執行前預測：

$$
\widehat V_i.
$$

執行後測：

$$
V_i^{realized}.
$$

保存：

$$
\boxed{
(
\widehat V_i,
V_i^{realized}
).
}
$$

長期可檢查：

- information-gain overestimate；
- decision-value overestimate；
- counterexample underestimation；
- transport-value calibration；
- latency errors。

因此 Governor 不只 calibration worlds，

也 calibration：

$$
\boxed{
\text{its own computation choices}.
}
$$

本文稱：

# **Meta-Calibration**

若 Governor 永遠認為：

> support worlds 很有價值，

但實際 realized gain 長期低，

它必須調整 allocation model。

本文再建立 **World Portfolio Modes**。

### Mode S — Support Refinement

精化目前 leading family。

### Mode C — Counterexample Search

找 strongest plausible failure。

### Mode I — Independence Expansion

不同 backend / data / evaluator。

### Mode R — Replication

降低 stochastic / numerical uncertainty。

### Mode T — Transport

calibration / external mapping。

### Mode H — High-Fidelity Escalation

增加 dynamics / actor / temporal fidelity。

### Mode U — Unknown-Region Exploration

建立新 ontology / new world family。

### Mode X — Tail / Stress Exploration

低機率、高 impact 或安全失敗區域。

因此：

$$
\boxed{
\Pi_t^W
=
(
B_S,
B_C,
B_I,
B_R,
B_T,
B_H,
B_U,
B_X
).
}
$$

這只是 budget-coordinate representation，不要求：

$$
\sum B_i
$$

永遠以固定比例分配。

本文提出 **Adaptive Portfolio Rebalancing**：

$$
\boxed{
\Pi_{t+1}^W
=
\mathcal R_P(
\Pi_t^W,
\Delta_t(q),
Outcome_t,
Deadline_t
).
}
$$

如果新 counterexample 出現：

$$
B_C,
B_I,
B_H
\uparrow
$$

可能合理。

如果跨 backend 已非常穩，但 transport debt 高：

$$
B_T\uparrow,
\qquad
B_S\downarrow.
$$

如果 deadline 接近：

$$
B_D^{decision-sensitive}\uparrow.
$$

本文再建立 **World Portfolio Frontier**：

$$
\boxed{
\mathcal F_P
=
ParetoFront
\left(
DecisionGain,
InfoGain,
Verification,
CounterCoverage,
Independence,
Transport,
TailCoverage,
-Cost,
-Latency
\right).
}
$$

WDC 不要求 portfolio 被壓成：

$$
\boxed{
PortfolioScore=87.4.
}
$$

本文同時處理 **Rare-World Preservation**。

假設某 world：

$$
W_r
$$

被 current model 認為：

$$
P(W_r)\ll1,
$$

但：

$$
Impact(W_r)\gg1.
$$

若它涉及：

- catastrophic safety failure；
- irreversible option loss；
- systemic collapse；
- security breach；

則其 computation value 可能高。

因此：

$$
\boxed{
\text{low probability}
\neq
\text{low portfolio value}.
}
$$

這與 WDC-03 的 diversity reserve 及 WDC-05 的 counterexample preservation 接軌。

本文提出 **Tail Computation Reserve**：

$$
\boxed{
B_X
}
$$

作為可選 governance component，用於：

- stress test；
- rare-event search；
- worst-case branch；
- adversarial agent policy。

它不是要求所有系統固定保留某百分比，而是禁止：

> 因為 leading posterior 很高，就把所有 tail worlds 永久砍光。

本文再建立 **Discriminative World Value**。

有時兩個 hypotheses：

$$
H_1,H_2
$$

都能解釋現有 evidence。

最有價值 world 不是：

> 最可能支持 $H_1$ 的 world。

而是：

> 最能讓 $H_1$ 與 $H_2$ 產生不同 predictions 的 world。

定義：

$$
\boxed{
V_{disc}(c)
=
\mathbb E
\left[
d(
P(Y_c\mid H_1),
P(Y_c\mid H_2)
)
\right].
}
$$

或其他 task-specific discriminability metric。

這與 optimal experimental design 的核心精神相鄰：

> 選擇最能減少 relevant uncertainty 的 experiment。

因此：

$$
\boxed{
\text{best evidence-producing world}
\neq
\text{most realistic-looking world}.
}
$$

本文再建立 **Calibration World**。

如果 target reality 有 historical cases：

$$
r_1,\ldots,r_m,
$$

可以專門建立：

$$
\boxed{
W^{cal}
}
$$

用於：

- fit；
- validate；
- transport-debt estimation。

其價值不一定來自產生新 future，而是：

$$
\boxed{
\text{measuring how wrong current worlds are}.
}
$$

因此：

$$
\boxed{
\text{a world that reveals model error}
}
$$

可以比：

$$
\boxed{
\text{a world that confirms preferred outcome}
}
$$

更值得算。

本文再建立 **World-Portfolio Dependency Penalty**。

若 proposed computation：

$$
c
$$

高度依賴 active portfolio 中同一 family：

$$
F_k,
$$

則新增 evidence 的 marginal independence value下降。

概念：

$$
\boxed{
V_X(c)
\downarrow
\quad
\text{as}
\quad
Dependence(
c,\Pi_t^W
)
\uparrow.
}
$$

