PNCW Paper 03
穩定高維投影載體：從活動認知域到機器原生計算表面
Stable High-Dimensional Projection Carriers:
From Active Cognitive Domains to Machine-Native Computational Surfaces
版本：v0.1 日期：2026-08-27 系列：Projection-Native Computational World Series / 投影原生計算世界系列 定位：Series Paper 03 / Stable Carrier and Projected-Native Computation Layer 依賴：PNCW Paper 00–02、SPET Paper 00–05、HDSRC Image Carrier v0.x research line 作者： Neo.K機構： EveMissLab／一言諾科技有限公司
摘要
本文延續 Projection-Native Computational World（PNCW）Series，建立 Stable High-Dimensional Projection Carrier（穩定高維投影載體） 的形式層，處理 PNCW 在認知投影之後的下一個問題：
當 Context MMU / Dynamic TCGCT–TCGQT / Gamma 已經從總記憶世界中建立一個有限、可驗證的活動認知域 C q , t a c t i v e C_{q,t}^{active} C q , t a c t i v e
本文以 Stable Projection Epoch Theory（SPET）與 HDSRC（High-Dimensional Symbolic Relational Compilation）作為主要形式與工程來源，提出 PNCW 的 carrier layer：
C q , t a c t i v e → P r o j R e a d y E k → Φ π k P k \boxed{
C_{q,t}^{active}
\xrightarrow{\mathsf{ProjReady}}
\mathcal E_k
\xrightarrow{\Phi_{\pi_k}}
P_k
} C q , t a c t i v e ProjReady E k Φ π k P k 其中：
C q , t a c t i v e C_{q,t}^{active} C q , t a c t i v e E k \mathcal E_k E k π k \pi_k π k P k P_k P k
本文首先重申 SPET 的核心非坍縮：
State Evolution ≠ Projection Evolution \boxed{
\text{State Evolution}
\neq
\text{Projection Evolution}
} State Evolution = Projection Evolution 與：
Projection Frame = Typed, Persistent, Epoch-Bounded Computational Contract . \boxed{
\text{Projection Frame}
=
\text{Typed, Persistent, Epoch-Bounded Computational Contract}.
} Projection Frame = Typed, Persistent, Epoch-Bounded Computational Contract . 這使 HDSRC 過去觀察到的 factor-aware frame drift 不再被當成「投影算法的小誤差」，而被重新理解為：當 operator 的 region、tile、address 或 locality semantics 依賴 frame 時，未經宣告的 dynamic re-projection 會改變 operator 本身的語義。因此，同一 epoch 內的 projected-native computation 必須以固定 π k \pi_k π k
本文將 projected carrier 定義為：
P k = ⟨ A k , V k , R k , T k , L k , Q k , H k , C k ⟩ \boxed{
P_k
=
\left\langle
A_k,
V_k,
R_k,
T_k,
L_k,
Q_k,
H_k,
C_k
\right\rangle
} P k = ⟨ A k , V k , R k , T k , L k , Q k , H k , C k ⟩ 其中 A k A_k A k V k V_k V k R k R_k R k T k T_k T k L k L_k L k Q k Q_k Q k H k H_k H k C k C_k C k
因此，本文不把 HDSRC image carrier 理解為「把高維向量畫成漂亮圖片」，而是：
Image-Native Carrier = Address Space + Semantic State + Relation Structure + Computational Surface . \boxed{
\text{Image-Native Carrier}
=
\text{Address Space}
+
\text{Semantic State}
+
\text{Relation Structure}
+
\text{Computational Surface}.
} Image-Native Carrier = Address Space + Semantic State + Relation Structure + Computational Surface . 本文也吸收 HDSRC v0.8–v0.10 的工程方向，將 multi-scale spatialization、predictive materialization、cost model、uncertainty-aware fast/oracle routing、online calibration 納入 PNCW carrier selection semantics，並提出：
Projection Carrier Selection ≠ Full Candidate Materialization . \boxed{
\text{Projection Carrier Selection}
\neq
\text{Full Candidate Materialization}.
} Projection Carrier Selection = Full Candidate Materialization . 也就是 Runtime 可以先預測用哪一種 scale、carrier profile、relation representation 與 regions / tiles，而不必先把所有候選 carrier 全部生成。
本文最終建立：
Active Cognition → Stable Projection Epoch → Machine-Native Carrier → Projected-Native Computation . \boxed{
\text{Active Cognition}
\rightarrow
\text{Stable Projection Epoch}
\rightarrow
\text{Machine-Native Carrier}
\rightarrow
\text{Projected-Native Computation}.
} Active Cognition → Stable Projection Epoch → Machine-Native Carrier → Projected-Native Computation . 關鍵詞： SPET、HDSRC、Projection Carrier、Stable Frame、Projected-Native Computation、Multi-Scale Materialization、Machine-Native Image、PNCW
0. 研究目的與 claim boundary
PNCW Paper 02 已建立：
M t t o t a l → C t r e s i d e n t → O t ( q ) → C q , t a c t i v e . \boxed{
\mathcal M_t^{total}
\rightarrow
C_t^{resident}
\rightarrow
\mathcal O_t^{(q)}
\rightarrow
C_{q,t}^{active}.
} M t t o t a l → C t r es i d e n t → O t ( q ) → C q , t a c t i v e . 本文從 C q , t a c t i v e C_{q,t}^{active} C q , t a c t i v e
本文不宣稱：
HDSRC 已是 universal runtime；
所有 operator 都能 projected-native；
predictive carrier selection 對所有 workload 都優於 oracle；
image carrier 是唯一最佳 carrier；
local semantic transform 已等於 local physical commit。
1. Active Cognitive Domain
令：
C q , t a c t i v e = ⟨ O , E , V , A , P , H ⟩ . C_{q,t}^{active}
=
\left\langle
O,E,V,A,P,H
\right\rangle. C q , t a c t i v e = ⟨ O , E , V , A , P , H ⟩ . 其中可包含 active objects、typed relations、values、attention profile、provenance、history/version。它不必是一條 token sequence，也可以是 graph、matrix、symbolic state 或 hybrid domain。
2. 為什麼不能每次都重新投影？
若：
π t = B u i l d F r a m e ( S t ) , \pi_t=\mathsf{BuildFrame}(S_t), π t = BuildFrame ( S t ) , 則一次小 state mutation 可能造成：
π t + 1 ≠ π t . \pi_{t+1}\neq\pi_t. π t + 1 = π t . 如果 operator 的 tile、region、address、locality semantics 依賴 frame，就可能：
F π t ≠ F π t + 1 . \boxed{
F^{\pi_t}
\neq
F^{\pi_{t+1}}.
} F π t = F π t + 1 . 這不是單純畫面漂移，而是 operator semantic drift。
3. Stable Projection Epoch
因此建立：
E k = ⟨ S k ⋆ , σ k , π k , G k , C k , I k s p a c e , I k a t t n , C e r t k , τ k ⟩ . \boxed{
\mathcal E_k
=
\left\langle
S_k^\star,
\sigma_k,
\pi_k,
\mathcal G_k,
\mathcal C_k,
\mathcal I_k^{space},
\mathcal I_k^{attn},
\mathsf{Cert}_k,
\tau_k
\right\rangle.