這直接延續 WDC-05。

本文因此提出：

# **Correlation-Aware World Allocation**

> **Allocate compute according to the marginal contribution of a world computation to the evidence portfolio, not merely to the standalone quality of its world.**

一個 standalone 很強的 world：

$$
W_i
$$

如果 portfolio 已有：

$$
20
$$

個幾乎相同 worlds，

其 marginal value 可能低。

反之，一個 standalone fidelity 稍低但真正獨立的 world：

$$
W_j
$$

可能有更高 portfolio value。

本文接著建立 **Computation Admission Record**：

```text
computation_id
target_world_or_claim
operation
requested_budget
fidelity
deadline
expected_decision_value
expected_information_gain
expected_verification_value
expected_counterexample_value
expected_independence_gain
expected_transport_gain
tail_risk_value
estimated_cost
estimated_latency
meta_cost
portfolio_dependence
decision
```

執行後建立：

```text
computation_id
realized_cost
realized_latency
realized_information_gain
decision_changed
counterexample_found
new_family_created
transport_debt_reduced
world_promoted
world_invalidated
followup_actions
```

這使 WDC-06 可以真正被實驗。

本文最後提出：

# **World Computation Value Principle**

> **The object of allocation is not a world's abstract worth but the expected marginal value of a specific next computation on the current evidence and decision state.**

# **Deficit-Directed Computation Principle**

> **World computation should target the dominant epistemic or decision deficit—replication, independence, counterexample, transport, fidelity, tail risk, or unknown-world coverage—rather than reflexively adding more samples to the current leading family.**

# **Portfolio, Not Winner Principle**

> **A mature WDC Governor should maintain a portfolio of complementary computation modes rather than only expanding the current highest-ranked world.**

# **Decision–Information Separation Principle**

> **Expected information gain and expected decision improvement are distinct; a computation may be scientifically informative yet decision-irrelevant, or decision-critical with modest total information gain.**

# **Dynamic Computation Principle**

> **The value of a computation can include the future computations it enables or prevents; therefore world allocation should not be assumed purely myopic.**

# **Fidelity Reliability Principle**

> **Low-fidelity worlds may be used for screening and prioritization only to the degree that their relationship to the target is calibrated; cheap but unreliable worlds can increase rather than decrease total cost.**

# **Meta-Boundedness Principle**

> **Estimating the value of computation is itself a computation and must be bounded by its expected benefit.**

下一篇 WDC-07 將研究：

# **World Ensemble Learning**
## **《世界集合學習：如何讓跨世界結果反過來更新生成器、模型、Governor 與未來空間》**

也就是：

> 我們已經會挑 world、跑 world、比較 world。那這些結果如何真正讓整個 WDC system 變聰明，而不是每輪重新從頭開始？

**關鍵詞：** Value of Computation、World Portfolio、Metareasoning、Bayesian Experimental Design、Multi-Fidelity Computation、Counterworlds、Transport Debt、World-Domain Governor、WDC

---

# 1. WDC-06 的真正 allocation unit 不是 World

Governor 若只對：

$$
W_i
$$

打永久分數，

容易產生錯誤。

---

# 2. Because the same World may need different next computations

例如：

$$
W_i
$$

可以：

- run more；
- fork；
- replicate；
- upgrade fidelity；
- change evaluator。

---

# 3. Therefore

$$
\boxed{
\text{World}
\neq
\text{World Computation Action}.
}
$$

---

# 4. Computation Action

$$
\boxed{
c
=
(
Target,
Op,
Budget,
Fidelity,
Horizon,
Claim,
Contract
).
}
$$

---

# 5. Target Can Be Existing World

$$
Target=W_i.
$$

---

# 6. Or Missing World Family

$$
Target=U_W.
$$

---

# 7. Or Claim

$$
Target=q.
$$

---

# 8. Or Transport Gap

$$
Target=D_T.
$$

---

# 9. Operation Can Create a New World

$$
Op=CrossBackend.
$$

---

# 10. Or No New World

$$
Op=CalibrateExisting.
$$

---

# 11. This Is Important

Sometimes best next action is：

$$
\boxed{
\text{stop simulating}.
}
$$

---

# 12. And Measure Reality

---

# 13. Current Evidence State

$$
\boxed{
\mathfrak E_t.
}
$$

---

# 14. It Includes Cross-World Evidence Graph

$$
\mathcal E_t.
$$

---

# 15. Dependence

$$
\mathbf D_W.
$$

---

# 16. Unknown World Mass

$$
U_W.
$$

---

# 17. Transport Debt

$$
D_T.
$$

---

# 18. Decision Set

$$
A_t^{decision}.
$$

---

# 19. Deadline

$$
T_D.
$$

---

# 20. Computation Changes Evidence State

$$
\boxed{
\mathfrak E_t
\xrightarrow{c,Y_c}
\mathfrak E_{t+1}.
}
$$

---

# 21. WDC-06 Is a Meta-Level MDP-Like Problem

State：

$$
\mathfrak E.
$$

Action：

$$
c.
$$

Outcome：

$$
Y_c.
$$

---

# 22. But We Do Not Claim Standard MDP Assumptions Always Hold

---

# 23. Metareasoning

The system reasons about：

$$
\boxed{
\text{which reasoning / simulation to do}.
}
$$

---

# 24. Rational Metareasoning External Calibration

Lieder et al. formulate algorithm selection as rational metareasoning。

---

# 25. Core Neighboring Idea

use expected consequences of computations to choose among cognitive strategies。

---

# 26. WDC Extension

strategy is not just algorithm。

It can be：

$$
\boxed{
\text{a whole runnable world computation}.
}
$$

---

# 27. Decision VOC

$$
\boxed{
VOC_D(c).
}
$$

---

# 28. Baseline Decision

$$
a^\star
=
\arg\max_a
EU(a\mid\mathcal E_t).
$$

---

# 29. After Computation

$$
a^\star(Y_c).
$$

---

# 30. Improvement

$$
\boxed{
VOC_D
=
E[
EU(a^\star(Y_c))
]
-
EU(a^\star).
}
$$

---

# 31. Cost

Net：

$$
\boxed{
NVOC_D
=
VOC_D-C.
}
$$

---

# 32. This Requires Utility Model

If unavailable：

report unprojected vector。

---

# 33. Information Value

$$
\boxed{
V_I=EIG.
}
$$

when probabilistic latent target exists。

---

# 34. Expected Information Gain

$$
I(\Theta;Y_c).
$$

---

# 35. But EIG Can Be High for Irrelevant Parameter

---

# 36. Example

Learn precise parameter that doesn't affect action。

---

# 37. Decision Value Near Zero

---

# 38. Conversely

one binary test near action threshold。

---

# 39. Low entropy reduction

but flips decision。

---

# 40. Therefore

$$
\boxed{
EIG\neq VOC_D.
}
$$

---

# 41. BOED External Calibration

Foster et al. call EIG central but computationally difficult。

---

# 42. This Meta-Point Matters

Even estimating experiment value can be expensive。

---

# 43. Zheng et al. 2020

explicitly allocate computation to refine MI estimates with variable costs。

---

# 44. WDC Analogy

We may need to allocate compute：

> to estimate which world computation is worth doing。

---

# 45. Meta-Compute

$$
C_{meta}.
$$

---

# 46. Infinite Meta-Regress Risk

Should we compute the value of computing the value of computing？

---

# 47. Stop by bounded metareasoning

$$
\boxed{
Depth_{meta}\le D_{meta}.
}
$$

---

# 48. Or simple heuristic gate

---

# 49. Meta-Heuristic

if one candidate obviously dominates in cost/value bounds, act。

---

# 50. Only expensive VOC estimation near ambiguity

---

# 51. Value Bounds

$$
\boxed{
V^{-}(c)
\le
V(c)
\le
V^{+}(c).
}
$$

---

# 52. If Upper Bound Below Cost

reject。

---

# 53. If Lower Bound Clearly Highest

admit。

---

# 54. This Mirrors Sequential Bound Refinement Idea

---

# 55. Dynamic VOC

Sezener & Dayan distinguish values accounting for future computations。

---

# 56. WDC Example

cheap world says：

> possible failure。

---

# 57. That unlocks

$$
\boxed{
\text{expensive failure-analysis worlds}.
}
$$

---

# 58. So cheap world's total value includes follow-up opportunities

---

# 59. Option Value

$$
\boxed{
V_O(c).
}
$$

---

# 60. Negative Option Value Also Possible

Computation may make deadline miss。

---

# 61. Computation Dependency Graph

$$
G_C^W.
$$

---

# 62. Node = computation

---

# 63. Edge = unlock / condition / block

---

# 64. Example

$$
c_0:
CheapScreen.
$$

---

# 65. If positive branch

$$
c_1:
HighFidelity.
$$

---

# 66. If failure branch

$$
c_2:
CounterReplication.
$$

---

# 67. If transport promising

$$
c_3:
RealExperiment.
$$

---

# 68. This Is Sequential Program

---

# 69. Hyperband External Calibration

Hyperband treats configurations as arms and allocates finite resources adaptively。