} E k = ⟨ S k ⋆ , σ k , π k , G k , C k , I k s p a ce , I k a tt n , Cert k , τ k ⟩ . 在：
t ∈ [ τ k , τ k + 1 ) t\in[\tau_k,\tau_{k+1}) t ∈ [ τ k , τ k + 1 ) 要求：
π ( t ) = π k . \boxed{
\pi(t)=\pi_k.
} π ( t ) = π k . Stable 不等於 permanent。Release 之後 π k → π k + 1 \pi_k\rightarrow\pi_{k+1} π k → π k + 1
4. ContextReady 與 CarrierReady
PNCW Paper 02 有：
C o n t e x t R e a d y . \mathsf{ContextReady}. ContextReady . 本文新增：
C a r r i e r R e a d y ( C q , t a c t i v e , σ k ) . \boxed{
\mathsf{CarrierReady}
(
C_{q,t}^{active},
\sigma_k
).
} CarrierReady ( C q , t a c t i v e , σ k ) . CarrierReady 至少要求：
scope 已足夠；
required identities stable；
relation contract known；
attention profile certified；
hard spatial constraints satisfiable；
version coherent；
carrier profile compatible。
所以：
C o n t e x t R e a d y ≠ C a r r i e r R e a d y . \boxed{
\mathsf{ContextReady}
\neq
\mathsf{CarrierReady}.
} ContextReady = CarrierReady . 5. Carrier Projection
定義：
Φ π k : C q , t a c t i v e → P k . \boxed{
\Phi_{\pi_k}
:
C_{q,t}^{active}
\rightarrow
P_k.
} Φ π k : C q , t a c t i v e → P k . P k P_k P k
6. Machine-Native Carrier
本文定義：
P k = ⟨ A k , V k , R k , T k , L k , Q k , H k , C k ⟩ . \boxed{
P_k
=
\left\langle
A_k,V_k,R_k,T_k,L_k,Q_k,H_k,C_k
\right\rangle.
} P k = ⟨ A k , V k , R k , T k , L k , Q k , H k , C k ⟩ . 其中：
A k A_k A k V k V_k V k R k R_k R k T k T_k T k L k L_k L k Q k Q_k Q k H k H_k H k C k C_k C k
7. Image Carrier 不等於 Human Image
Image Carrier ≠ Human Illustration . \boxed{
\text{Image Carrier}
\neq
\text{Human Illustration}.
} Image Carrier = Human Illustration . HDSRC carrier 可以是 tiled grayscale、multi-channel plane、BigTIFF、sparse relation sidecar、attention plane、metadata plane 等。
其「image」首先是 machine-addressable carrier convention。
8. Carrier / Presentation Non-Collapse
同一：
P k P_k P k 可以有：
Π m a c h i n e ( P k ) \Pi_{machine}(P_k) Π ma c hin e ( P k ) 以及：
Π h u m a n ( P k ) . \Pi_{human}(P_k). Π h u man ( P k ) . 所以：
Carrier ≠ Presentation . \boxed{
\text{Carrier}
\neq
\text{Presentation}.
} Carrier = Presentation . 9. Carrier / Canonical State Non-Collapse
即使：
D π k ( P k ) = S k , D_{\pi_k}(P_k)=S_k, D π k ( P k ) = S k , 仍然：
Canonical State ≠ Projected Carrier . \boxed{
\text{Canonical State}
\neq
\text{Projected Carrier}.
} Canonical State = Projected Carrier . 10. Round-Trip Equivalence
最低 carrier correctness：
D π k ( Φ π k ( S ) ) = S . \boxed{
D_{\pi_k}
(
\Phi_{\pi_k}(S)
)
=
S.
} D π k ( Φ π k ( S )) = S . 但：
Round-Trip ⇏ Native Compute . \boxed{
\text{Round-Trip}
\not\Rightarrow
\text{Native Compute}.
} Round-Trip ⇒ Native Compute . 11. Projected-Native Query
Q P : P k → Y . \boxed{
Q_P:P_k\rightarrow Y.
} Q P : P k → Y . 若：
Q P ( Φ π k ( S ) ) = Q S π k ( S ) , Q_P(
\Phi_{\pi_k}(S)
)
=
Q_S^{\pi_k}(S), Q P ( Φ π k ( S )) = Q S π k ( S ) , 則為 exact projected-native query。
12. Projected-Native Transform
F P : P k → P k ′ . \boxed{
F_P:P_k\rightarrow P_k'.
} F P : P k → P k ′ . 若：
D π k ( F P ( Φ π k ( S ) ) ) = F S π k ( S ) , D_{\pi_k}
(
F_P(
\Phi_{\pi_k}(S)
)
)
=
F_S^{\pi_k}(S), D π k ( F P ( Φ π k ( S ))) = F S π k ( S ) , 則：
F P ≡ π k e x a c t F S . \boxed{
F_P\equiv_{\pi_k}^{exact}F_S.
} F P ≡ π k e x a c t F S . 13. Frame-Relative Semantics
本文使用：
F S π k F_S^{\pi_k} F S π k 而不是 context-free F S F_S F S
14. Native Operator Family
F k n a t i v e = { F : F has a valid projected implementation under π k } . \boxed{
\mathfrak F_k^{native}
=
\{
F:
F
\text{ has a valid projected implementation under }
\pi_k
\}.
} F k na t i v e = { F : F has a valid projected implementation under π k } . 15. Epoch-Safe Operator
F k e p o c h − s a f e = F k s p a c e − s a f e ∩ F k a t t n − s a f e ∩ F k s c o p e − s a f e . \boxed{
\mathcal F_k^{epoch-safe}
=
\mathcal F_k^{space-safe}
\cap
\mathcal F_k^{attn-safe}
\cap
\mathcal F_k^{scope-safe}.
} F k e p oc h − s a f e = F k s p a ce − s a f e ∩ F k a tt n − s a f e ∩ F k sco p e − s a f e . 16. Operator Signature
F = ⟨ N a m e , F r a m e T y p e , S c o p e , R e a d S e t , W r i t e S e t , D e p S e t , I n v S e t , C e r t S e t , C o s t , E f f e c t ⟩ . \boxed{
F
=
\left\langle
Name,
FrameType,
Scope,
ReadSet,
WriteSet,
DepSet,
InvSet,
CertSet,
Cost,
Effect
\right\rangle.
} F = ⟨ N am e , F r am e T y p e , S co p e , R e a d S e t , W r i t e S e t , D e pS e t , I n v S e t , C er tS e t , C os t , E f f ec t ⟩ . 17. Materialization Set
M a t S e t ( F , P k ) \boxed{
\mathsf{MatSet}(F,P_k)
} MatSet ( F , P k ) 表示某次 operator 實際 materialize 的 carrier units。
定義：
λ F = ∣ M a t S e t ( F , P k ) ∣ ∣ P k ∣ . \boxed{
\lambda_F
=
\frac{
|\mathsf{MatSet}(F,P_k)|
}{
|P_k|
}.