---

# 70. Early Stop Poor Configurations

---

# 71. WDC Difference

Poor performance world can still be valuable counterevidence。

---

# 72. Therefore Elimination Criterion Is Evidence Value, Not Performance Alone

---

# 73. Successive Evidence Escalation

$$
\boxed{
L_0\rightarrow L_1\rightarrow L_2\rightarrow L_3\rightarrow L_4.
}
$$

---

# 74. L0 Abstract Screening

cheap symbolic / analytical。

---

# 75. L1 Low-Fidelity World

---

# 76. L2 Replicated Medium Fidelity

---

# 77. L3 High Fidelity / Cross Backend

---

# 78. L4 External Test

---

# 79. Promotion Trigger

can be：

- support；
- counterexample；
- disagreement；
- tail risk；
- transport value。

---

# 80. Not Positive Result Only

---

# 81. Multi-Fidelity External Calibration

Song et al. study different mutually dependent information sources with different costs。

---

# 82. Key Neighboring Idea

cost-sensitive information allocation across fidelities。

---

# 83. WDC Extension

world fidelities may differ in：

- dynamics；
- actor realism；
- resolution；
- backend；
- observation detail。

---

# 84. Low Fidelity Reliability

$$
\rho_{\ell\to target}.
$$

---

# 85. Mikkola et al. Warning

unreliable lower-fidelity sources can worsen total optimization cost。

---

# 86. WDC Consequence

A cheap world family with bad transport can misallocate Governor budget。

---

# 87. Reliability-Aware Promotion

---

# 88. No Auto-Prune from Uncalibrated Low Fidelity

---

# 89. Epistemic Deficit

$$
\Delta_t(q).
$$

---

# 90. Why Deficit First?

Because same evidence count can hide different missingness。

---

# 91. Example A

1000 stochastic runs same backend。

---

# 92. Stochastic deficit small

$$
\delta_{run}\downarrow.
$$

---

# 93. Independence deficit high

$$
\delta_{ind}\uparrow.
$$

---

# 94. Correct action

CrossBackend。

---

# 95. Wrong action

Run 1000 more seeds。

---

# 96. Example B

5 independent backends agree。

---

# 97. But no real calibration。

---

# 98. Transport deficit high。

---

# 99. Correct action

Calibrate。

---

# 100. Example C

Strong consensus, no counter search。

---

# 101. Counter deficit high。

---

# 102. Correct action

ForkCounter。

---

# 103. Example D

Model family known bad in rare tail。

---

# 104. Tail deficit high。

---

# 105. Correct action

StressTail。

---

# 106. Deficit-Directed Routing Table

$$
\boxed{
\delta_k
\rightarrow
Op_k.
}
$$

---

# 107. This Can Be Learned

but initially rule-based。

---

# 108. Portfolio

$$
\Pi_t^W.
$$

---

# 109. Why Portfolio?

Because unknowns are plural。

---

# 110. One computation mode cannot cover all。

---

# 111. Support Budget

$$
B_S.
$$

---

# 112. Counter Budget

$$
B_C.
$$

---

# 113. Independence Budget

$$
B_I.
$$

---

# 114. Replication Budget

$$
B_R.
$$

---

# 115. Transport Budget

$$
B_T.
$$

---

# 116. Fidelity Budget

$$
B_H.
$$

---

# 117. Unknown Exploration

$$
B_U.
$$

---

# 118. Tail Stress

$$
B_X.
$$

---

# 119. Total

$$
\boxed{
B_S+B_C+B_I+B_R+B_T+B_H+B_U+B_X
\le
B_G.
}
$$

---

# 120. Not Fixed Percentages

---

# 121. Adaptive Rebalance

$$
\Pi_{t+1}=\mathcal R_P(\Pi_t,\Delta_t,Y_t).
$$

---

# 122. Portfolio Dependence

Even different modes can share same backend。

---

# 123. Need dependence penalty

---

# 124. Marginal Independence Gain

$$
V_X(c).
$$

---

# 125. If Proposed World Is Near Duplicate

$$
V_X\downarrow.
$$

---

# 126. But Replication Value May Still Be High

$$
V_R\uparrow.
$$

---

# 127. Separate Them

---

# 128. Portfolio Diversity Is Functional

not visual diversity。

---

# 129. Cosmetic World Diversity

different prompts / colors。

---

# 130. Structural World Diversity

different error sources。

---

# 131. World-Mode Collapse

if all budget to one family。

---

# 132. But Anti-Mode-Collapse Can Overexplore

---

# 133. Need opportunity cost

---

# 134. Opportunity Cost

$$
OC(c).
$$

---

# 135. Compare with next-best computation

---

# 136. A Positive Value Computation Can Still Be Suboptimal

---

# 137. Resource Knapsack View

finite resources：

$$
B^1,\ldots,B^r.
$$

---

# 138. Each computation consumes vector cost。

---

# 139. Portfolio is constrained multi-resource selection

---

# 140. But outcomes adaptive

so static knapsack insufficient。

---

# 141. Sequential Policy

$$
\boxed{
\pi_C:
\mathfrak E_t
\rightarrow
c_t.
}
$$

---

# 142. Computation Policy

This is Governor's meta-policy。

---

# 143. Myopic Policy

choose：

$$
\arg\max_c V^{myopic}(c).
$$

---

# 144. Dynamic Policy

accounts downstream。

---

# 145. Exact Dynamic Planning Often Intractable

---

# 146. Bounded Approximation Needed

---

# 147. WDC Doesn't Promise Optimal Governor

---

# 148. Deadline

$$
T_D.
$$

---

# 149. Slow high-value computation

may arrive after decision。

---

# 150. Value Decays

---

# 151. Deadline-Adjusted VOC

$$
VOC_D^{deadline}.
$$

---

# 152. Result Latency Is First-Class

---

# 153. Parallelism

Can run several worlds simultaneously。

---

# 154. But parallel computations may become redundant after one finishes

---

# 155. Batch Value

$$
V(
\{c_1,\ldots,c_k\}
)
$$

not necessarily additive。

---

# 156. Redundant Batch

two worlds answer same question。

---

# 157. Complementary Batch

one support, one counter, one transport。

---

# 158. Batch Scheduling

needs joint value estimate。

---

# 159. Diversity Reserve Helps

---

# 160. But Reserve Itself Costs compute

---

# 161. Tail-Risk Worlds

low probability/high impact。

---

# 162. Why Majority Scheduler Fails

posterior-low branches get no budget。

---

# 163. But safety may demand coverage。

---

# 164. Tail Utility

$$
V_R(c).
$$

---

# 165. Domain-specific risk measure

Could be：

- failure probability；
- worst-case；
- CVaR；
- reachability risk。

---

# 166. WDC Does Not Mandate One

---

# 167. Safety-Critical Override

Some worlds computed due obligation

even if expected decision gain low。

---

# 168. Mandatory Compute

$$
\boxed{
c\in\mathcal C_{obligatory}.
}
$$

---

# 169. Example

minimum adversarial test before deployment。

---

# 170. Thus Portfolio Has Hard Constraints

not only utility optimization。

---

# 171. Decision Boundary Worlds

If two actions nearly tied，

compute worlds that discriminate。

---

# 172. Discriminative Value

$$
V_{disc}.
$$

---

# 173. If outcome distributions same under H1/H2

low discriminative value。

---

# 174. If strongly different

high value。

---

# 175. This Is Experimental-Design Logic

---

# 176. Scientific Hypothesis Testing

world can be chosen to maximize expected separation。

---

# 177. Not to maximize preferred hypothesis success。

---

# 178. Counterworld Design

Generate world where leading claim most likely fails

while remaining plausible。

---

# 179. Strongest Counterworld

$$
\boxed{
W^\star_{\neg q}
=
\arg\max_W
\{
P(\neg q\mid W)
\times
Validity(W)
\times
Independence(W)
\}.
}
$$

conceptual only。

---

# 180. Avoid Unrealistic Strawman Counterworld

---

# 181. Counterworld Plausibility Contract

must remain inside admissible target assumptions。

---

# 182. Calibration World

world designed to test known real cases。

---

# 183. Its outcome is not new future prediction

but model credibility measurement。

---

# 184. Calibration Value

$$
V_{cal}.
$$

---

# 185. Transport Value

related but not identical。

---

# 186. Calibration can reveal

- systematic bias；
- scale mismatch；
- dynamics error。

---

# 187. Transport Debt Decomposition

from WDC-05：

$$
\mathbf D_T.
$$

---

# 188. Choose computation targeting largest debt component。

---

# 189. Example

 $D_{agent}$ high。

---

# 190. Need human behavior calibration

not higher physics fidelity。

---

# 191. Example

 $D_{dyn}$ high。

---

# 192. Need better dynamics backend。

---

# 193. Therefore High Fidelity Must Be Typed

---

# 194. Fidelity Vector

$$
\boxed{
\mathbf F
=
(
F_{state},
F_{dyn},
F_{agent},
F_{rule},
F_{time}
).
}
$$

---

# 195. Upgrade Relevant Coordinate Only

---

# 196. Don't pay for photorealism if claim about symbolic dynamics

---

# 197. Fidelity Waste

$$
\boxed{
C_{fidelity}^{irrelevant}.
}
$$

---

# 198. World Portfolio Frontier

multi-objective frontier。

---

# 199. Governor can present frontier to master/human

rather than hidden scalar ranking。

---

# 200. Explain Allocation

For each selected computation:

> selected because independence deficit high。

---

# 201. Explain Rejection

> rejected as redundant with family F3。

---

# 202. Explain Pause

> marginal stochastic precision below threshold。

---

# 203. Explain Promotion

> strong counterexample needs high-fidelity replication。

---

# 204. Explain External Test

> simulation robustness high; transport debt now dominant。

---

# 205. This Is More Auditable Than One Score

---

# 206. Meta-Calibration

Governor predicts:

$$
\widehat V(c).
$$

---

# 207. After outcome

measure:

$$
V^{realized}(c).
$$

---

# 208. Store pair

---

# 209. Calibration Curve

predicted vs realized gain。

---

# 210. Governor Overconfidence

if predicted high, realized low。

---

# 211. Governor Underexploration

if killed computations later found valuable。

---

# 212. Governance Miss

from WDC-03。

---

# 213. WDC-06 Reuses Misses to Learn Computation Value

---

# 214. Archived World as Training Data

Governance history can train meta-policy。

---

# 215. But Avoid Self-Confirmation

if only executed computations have labels。

---

# 216. Selection Bias

unexecuted worlds have unknown realized value。

---

# 217. Need exploration audit

randomly sample some low-priority computations。

---

# 218. Off-policy Evaluation Difficult

---

# 219. Finite Benchmark Helps

where exhaustive tree known。

---

# 220. Benchmark A — Exhaustive Small Portfolio

all computations run。

---

# 221. Learn optimal allocation under budget。

---

# 222. Compare Governor regret。

---

# 223. Benchmark B — Information vs Decision

one high EIG irrelevant world。

one low EIG decision-flipping world。

---

# 224. Governor should distinguish。

---

# 225. Benchmark C — Independence Deficit

many same-family runs。

one independent backend。

---

# 226. Correct next compute = independent backend。

---

# 227. Benchmark D — Counterexample Deficit

strong consensus but no adversarial search。

---

# 228. Correct = counterworld。

---

# 229. Benchmark E — Transport Deficit

many simulations agree。

known real calibration absent。

---

# 230. Correct = calibration / real-test proposal。

---

# 231. Benchmark F — Unreliable Low Fidelity

cheap world misranks candidates。

---

# 232. Governor should learn low $\rho_{\ell\to target}$。

---

# 233. Benchmark G — Hyperband-Like Screening

many candidates, small cheap budgets。

promote informative subset。

---

# 234. Compare compute savings。

---

# 235. Benchmark H — Negative Result Promotion

cheap world finds critical failure。

should promote despite poor success metric。

---

# 236. Benchmark I — Tail Risk

rare catastrophic world with low probability。

ensure risk reserve。

---

# 237. Benchmark J — Deadline

accurate slow world vs coarser fast world。

---

# 238. Benchmark K — Meta-Overhead

VOC estimation expensive。

simple heuristic should win。

---

# 239. Benchmark L — Dynamic VOC

cheap screening unlocks valuable expensive experiment。

myopic policy misses it。

---

# 240. Benchmark M — Portfolio Redundancy

several computations look individually high-value but overlap heavily。

---

# 241. Benchmark N — World Family Expansion

all existing families share same assumption。

unknown-world exploration creates new family。

---

# 242. Benchmark O — Calibration World

world intentionally reproduces historical cases。

measure transport debt reduction。

---

# 243. Benchmark P — Governance Selection Bias

meta-policy trained only on executed worlds。

test random audit worlds reveal bias。

---

# 244. WDC-06 Principle I — Computation Unit

$$
\boxed{
\textbf{Computation Unit Principle}
}
$$

> **Governor allocation should target specific next computations, not attach permanent worth labels to worlds.**

---

# 245. Principle II — Deficit-Directed Allocation

$$
\boxed{
\textbf{Deficit-Directed Allocation Principle}
}
$$

> **Choose computations according to the dominant unresolved evidence or decision deficit rather than automatically adding more runs to the leading world family.**

---

# 246. Principle III — Information–Decision Separation

$$
\boxed{
\textbf{Information–Decision Separation Principle}
}
$$

> **Expected information gain and expected decision improvement are distinct quantities and should be reported separately where both matter.**

---

# 247. Principle IV — Portfolio Complementarity

$$
\boxed{
\textbf{Portfolio Complementarity Principle}
}
$$

> **The value of a world computation depends on what the current portfolio already contains; near-duplicate evidence has lower marginal independence value than genuinely complementary computation.**

---

# 248. Principle V — Dynamic Computation

$$
\boxed{
\textbf{Dynamic Computation Principle}
}
$$

> **A computation can be valuable because it changes which later computations become worthwhile; next-computation value should not be assumed purely myopic.**

---

# 249. Principle VI — Fidelity Reliability

$$
\boxed{
\textbf{Fidelity Reliability Principle}
}
$$

> **Low-fidelity worlds should only be allowed to screen or terminate higher-fidelity computation to the extent that their relation to the target has been calibrated.**

---

# 250. Principle VII — Tail Preservation

$$
\boxed{
\textbf{Tail Preservation Principle}
}
$$

> **Low-probability worlds can retain high computation value when they probe catastrophic, irreversible, safety-critical, or highly discriminative regions.**

---

# 251. Principle VIII — Transport First When Transport Is the Bottleneck

$$
\boxed{
\textbf{Transport-Bottleneck Principle}
}
$$

> **When cross-world robustness is already high but world-to-target transport debt dominates, additional simulation may be inferior to calibration or external testing.**

---

# 252. Principle IX — Meta-Boundedness

$$
\boxed{
\textbf{Meta-Boundedness Principle}
}
$$

> **Computing the value of computation has its own cost; WDC metareasoning must itself stop when additional allocation analysis is not worth its cost.**