} λ F = ∣ P k ∣ ∣ MatSet ( F , P k ) ∣ . strong-local operator 期望：
λ F ≪ 1. \lambda_F\ll1. λ F ≪ 1. 18. Partial Materialization
所以：
Carrier Exists ≠ Carrier Fully Materialized . \boxed{
\text{Carrier Exists}
\neq
\text{Carrier Fully Materialized}.
} Carrier Exists = Carrier Fully Materialized . 這與 PNCW Paper 01 的：
Logical Completeness ≠ Full Physical Residency \text{Logical Completeness}
\neq
\text{Full Physical Residency} Logical Completeness = Full Physical Residency 直接相容。
19. Multi-Scale Carrier
令：
S = { s 0 , s 1 , … , s m } . \boxed{
\mathfrak S
=
\{s_0,s_1,\ldots,s_m\}.
} S = { s 0 , s 1 , … , s m } . 不同 scale 可代表：
coarse overview；
relation summary；
medium region；
fine chunk；
exact tile。
20. Scale Selection
s ⋆ = S e l e c t S c a l e ( q , B u d g e t , C o s t , U n c e r t a i n t y , R e q u i r e d S e m a n t i c s ) . \boxed{
s^\star
=
\mathsf{SelectScale}
(
q,
Budget,
Cost,
Uncertainty,
RequiredSemantics
).
} s ⋆ = SelectScale ( q , B u d g e t , C os t , U n cer t ain t y , R e q u i r e d S e man t i cs ) . 高解析不一定永遠最好：
Finer ≠ Always Better . \boxed{
\text{Finer}
\neq
\text{Always Better}.
} Finer = Always Better . 21. Multi-Scale Materialization
同一 logical carrier 可同時含：
P k c o a r s e , P k m i d , P k f i n e . P_k^{coarse},
P_k^{mid},
P_k^{fine}. P k co a r se , P k mi d , P k f in e . 不同 region 不必全部展開 fine。
22. Relation Carrier
R k R_k R k
dense；
CSR-like；
CSC-like；
block-sparse；
spatialized relation map；
hybrid。
因此 relation representation 也可以 workload-relative。
23. Carrier Profile
定義：
χ = ⟨ S c a l e , T i l e S h a p e , P r e c i s i o n , R e l a t i o n E n c o d i n g , C o m p r e s s i o n , I n t e g r i t y , L a y o u t ⟩ . \boxed{
\chi
=
\left\langle
Scale,
TileShape,
Precision,
RelationEncoding,
Compression,
Integrity,
Layout
\right\rangle.
} χ = ⟨ S c a l e , T i l e S ha p e , P r ec i s i o n , R e l a t i o n E n co d in g , C o m p r ess i o n , I n t e g r i t y , L a y o u t ⟩ . 24. Carrier Candidate Set
X = { χ 1 , … , χ n } . \boxed{
\mathcal X
=
\{\chi_1,\ldots,\chi_n\}.
} X = { χ 1 , … , χ n } . 傳統 brute-force 可以把所有 χ i \chi_i χ i
25. Predictive Materialization
定義：
P r e d i c t ( χ i , W o r k l o a d , S t a t e F e a t u r e s ) → C ^ i . \boxed{
\mathsf{Predict}
(
\chi_i,
Workload,
StateFeatures
)
\rightarrow
\hat C_i.
} Predict ( χ i , W or k l o a d , S t a t e F e a t u r es ) → C ^ i . 然後先選：
χ ⋆ = arg min i C ^ i . \chi^\star
=
\arg\min_i\hat C_i. χ ⋆ = arg i min C ^ i . 26. Prediction / Materialization Non-Collapse
PNCW 採：
Carrier Prediction ≠ Candidate Materialization . \boxed{
\text{Carrier Prediction}
\neq
\text{Candidate Materialization}.
} Carrier Prediction = Candidate Materialization . Runtime 可以先估：
projected size；
expected read fraction；
expected write amplification；
latency；
memory；
uncertainty；
而不先生成每個 candidate。
27. Fast Path / Oracle Path
R o u t e M o d e ∈ { F A S T , O R A C L E } . \boxed{
\mathsf{RouteMode}
\in
\{
\mathsf{FAST},
\mathsf{ORACLE}
\}.
} RouteMode ∈ { FAST , ORACLE } . Fast path 使用 predictor；Oracle path 使用實測或更完整 evaluation。
28. Uncertainty-Aware Routing
若：
u ( χ ) > u m a x , u(\chi)>u_{max}, u ( χ ) > u ma x , 則：
F a l l b a c k T o O r a c l e . \boxed{
\mathsf{FallbackToOracle}.
} FallbackToOracle . 29. Prediction Miss / Semantic Failure Non-Collapse
如果 fast path 選錯，但 fallback 修正：
Prediction Miss ≠ Authoritative Semantic Failure . \boxed{
\text{Prediction Miss}
\neq
\text{Authoritative Semantic Failure}.
} Prediction Miss = Authoritative Semantic Failure . 這使 prediction 可以被當成 bounded optimization，而不是 correctness authority。
30. Online Calibration
令 residual：
e t = C t a c t u a l − C ^ t . e_t
=
C_t^{actual}
-
\hat C_t. e t = C t a c t u a l − C ^ t . 可更新：
C a l i b r a t e t + 1 = f ( C a l i b r a t e t , e t ) . \boxed{
\mathsf{Calibrate}_{t+1}
=
f(
\mathsf{Calibrate}_t,
e_t
).
} Calibrate t + 1 = f ( Calibrate t , e t ) . 但 calibration 必須 bounded、可回退、可稽核。
31. Distribution Shift
若：
D t ≠ D c a l i b , \mathcal D_t
\neq
\mathcal D_{calib}, D t = D c a l ib , prediction error 可以增加。
因此：
Calibrated ≠ Distribution-Shift Immune . \boxed{
\text{Calibrated}
\neq
\text{Distribution-Shift Immune}.
} Calibrated = Distribution-Shift Immune . 32. Carrier Selection / Operator Selection Non-Collapse
Carrier Selection ≠ Operator Selection . \boxed{
\text{Carrier Selection}
\neq
\text{Operator Selection}.
} Carrier Selection = Operator Selection . 同樣：
Carrier Profile ≠ Physical Resource Allocation . \boxed{
\text{Carrier Profile}
\neq
\text{Physical Resource Allocation}.
} Carrier Profile = Physical Resource Allocation . 這些可以由 GCM 在更高層組合。
33. Carrier Residency
同一 logical carrier 可以：
R e s i d e n c y ( P k ) ⊆ { R A M , V R A M , S S D , N A S , R e m o t e } . \mathsf{Residency}(P_k)
\subseteq
\{
RAM,VRAM,SSD,NAS,Remote
\}. Residency ( P k ) ⊆ { R A M , V R A M , S S D , N A S , R e m o t e } . 因此：
CarrierID ≠ StoragePath . \boxed{
\text{CarrierID}
\neq
\text{StoragePath}.
} CarrierID = StoragePath . 34. Carrier ID
定義：
C I D k = H ( S t a t e A n c h o r , S c o p e , F r a m e I D , C a r r i e r P r o f i l e , S e m a n t i c D i g e s t , V e r s i o n ) . \boxed{
CID_k
=
H(
StateAnchor,
Scope,
FrameID,
CarrierProfile,
SemanticDigest,
Version
).
} C I D k = H ( S t a t e A n c h or , S co p e , F r am e I D , C a r r i er P r o f i l e , S e man t i cD i g es t , V er s i o n ) . 35. Frame ID
F I D k = H ( A d d r e s s M a p , R e g i o n P a r t i t i o n , T i l e S t r u c t u r e , L o c a l i t y P r o f i l e , T o p o l o g y , V e r s i o n ) . \boxed{
FID_k
=
H(
AddressMap,
RegionPartition,
TileStructure,
LocalityProfile,
Topology,
Version
).
} F I D k = H ( A dd r ess M a p , R e g i o n P a r t i t i o n , T i l e S t r u c t u r e , L oc a l i t y P r o f i l e , T o p o l o g y , V er s i o n ) . Carrier 必須綁定 FrameID，不能只知道 bytes。
36. Spatial Invariants
I k s p a c e = { I a d d r , I i d e n t i t y , I r e g i o n , I t i l e , I l o c a l i t y , I r e a c h , I t o p o l o g y } . \boxed{
\mathcal I_k^{space}
=
\{
I_{addr},
I_{identity},
I_{region},
I_{tile},
I_{locality},
I_{reach},
I_{topology}
\}.
} I k s p a ce = { I a dd r , I i d e n t i t y , I r e g i o n , I t i l e , I l oc a l i t y , I r e a c h , I t o p o l o g y } . 37. Attention Invariants
I k a t t n = { I s u p p o r t , I r a n k , I m a s s , I l o c a l i t y , I r e a c h , I i d e n t i t y , I e n t r y , I e x i t } . \boxed{
\mathcal I_k^{attn}
=
\{
I_{support},
I_{rank},
I_{mass},
I_{locality},
I_{reach},
I_{identity},
I_{entry},
I_{exit}
\}.
} I k a tt n = { I s u pp or t , I r ank , I ma ss , I l oc a l i t y , I r e a c h , I i d e n t i t y , I e n t r y , I e x i t } . 38. Attention Support Intrusion
如果 outsider c j c_j c j
No Direct Protected Mutation ⇏ Attention Preservation . \boxed{
\text{No Direct Protected Mutation}
\not\Rightarrow
\text{Attention Preservation}.
} No Direct Protected Mutation ⇒ Attention Preservation . 所以 post-transform global attention verification 必要。
39. Carrier Verification
對：
F P ( P ) = P ′ , F_P(P)=P', F P ( P ) = P ′ , 至少需要：
V e r i f y S p a c e ( P ′ ) = P A S S , \mathsf{VerifySpace}(P')=\mathrm{PASS}, VerifySpace ( P ′ ) = PASS , V e r i f y A t t n ( P ′ ) = P A S S . \mathsf{VerifyAttn}(P')=\mathrm{PASS}. VerifyAttn ( P ′ ) = PASS . 40. Speculative Carrier State
可以先：
P s p e c . P^{spec}. P s p ec . 但：
P s p e c ≠ P a u t h . \boxed{
P^{spec}
\neq
P^{auth}.
} P s p ec = P a u t h . 41. Carrier Transaction
T x n P = R e a d → C o m p u t e → V e r i f y → C o m m i t / A b o r t . \boxed{
\mathsf{Txn}_P
=
\mathsf{Read}
\rightarrow
\mathsf{Compute}
\rightarrow
\mathsf{Verify}
\rightarrow
\mathsf{Commit/Abort}.
} Txn P = Read → Compute → Verify → Commit/Abort . 42. Semantic Locality
對局部 mutation：
∣ Δ S ∣ ≪ ∣ S ∣ , |\Delta S|\ll|S|, ∣Δ S ∣ ≪ ∣ S ∣ , 可以期待：
∣ Δ P ∣ ≪ ∣ P ∣ . |\Delta P|\ll|P|. ∣Δ P ∣ ≪ ∣ P ∣. 但這只證明 semantic/computational locality。
43. Semantic / Physical Commit Locality Non-Collapse
若 integrity 仍需 global rewrite：
C c o m m i t C_{commit} C co mmi t 仍可能很高。
所以：
Semantic Locality ≠ Physical Commit Locality . \boxed{
\text{Semantic Locality}
\neq
\text{Physical Commit Locality}.
} Semantic Locality = Physical Commit Locality . 44. Commit Amplification
A c o m m i t = bytes rehashed/recommitted semantic bytes changed . \boxed{
A_{commit}
=
\frac{
\text{bytes rehashed/recommitted}
}{
\text{semantic bytes changed}
}.
} A co mmi t = semantic bytes changed bytes rehashed/recommitted . 下一代 runtime 應降低 A c o m m i t A_{commit} A co mmi t
45. Local Integrity
真正 local commit 需要：
Tile-Local Hash + Hierarchical Root + Local Update Proof . \boxed{
\text{Tile-Local Hash}
+
\text{Hierarchical Root}
+
\text{Local Update Proof}.
} Tile-Local Hash + Hierarchical Root + Local Update Proof . 例如 Merkle-like integrity structure。
46. Runtime-Native 最低條件
Local Compute + Local Verify + Local Integrity + Local Commit . \boxed{
\text{Local Compute}
+
\text{Local Verify}
+
\text{Local Integrity}
+
\text{Local Commit}.
} Local Compute + Local Verify + Local Integrity + Local Commit . 47. Query / Transform / Runtime Native Separation
Query-Native ≠ Transform-Native ≠ Runtime-Native . \boxed{
\text{Query-Native}
\neq
\text{Transform-Native}
\neq
\text{Runtime-Native}.
} Query-Native = Transform-Native = Runtime-Native . 48. Carrier Evidence Ladder
E 0 < E 1 < E 2 < E 3 < E 4 . \boxed{
E_0<E_1<E_2<E_3<E_4.
} E 0 < E 1 < E 2 < E 3 < E 4 .
E 0 E_0 E 0 E 1 E_1 E 1 E 2 E_2 E 2 E 3 E_3 E 3 E 4 E_4 E 4
目前應保守描述為：
candidate computational substrate for tested operator families . \boxed{
\text{candidate computational substrate for tested operator families}.
} candidate computational substrate for tested operator families . 49. Projected Carrier Epoch
PNCW 定義：
P C E k = ⟨ C I D k , F I D k , S c o p e , P r o f i l e , I n v a r i a n t C e r t s , O p e r a t o r S e t , V a l i d i t y , T i m e ⟩ . \boxed{
\mathcal PCE_k
=
\left\langle
CID_k,
FID_k,
Scope,
Profile,
InvariantCerts,
OperatorSet,
Validity,
Time
\right\rangle.