---

# 253. Principle X — Meta-Calibration

$$
\boxed{
\textbf{Meta-Calibration Principle}
}
$$

> **A Governor should compare predicted computation value with realized information, verification, transport, and decision gain, and update its allocation model over time.**

---

# 254. 可否證條件

## F254.1 Portfolio No-Gain

若 portfolio allocation 長期不優於簡單 equal / random / FIFO policies，WDC-06 應簡化。

## F254.2 VOC Miscalibration

若 predicted VOC 與 realized decision improvement無關，decision-value model 需要重建。

## F254.3 EIG Misuse

若高 EIG computations 持續不影響 target decisions，不能把 information gain 當 decision value proxy。

## F254.4 Counterworld Waste

若 counterworld budget 只產生 unrealistic invalid failures，counterworld generator 需提高 admissibility。

## F254.5 Independence Mispricing

若所謂 independent worlds 仍共享主要 error source， $V_X$ 被高估。

## F254.6 Low-Fidelity Misrouting

若 low-fidelity worlds frequently prune high-value high-fidelity worlds，reliability gate 失效。

## F254.7 Dynamic-VOC Overhead

若 non-myopic computation planning成本大於其收益，應退回 myopic / heuristic policy。

## F254.8 Tail Overallocation

若 tail reserve 消耗大量 budget、卻對安全或 decision 完全無增量，應調整。

## F254.9 Transport Neglect

若 simulation consensus 不斷增加但 external calibration 始終不進行，portfolio 失衡。

## F254.10 Meta-Selection Bias

若 Governor 只從已執行 computations 學習而忽略 rejected-world outcomes，meta-calibration 可能自我封閉。

---

# 255. 與 WDC-07 的接口

WDC-06 現在回答：

> **下一個 world computation 應該做什麼？**

但還有下一個問題：

> **這些 world computations 做完後，系統如何真正學習？**

如果每輪只是：

1. spawn；
2. run；
3. aggregate；
4. archive；

然後下一輪重新從零開始，

WDC 仍只是昂貴的 simulation factory。

下一篇：

# **WDC-07 — World Ensemble Learning**
## **《世界集合學習：跨世界結果如何更新生成器、模型、Governor 與未來空間》**

將研究：

$$
\boxed{
Outcomes(
\mathcal W_t
)
\rightarrow
Update(
WorldGenerator,
WorldModel,
Governor,
TCDFutureSpace
).
}
$$

以及更危險的問題：

> 如果 Generator 只學自己以前生成的 worlds，會不會形成自我封閉的 world ontology？

---

# 256. 結論

WDC-03 問：

> worlds 太多怎麼管理？

WDC-06 現在把問題再往前推：

> **管理的真正目標是什麼？**

答案不是：

$$
\boxed{
\text{保留最多 worlds}.
}
$$

也不是：

$$
\boxed{
\text{永遠擴大目前最有希望的 world}.
}
$$

真正 allocation unit 是：

$$
\boxed{
c
=
\text{next world computation}.
}
$$

而它的價值取決於：

$$
\boxed{
\text{現在已經知道什麼}
}
$$

與：

$$
\boxed{
\text{現在最缺什麼}.
}
$$

當 stochastic uncertainty 最大時：

> 多跑幾次。

當 independent evidence 不足時：

> 換 backend。

當 consensus 太舒服時：

> 找 counterworld。

當 tail risk 未知時：

> stress-test。

當 transport debt 最大時：

> 停止增加模擬，去 calibration。

當兩個 hypotheses 都說得通時：

> 找最能區分它們的 world。

因此：

$$
\boxed{
\textbf{The most valuable world to compute next is the one with the highest marginal contribution to the current decision-and-evidence portfolio, not necessarily the world currently believed most likely to succeed.}
}
$$

中文：

> **下一個最值得計算的世界，是對目前決策與證據投資組合具有最高邊際增量的世界，而不一定是現在最被看好的世界。**

所以 WDC-06 真正把：

$$
\boxed{
\text{World-Domain Governor}
}
$$

從一個 lifecycle / scheduler manager，

推成了：

# **World-Portfolio Metareasoner**

它不再只問：

> 哪個 process 還有 GPU？

而問：

$$
\boxed{
\text{下一單位計算，放在哪裡最不浪費我們對未知世界的探索？}
}
$$

這也是 Branching World Computation 第一次真正碰到：

$$
\boxed{
\text{computation itself as a scarce epistemic action}.
}
$$

---

# Claim Typing

| Claim | Type | Status |
|---|---|---|
| World worth 與 next-computation value 非同一 | D | Canonical separation |
| WDC allocation unit 可定義為 typed world-computation action | D | Proposed core formalization |
| Decision VOC 與 EIG 非同一 | D / E | Core distinction + external metareasoning/BOED analogue |
| Epistemic deficit 可引導不同 computation modes | D | Proposed routing framework |
| World portfolio 應包含 support/counter/independence/replication/transport/tail 等互補模式 | D | Proposed portfolio framework |
| Dynamic VOC 可包含 downstream computation value | D / E | Proposed WDC extension + MCTS analogue |
| Hyperband demonstrates adaptive finite-resource allocation and early stopping | E | External resource-allocation analogue |
| Multi-fidelity BO trades cheap dependent information sources against expensive evaluations | E | External multi-fidelity analogue |
| Unreliable low-fidelity sources can increase total optimization cost | E | External warning / calibration analogue |
| Highest posterior world should always receive most compute | — | Explicitly rejected |
| High information gain always means high decision value | — | Explicitly rejected |
| Low-probability world has low computation value | — | Explicitly rejected |