} P C E k = ⟨ C I D k , F I D k , S co p e , P r o f i l e , I n v a r ian tC er t s , O p er a t or S e t , V a l i d i t y , T im e ⟩ . 50. Context Epoch / Carrier Epoch Non-Collapse
PNCW Paper 02 的：
C P E j \mathcal CPE_j C P E j 與本文：
P C E k \mathcal PCE_k P C E k 不是同一個 epoch。
因此：
C P E j ≠ P C E k . \boxed{
\mathcal CPE_j
\neq
\mathcal PCE_k.
} C P E j = P C E k . 51. Context Refresh 不等於 Full Carrier Rebuild
若：
C q , t + 1 a c t i v e = C q , t a c t i v e + Δ C C_{q,t+1}^{active}
=
C_{q,t}^{active}
+
\Delta C C q , t + 1 a c t i v e = C q , t a c t i v e + Δ C 且 Δ C \Delta C Δ C
Context Update ⇏ Full Reprojection . \boxed{
\text{Context Update}
\not\Rightarrow
\text{Full Reprojection}.
} Context Update ⇒ Full Reprojection . 52. Carrier Reuse Map
Γ P j → j + 1 = { ( R i o l d , R i n e w , r e u s e i ) } . \boxed{
\Gamma_P^{j\to j+1}
=
\{
(R_i^{old},R_i^{new},reuse_i)
\}.
} Γ P j → j + 1 = {( R i o l d , R i n e w , r e u s e i )} . semantic identity / version stable 的 region 可以 reuse。
53. Carrier Migration
跨 frame：
M k → k + 1 : P k → P k + 1 . \boxed{
M_{k\to k+1}:P_k\rightarrow P_{k+1}.
} M k → k + 1 : P k → P k + 1 . 可採 sparse remap、tile shuffle、streaming migration、partial decode/re-encode、canonical reconstruction。
54. Migration Cost
C m i g = C m o v e + C r e i n d e x + C c a c h e + C v e r i f y + C a t t e n t i o n + C h i s t o r y . \boxed{
C_{mig}
=
C_{move}
+
C_{reindex}
+
C_{cache}
+
C_{verify}
+
C_{attention}
+
C_{history}.
} C mi g = C m o v e + C r e in d e x + C c a c h e + C v er i f y + C a tt e n t i o n + C hi s t or y . 55. Reprojection Benefit
B r e p r o j = B l o c a l i t y + B t a s k + B c o m p r e s s i o n + B a t t e n t i o n + B e x e c u t i o n . \boxed{
B_{reproj}
=
B_{locality}
+
B_{task}
+
B_{compression}
+
B_{attention}
+
B_{execution}.
} B r e p r o j = B l oc a l i t y + B t a s k + B co m p r ess i o n + B a tt e n t i o n + B e x ec u t i o n . 工程判斷可用：
B r e p r o j > C m i g + C r i s k , B_{reproj}>C_{mig}+C_{risk}, B r e p r o j > C mi g + C r i s k , 但必須：
Admissibility before optimization . \boxed{
\text{Admissibility before optimization}.
} Admissibility before optimization . 56. Carrier Staleness
C a r r i e r S t a l e k ( t ) = d ( π k , B u i l d F r a m e ( S t ) ) . \boxed{
\mathsf{CarrierStale}_k(t)
=
d(
\pi_k,
\mathsf{BuildFrame}(S_t)
).
} CarrierStale k ( t ) = d ( π k , BuildFrame ( S t )) . stale > 0 >0 > 0
57. Carrier Debt
Δ P = ⟨ δ l o c a l i t y , δ t i l e , δ a t t e n t i o n , δ r e a c h , δ c o m p r e s s i o n , δ c o s t ⟩ . \boxed{
\Delta_P
=
\left\langle
\delta_{locality},
\delta_{tile},
\delta_{attention},
\delta_{reach},
\delta_{compression},
\delta_{cost}
\right\rangle.
} Δ P = ⟨ δ l oc a l i t y , δ t i l e , δ a tt e n t i o n , δ r e a c h , δ co m p r ess i o n , δ cos t ⟩ . 超出 budget 才要求 Release / Reproject。
58. State / Frame Frequency
可以：
f s t a t e ≫ f f r a m e . \boxed{
f_{state}\gg f_{frame}.
} f s t a t e ≫ f f r am e . 這是 Stable Projection Epoch 的重要工程價值。
59. Context / Carrier / Visibility Frequency
PNCW 允許：
f c o n t e x t ≥ f c a r r i e r ≥ f v i s i b i l i t y \boxed{
f_{context}
\ge
f_{carrier}
\ge
f_{visibility}
} f co n t e x t ≥ f c a r r i er ≥ f v i s ibi l i t y 作為常見但非普遍的配置。
60. 三種 Epoch
目前 PNCW 至少有：
Context Projection Epoch ≠ Carrier Projection Epoch ≠ Visibility Epoch . \boxed{
\text{Context Projection Epoch}
\neq
\text{Carrier Projection Epoch}
\neq
\text{Visibility Epoch}.
} Context Projection Epoch = Carrier Projection Epoch = Visibility Epoch . 這三者不必同步更新。
61. Carrier as Cognitive Residency Space
若 AI 可以直接：
Q P ( P k ) , Q_P(P_k), Q P ( P k ) , 與：
F P ( P k ) , F_P(P_k), F P ( P k ) , 則：
P k can become a cognitive computational residency space . \boxed{
P_k
\text{ can become a cognitive computational residency space}.
} P k can become a cognitive computational residency space . 它不是只用來 export。
62. Shared Carrier / Shared View Non-Collapse
多 Agent 可以共享 certified carrier regions，但取得不同：
tiles；
relation layers；
precision；
permissions；
presentation。
所以：
Shared Carrier ≠ Shared View . \boxed{
\text{Shared Carrier}
\neq
\text{Shared View}.
} Shared Carrier = Shared View . 63. Human Visible Fraction
Human 可能只看：
ρ H ≪ 1 \rho_H\ll1 ρ H ≪ 1 的 visual surface，但 machine carrier 維持較大 logical state。
所以：
Human Visible Fraction ≠ Carrier Active Fraction . \boxed{
\text{Human Visible Fraction}
\neq
\text{Carrier Active Fraction}.
} Human Visible Fraction = Carrier Active Fraction . 64. HDSRC → MRMIC Interface
理想：
P k → Ψ c a n v a s V q , k . \boxed{
P_k
\xrightarrow{\Psi_{canvas}}
V_{q,k}.
} P k Ψ c an v a s V q , k . 不需要先把 P k P_k P k
65. Carrier Region → Canvas Object
R i c a r r i e r ↦ O i c a n v a s . \boxed{
R_i^{carrier}
\mapsto
O_i^{canvas}.
} R i c a r r i er ↦ O i c an v a s . Canvas Object 可持有：
carrier region reference；
geometry；
visualization profile；
interaction contract；
provenance。
66. Canvas Object 不取得 Canonical Authority
如果 object 只是 projection：
A u t h o r i t y ( O i c a n v a s ) ≠ A u t h o r i t y ( C a n o n i c a l i ) . \boxed{
\mathsf{Authority}(O_i^{canvas})
\neq
\mathsf{Authority}(Canonical_i).
} Authority ( O i c an v a s ) = Authority ( C an o ni c a l i ) . 67. Visual Mutation
Canvas operation：
a t a_t a t 可產生：
Δ P p r o p o s a l . \Delta P^{proposal}. Δ P p r o p os a l . 但回程必須：
Δ P p r o p o s a l → V e r i f y → C o m m i t G a t e . \boxed{
\Delta P^{proposal}
\rightarrow
\mathsf{Verify}
\rightarrow
\mathsf{CommitGate}.
} Δ P p r o p os a l → Verify → CommitGate . 68. PNCW Carrier Contract
C a r r i e r C o n t r a c t = ⟨ S c o p e , F r a m e , P r o f i l e , P r e c i s i o n , A d d r e s s i n g , R e l a t i o n E n c o d i n g , I n v a r i a n t s , O p e r a t o r C a p a b i l i t i e s , I n t e g r i t y , M i g r a t i o n , F a l l b a c k ⟩ . \boxed{
\mathsf{CarrierContract}
=
\left\langle
Scope,
Frame,
Profile,
Precision,
Addressing,
RelationEncoding,
Invariants,
OperatorCapabilities,
Integrity,
Migration,
Fallback
\right\rangle.
} CarrierContract = ⟨ S co p e , F r am e , P r o f i l e , P r ec i s i o n , A dd r ess in g , R e l a t i o n E n co d in g , I n v a r ian t s , O p er a t or C a p abi l i t i es , I n t e g r i t y , M i g r a t i o n , F a l l ba c k ⟩ . 69. Carrier Capability Advertisement
Runtime 可宣告：
carrier_profile
supported_queries
supported_transforms
scale_levels
relation_encodings
integrity_mode
local_commit_capability
migration_modes
讓 GCM / MRMIC 做 capability negotiation。
70. Carrier Selection by GCM
GCM 可以把 carrier profile 當成 computational configuration：
γ = ⟨ R e p r e s e n t a t i o n , O p e r a t o r , E x e c u t o r , R e s o u r c e , C a r r i e r P r o f i l e ⟩ . \boxed{
\gamma
=
\left\langle
Representation,
Operator,
Executor,
Resource,
CarrierProfile
\right\rangle.
} γ = ⟨ R e p r ese n t a t i o n , O p er a t or , E x ec u t or , R eso u r ce , C a r r i er P r o f i l e ⟩ . 71. Constraint First
對 carrier candidate χ i \chi_i χ i
A d m i s s i b l e ( χ i ) = 1. \mathsf{Admissible}(\chi_i)=1. Admissible ( χ i ) = 1. 再做 cost / Pareto selection。
因此：
Carrier Feasible ≠ Carrier Preferred . \boxed{
\text{Carrier Feasible}
\neq
\text{Carrier Preferred}.
} Carrier Feasible = Carrier Preferred . 72. Predictive Carrier Selection × Pareto
對候選：
χ i \chi_i χ i 可以建立：
o ( χ i ) = ( L a t e n c y , M e m o r y , I O , A c c u r a c y , R i s k , M i g r a t i o n C o s t ) . \mathbf o(\chi_i)
=
(
Latency,
Memory,
IO,
Accuracy,
Risk,
MigrationCost
). o ( χ i ) = ( L a t e n cy , M e m or y , I O , A cc u r a cy , R i s k , M i g r a t i o n C os t ) . 先取 Pareto frontier，再由 explicit policy 選：
χ ⋆ . \chi^\star. χ ⋆ . 73. AI Proposal / Selection Authority Separation
AI 可以建議：
χ ^ , \hat\chi, χ ^ , 但：
AI Carrier Proposal ≠ Carrier Selection Authority . \boxed{
\text{AI Carrier Proposal}
\neq
\text{Carrier Selection Authority}.
} AI Carrier Proposal = Carrier Selection Authority . 74. Carrier Obstruction
O P = ⟨ C a r r i e r C a n d i d a t e , S c o p e , I n v a r i a n t , M e c h a n i s m , S e v e r i t y , C e r t i f i c a t e ⟩ . \boxed{
O_P
=
\left\langle
CarrierCandidate,
Scope,
Invariant,
Mechanism,
Severity,
Certificate
\right\rangle.
} O P = ⟨ C a r r i er C an d i d a t e , S co p e , I n v a r ian t , M ec hani s m , S e v er i t y , C er t i f i c a t e ⟩ . 例如 address collision、unsupported relation、attention instability、precision loss、integrity impossibility、memory overflow。
75. Carrier Fallback
若 preferred profile 不 admissible：
χ f i n e → χ c o a r s e → χ c a n o n i c a l . \boxed{
\chi_{fine}
\rightarrow
\chi_{coarse}
\rightarrow
\chi_{canonical}.
} χ f in e → χ co a r se → χ c an o ni c a l . Fallback 必須保留 semantic contract。
76. Strong Native Carrier
定義：
S t r o n g N a t i v e ( P k ) \boxed{
\mathsf{StrongNative}(P_k)
} StrongNative ( P k ) 若：
common query 無需 full decode；
local transforms exist；
finite composition exists；
invariants certified；
materialization bounded；
carrier identity stable。
77. Runtime Native Carrier
更強：
R u n t i m e N a t i v e ( P k ) \boxed{
\mathsf{RuntimeNative}(P_k)
} RuntimeNative ( P k ) 還要求：
local integrity；
local commit；
concurrency；
fault recovery；
migration；
authority isolation。
78. Carrier Computational Algebra
A k P = ⟨ P k , F k n a t i v e , ∘ , E q , C e r t ⟩ . \boxed{
\mathfrak A_k^P
=
\left\langle
P_k,
\mathfrak F_k^{native},
\circ,
\mathsf{Eq},
\mathsf{Cert}
\right\rangle.
} A k P = ⟨ P k , F k na t i v e , ∘ , Eq , Cert ⟩ . 79. Equivalence Family
E q = { = , ∼ s e m a n t i c , ∼ t a s k , ∼ o b s , ∼ e x e c } . \mathsf{Eq}
=
\{
=,
\sim_{semantic},
\sim_{task},
\sim_{obs},
\sim_{exec}
\}. Eq = { = , ∼ se man t i c , ∼ t a s k , ∼ o b s , ∼ e x ec } . 每個 operator 必須聲明 correctness relation。
80. Error Budget
對 approximate operator sequence：
F 1 , … , F n F_1,\ldots,F_n F 1 , … , F n 要求：
ε t o t a l ≤ B E . \boxed{
\varepsilon_{total}\le B_{\mathcal E}.