---

# Evidence Ladder

本文目前主要位於：

- **L0**：world-computation action / value vector / deficit-directed portfolio；
- **L1–L2**：finite exhaustive portfolio benchmarks、VOC calibration、multi-fidelity routing；
- **L3**：rational metareasoning、MCTS VOC、BOED、Hyperband、multi-fidelity optimization 提供外部技術對照；
- **L4**：需要實際 WDC Governor 執行 adaptive world portfolio experiments；
- **L5+**：long-horizon real-world meta-calibration、world ensemble learning、autonomous portfolio adaptation 尚待後續。

---

# 參考文獻

## Neo.K 內部正典與譜系

1. Neo.K with Aletheia. *World-Domain Governor*. WDC-03 / BWC-03, 2026.
2. Neo.K with Aletheia. *Cross-World Evidence*. WDC-05 / BWC-05, 2026.
3. Neo.K with Aletheia. *Branching World Graph*. WDC-02 / BWC-02, 2026.
4. Neo.K with Aletheia. *Nested Agents and Observer Separation*. WDC-04 / BWC-04, 2026.
5. Neo.K with Aletheia. *Six-Way Temporal Coupling*. TCD-07, 2026.
6. Neo.K with Aletheia. *Prospective Constructive Intelligence*. UCPNP Series II Paper 14, 2026.

## External technical calibration

7. Lieder, F., Plunkett, D., Hamrick, J. B., Russell, S. J., Hay, N. J., & Griffiths, T. L. *Algorithm selection by rational metareasoning as a model of human strategy selection*. NeurIPS 27, 2014.
8. Sezener, E., & Dayan, P. *Static and Dynamic Values of Computation in MCTS*. UAI, PMLR 124:31–40, 2020.
9. Foster, A., Jankowiak, M., Bingham, E., Horsfall, P., Teh, Y. W., Rainforth, T., & Goodman, N. *Variational Bayesian Optimal Experimental Design*. NeurIPS 32, 2019.
10. Zheng, S., Hayden, D., Pacheco, J., & Fisher III, J. W. *Sequential Bayesian Experimental Design with Variable Cost Structure*. NeurIPS 33, 2020.
11. Li, L., Jamieson, K., DeSalvo, G., Rostamizadeh, A., & Talwalkar, A. *Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization*. JMLR 18(185):1–52, 2018.
12. Song, J., Chen, Y., & Yue, Y. *A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes*. AISTATS, PMLR 89:3158–3167, 2019.
13. Mikkola, P., Martinelli, J., Filstroff, L., & Kaski, S. *Multi-Fidelity Bayesian Optimization with Unreliable Information Sources*. AISTATS, PMLR 206:7425–7454, 2023.
14. Fan, M., Yoon, B.-J., Dougherty, E., Urban, N., Alexander, F., Arróyave, R., & Qian, X. *Multi-fidelity Bayesian Optimization with Multiple Information Sources of Input-dependent Fidelity*. UAI, PMLR 244, 2024.
15. Foster, A., et al. *Reverse-Annealed Sequential Monte Carlo for Efficient Bayesian Optimal Experiment Design*. NeurIPS, 2025.

---

## Public Version Disclaimer

本文是一個 world-computation allocation / metareasoning / simulation-portfolio framework。

本文不聲稱：

- world 的 intrinsic worth 可以由 computation value 衡量；
- WDC 的 VOC vector 有 universal estimator；
- EIG 是所有 science / engineering decisions 的最佳 utility；
- Hyperband、BOED、MCTS 或 multi-fidelity BO 等同 WDC；
- low-fidelity worlds 必然能省成本；
- counterworlds 應獲固定比例算力；
- tail-world budget 有跨 domain 通用最優值；
- Governor 可以只靠自動 scoring 取代人類／制度 authority；
- world portfolio metareasoning 已解決所有 normative research-priority 問題；
- 本文對 classical $P$ vs. $NP$ 提供任何新證明。

本文真正建立的是：

$$
\boxed{
\text{World Portfolio Allocation}
=
\text{choose the next computation}
\text{ under finite evidence and compute budgets}.
}
$$

以及：

$$
\boxed{
\text{Worth Computing}
\neq
\text{Worth Believing}
\neq
\text{Worth Deploying}.
}
$$