} ε t o t a l ≤ B E . 超過 budget：
⇒ R e l e a s e . \Rightarrow
\mathsf{Release}. ⇒ Release . 81. Proposition 1 — Stable Frame Enables Reproducible Frame-Dependent Operators
若：
π k \pi_k π k operator 的 tile/region semantics 綁定 π k \pi_k π k
post-transform invariants PASS；
則 F π k F^{\pi_k} F π k
82. Proposition 2 — Context Update Need Not Force Full Carrier Rebuild
若：
C q , t + 1 a c t i v e = C q , t a c t i v e + Δ C C_{q,t+1}^{active}
=
C_{q,t}^{active}
+
\Delta C C q , t + 1 a c t i v e = C q , t a c t i v e + Δ C 且 Δ C \Delta C Δ C
Context Update ⇏ Full Carrier Rebuild . \boxed{
\text{Context Update}
\not\Rightarrow
\text{Full Carrier Rebuild}.
} Context Update ⇒ Full Carrier Rebuild . 83. Proposition 3 — Carrier Selection Can Precede Candidate Materialization
若存在：
C ^ ( χ ) \hat C(\chi) C ^ ( χ ) 與 uncertainty bound：
u ( χ ) , u(\chi), u ( χ ) , 則 selection 可先於：
M a t e r i a l i z e ( χ ) . \mathsf{Materialize}(\chi). Materialize ( χ ) . 84. Proposition 4 — Logical Carrier Availability Can Precede Full Residency
若：
CID stable；
manifest stable；
required active regions available；
則：
C a r r i e r A v a i l a b l e ( P k ) = 1 \mathsf{CarrierAvailable}(P_k)=1 CarrierAvailable ( P k ) = 1 可以同時：
ρ P k < 1. \rho_{P_k}<1. ρ P k < 1. 85. Proposition 5 — Machine-Native Projection Need Not Be Human-Readable
存在 P k P_k P k
Π H ( P k ) . \Pi_H(P_k). Π H ( P k ) . 因此：
Machine Usability ⇏ Human Readability . \boxed{
\text{Machine Usability}
\not\Rightarrow
\text{Human Readability}.
} Machine Usability ⇒ Human Readability . 86. PNCW Paper 03 規範 v0.1
PNCW-P1 — Context / Carrier Separation
Active cognitive domain 不等於 projected carrier。
PNCW-P2 — Stable Frame Requirement
Frame-dependent native operator 必須綁定明確 epoch frame。
PNCW-P3 — Carrier / Presentation Separation
Machine carrier 不得與 human image 塌縮。
PNCW-P4 — Round-Trip / Native Compute Separation
可逆不代表 native computation。
PNCW-P5 — Partial Materialization
Carrier logical existence 不要求 full residency。
PNCW-P6 — Explicit Operator Capability
Native claims 必須綁定 operator family。
PNCW-P7 — Invariant-Safe Transform
Authoritative transform 後必須 re-certify required invariants。
PNCW-P8 — Carrier Prediction / Materialization Separation
不得要求先完整 materialize 所有 candidates 才可選 carrier。
PNCW-P9 — Uncertainty-Aware Fallback
Predictive path 必須有 bounded fallback / oracle strategy。
PNCW-P10 — Semantic / Physical Locality Separation
Local semantic transform 不得偷換成 local physical commit claim。
PNCW-P11 — Epoch / Visibility Separation
Carrier update 不自動等於 human reveal。
PNCW-P12 — Native Claim Boundary
目前 evidence 不得升級成 universal runtime claim。
87. 對 PNCW 的核心意義
Paper 02 解決：
What should be cognitively active? \boxed{
\text{What should be cognitively active?}
} What should be cognitively active? Paper 03 解決：
How should that active cognition become a stable machine-native computational surface? \boxed{
\text{How should that active cognition become a stable machine-native computational surface?}
} How should that active cognition become a stable machine-native computational surface? 88. Context Address / Carrier Address Non-Collapse
Context VM 提供：
a i c o n t e x t . a_i^{context}. a i co n t e x t . Carrier 提供：
a i c a r r i e r . a_i^{carrier}. a i c a r r i er . 所以：
a i c o n t e x t ≠ a i c a r r i e r . \boxed{
a_i^{context}
\neq
a_i^{carrier}.
} a i co n t e x t = a i c a r r i er . 但可以建立 mapping。
89. Context-to-Carrier Mapping
Γ C → P = { ( C o n t e x t I D , C a r r i e r A d d r e s s , F r a m e I D , V e r s i o n ) } . \boxed{
\Gamma_{C\to P}
=
\{
(ContextID,
CarrierAddress,
FrameID,
Version)
\}.
} Γ C → P = {( C o n t e x t I D , C a r r i er A dd r ess , F r am e I D , V er s i o n )} . 這使 carrier 可回溯到 stable Context identity。
90. Carrier-to-Canvas Mapping
下一層：
Γ P → V = { C a r r i e r R e g i o n , C a n v a s O b j e c t , V i e w p o r t P o l i c y , I n t e r a c t i o n P r o f i l e } . \boxed{
\Gamma_{P\to V}
=
\{
CarrierRegion,
CanvasObject,
ViewportPolicy,
InteractionProfile
\}.
} Γ P → V = { C a r r i er R e g i o n , C an v a s O bj ec t , V i e w p or tP o l i cy , I n t er a c t i o n P r o f i l e } . 91. 整體 Projection Chain
目前 PNCW 已形成：
M t o t a l → C q a c t i v e → E k → P k → V q , k . \boxed{
\mathcal M^{total}
\rightarrow
C_q^{active}
\rightarrow
\mathcal E_k
\rightarrow
P_k
\rightarrow
V_{q,k}.
} M t o t a l → C q a c t i v e → E k → P k → V q , k . 92. Vertical Slice — Carrier Phase
PNCW 最小垂直實驗中的 Carrier phase：
接收已驗證 active Context；
建立 projection scope；
Freeze frame；
選 carrier profile；
materialize required regions；
跑 native query；
跑 local transform；
re-certify；
記錄 materialization ratio；
將 carrier regions 暴露給 Canvas。
93. Carrier Metrics
M P = ⟨ R o u n d T r i p , N a t i v e E q , M a t R a t i o , P e a k M e m o r y , R e a d I O , W r i t e I O , C o m m i t A m p , D r i f t , M i g r a t i o n C o s t , P r e d i c t i o n R e g r e t , F a l l b a c k R a t e ⟩ . \boxed{
\mathbf M_P
=
\left\langle
RoundTrip,
NativeEq,
MatRatio,
PeakMemory,
ReadIO,
WriteIO,
CommitAmp,
Drift,
MigrationCost,
PredictionRegret,
FallbackRate
\right\rangle.
} M P = ⟨ R o u n d T r i p , N a t i v e E q , M a tR a t i o , P e ak M e m or y , R e a d I O , W r i t e I O , C o mmi t A m p , D r i f t , M i g r a t i o n C os t , P r e d i c t i o n R e g r e t , F a l l ba c k R a t e ⟩ . 94. Multi-Scale Metrics
M S = ⟨ S c a l e , C o v e r a g e , L a t e n c y , M e m o r y , S e m a n t i c E r r o r , R e u s e R a t e ⟩ . \boxed{
\mathbf M_S
=
\left\langle
Scale,
Coverage,
Latency,
Memory,
SemanticError,
ReuseRate
\right\rangle.
} M S = ⟨ S c a l e , C o v er a g e , L a t e n cy , M e m or y , S e man t i c E r r or , R e u se R a t e ⟩ . 95. Predictive Metrics
M p r e d = ⟨ S e l e c t i o n A c c u r a c y , R e g r e t , C o n f i d e n c e C a l i b r a t i o n , F a l l b a c k R a t e , S e l e c t i o n O v e r h e a d ⟩ . \boxed{
\mathbf M_{pred}
=
\left\langle
SelectionAccuracy,
Regret,
ConfidenceCalibration,
FallbackRate,
SelectionOverhead
\right\rangle.
} M p r e d = ⟨ S e l ec t i o n A cc u r a cy , R e g r e t , C o n f i d e n ce C a l ib r a t i o n , F a l l ba c k R a t e , S e l ec t i o n O v er h e a d ⟩ . 96. Distribution-Shift Test
必須測：
D t e s t ≠ D c a l i b . \mathcal D_{test}
\neq
\mathcal D_{calib}. D t es t = D c a l ib . 不允許只在同一 workload 反覆調參後宣稱 robustness。
97. Failure Conditions
若：
frame drift 破壞 operator semantics；
native query 必須 full decode；
local transform 造成 global semantic divergence；
predictive path 在 shift 下沒有安全 fallback；
carrier migration cost 高於收益；
commit amplification 持續接近 global rewrite；
則 PNCW carrier claim 必須降低。
98. 與 Paper 04 的接口
Paper 03 的輸出：
P k . P_k. P k . 下一篇將研究：
如何把 machine-native projected carrier 與外部 resources 映射為 recursive multimodal visual computational canvas，使 AI 與人類可以在不 materialize 整個 canonical world 的前提下觀察、操作、分支與回放。
即：
P k → V q , k . \boxed{
P_k
\rightarrow
V_{q,k}.
} P k → V q , k . 99. 系列位置
P 00 : Projection-Native World Foundations P 01 : Visibility / Atomic Reveal P 02 : Virtual Context Projection P 03 : Stable High-D Projection Carrier P 04 : Visual Computational Canvas P 05 : Global Compute / Local Materialization P 06 : Non-Sequential AI Output Architecture \boxed{
\begin{aligned}
P00 &: \text{Projection-Native World Foundations}\\
P01 &: \text{Visibility / Atomic Reveal}\\
P02 &: \text{Virtual Context Projection}\\
P03 &: \text{Stable High-D Projection Carrier}\\
P04 &: \text{Visual Computational Canvas}\\
P05 &: \text{Global Compute / Local Materialization}\\
P06 &: \text{Non-Sequential AI Output Architecture}
\end{aligned}
} P 00 P 01 P 02 P 03 P 04 P 05 P 06 : Projection-Native World Foundations : Visibility / Atomic Reveal : Virtual Context Projection : Stable High-D Projection Carrier : Visual Computational Canvas : Global Compute / Local Materialization : Non-Sequential AI Output Architecture 100. 結論
本文建立 PNCW 的第二個核心 projection layer：
C q , t a c t i v e → E k → P k . \boxed{
C_{q,t}^{active}
\rightarrow
\mathcal E_k
\rightarrow
P_k.
} C q , t a c t i v e → E k → P k . 第一個原則：
State Evolution ≠ Projection Evolution . \boxed{
\text{State Evolution}
\neq
\text{Projection Evolution}.
} State Evolution = Projection Evolution . 當 projected-native operator 依賴 address、tile、region 或 locality 時，frame 不應因每個 state mutation 隱式重建。
第二個原則：
Image Carrier ≠ Human Image . \boxed{
\text{Image Carrier}
\neq
\text{Human Image}.
} Image Carrier = Human Image . HDSRC 類 carrier 更接近：
Address Space + Values + Relations + Attention + History + Operator Surface . \boxed{
\text{Address Space}
+
\text{Values}
+
\text{Relations}
+
\text{Attention}
+
\text{History}
+
\text{Operator Surface}.
} Address Space + Values + Relations + Attention + History + Operator Surface . 第三個原則：
Carrier Prediction ≠ Carrier Materialization . \boxed{
\text{Carrier Prediction}
\neq
\text{Carrier Materialization}.
} Carrier Prediction = Carrier Materialization . Runtime 可以先依 workload、cost、uncertainty 與 scale 選擇 carrier profile，再只 materialize 真正需要的 regions。
第四個原則：
Semantic Locality ≠ Physical Commit Locality . \boxed{
\text{Semantic Locality}
\neq
\text{Physical Commit Locality}.
} Semantic Locality = Physical Commit Locality . 下一個工程門檻仍是：
Local Compute + Local Verify + Local Integrity + Local Commit . \boxed{
\text{Local Compute}
+
\text{Local Verify}
+
\text{Local Integrity}
+
\text{Local Commit}.
} Local Compute + Local Verify + Local Integrity + Local Commit . 因此，PNCW 的 machine-native carrier 不是「一張完成後拿來看的圖」，而是：
A stable, epoch-bounded, machine-addressable computational surface . \boxed{
\text{A stable, epoch-bounded, machine-addressable computational surface}.
} A stable, epoch-bounded, machine-addressable computational surface . 它可以部分 materialize、局部 query、局部 transform、跨 observer 提供不同 projection，也可以在下一個 epoch 被合法 migration / reproject。
至此，PNCW 已完成：
Total Cognitive World → Finite Active Cognitive Domain → Stable Machine-Native Carrier . \boxed{
\text{Total Cognitive World}
\rightarrow
\text{Finite Active Cognitive Domain}
\rightarrow
\text{Stable Machine-Native Carrier}.
} Total Cognitive World → Finite Active Cognitive Domain → Stable Machine-Native Carrier . 下一步就是：
Stable Machine-Native Carrier → Recursive Visual Computational World . \boxed{
\text{Stable Machine-Native Carrier}
\rightarrow
\text{Recursive Visual Computational World}.
} Stable Machine-Native Carrier → Recursive Visual Computational World . 內部理論與工程血統
本文主要承接：
PNCW Paper 00 — Projection-Native Computational Worlds；
PNCW Paper 01 — Projection Readiness, Batched Reveal, and Atomic Observation；
PNCW Paper 02 — Virtual Context Projection；
SPET Paper 00–05；
HDSRC High-Dimensional Symbolic Relational Compilation；
HIC1 / SNIC1 / SFPIC1 / HDT1 carrier line；
HST1 / HCT1 / HBT1 / HRT1 relation and routing line；
HMBT1 / HMR1 multi-scale materialization line；
HPCM1 / HPCM2 predictive materialization and uncertainty-aware routing line；
GCM representation / materialization / allocation interfaces；
MRMIC/NVCL downstream visual computational surface。
本文保守採用現有 HDSRC 實驗為「tested operator family 下的 candidate computational substrate」證據，不宣稱 HDSRC 已形成 universal runtime，也不宣稱 predictive carrier selection 對所有 workload 都優於 oracle path。