# Navier–Stokes C5-M
# Unified Defect-State Closure、Compatibility Graph Audit 與 C5 Phase Boundary

**Version:** v0.1  
**Date:** 2026-08-15  
**Status:** Research-program phase closure / finite residual defect graph  
**Epistemic status:** This closes the C5 state-space/defect-classification phase, not the Navier–Stokes problem.

---

## 0. 本輪定位

C5 的工作不是再找一條 magic inequality，而是把 C4 的 recurrent compensation motifs 轉成 compact recurrent states，再把表面上不同的逃逸做 debt-routing。

C5-A 到 C5-L 已依序處理：

- motif-level compactness；
- temporal Young oscillation / concentration；
- temporal phase ordering；
- spatial–matrix convex incompatibility；
- middle-gap / strain-direction defects；
- pressure-axis / signature geometry；
- fixed-order derivative theorem gate；
- all-order static-volume no-go；
- derivative sign microgeometry；
- line fragmentation；
- chain-time stitching；
- persistent theorem-window defects；
- root turnover；
- chain-clock variation。

本輪只做 closure audit。

結論：

$$
\boxed{\textbf{C5 should close as a research phase.}}
$$

但：

$$
\boxed{\textbf{Navier--Stokes global regularity remains open.}}
$$

---

## 1. C5 closure criterion

C5 的 phase closure要求：

1. 所有 C4/C5 encountered motifs 都已 external-killed、routed，或保留成 finite residual class；
2. retained classes都有 compact scalar / measure / finite-dimensional state；
3. 不再有 unresolved branch只是因為「尚未命名」；
4. 下一個真正問題已變成 finite residual classes 是否能形成 infinite recurrent cycle。

---

## 2. External theorem gates

### Miller middle-eigenvalue gate

finite-time blow-up必須逃出 middle-strain scale-critical regularity regime。

### Miller strain-vorticity operator gate

$$
\langle-\Delta S,\omega\otimes\omega\rangle=0,
$$

且：

$$
\mathcal Q_{SV}
=
P_{st}\left(
(u\cdot\nabla)S
+
S^2
+
\frac34\omega\otimes\omega
\right).
$$

### Grujić–Xu fixed-order gate

Theorem 3.5：在 theorem-admissible later time，若 selected $D^ku$ 或 $D^k\omega$ component/sign superlevel set在 theorem scale 1D sparse，則 $T^*$ 不是 blow-up time。

### Grujić–Xu chain gate

Theorem 3.14：在 derivative-chain setup、time window、component/sign geometry等 hypotheses成立時，dynamic interpolation / harmonic measure machinery排除 blow-up。

### Pressure gates

Bradshaw–Tsai提供 local pressure expansion的 rigorous provenance；Constantin提供 critical pressure / intermittency regularity boundary。

---

# 3. Residual Class A — Legality / Ancestry / Setup

$$
\boxed{\mathsf A}
$$

包含：

- C3-G / C4 的 UV ancestry legality；
- eventual local-source dominance；
- legal parent routing；
- Grujić–Xu theorem setup、parameter、remaining-time antecedents。

這不是 physical singularity mechanism，而是：

$$
\boxed{\textbf{proof/theorem-entry legality defect}.}
$$

---

# 4. Residual Class T — Temporal Phase Defect

$$
\boxed{\mathsf T}
$$

包含 C5-B/C 的：

- Young phase oscillation；
- temporal load concentration；
- separated scalar compensation cycle。

C5 已修復 separate weak-limit phase blindness。

仍然 open 的是：

$$
\boxed{\text{temporal scalar compensation能否被 universal PDE shared-source coupling強迫進 G/P/H}.}
$$

---

# 5. Residual Class G — Field-Geometry Degeneration

$$
\boxed{\mathsf G}
$$

包含：

- middle-gap defect；
- strain-direction / compressive-axis dispersion；
- derivative strain fluctuation；
- vorticity-dominant leakage；
- cubic strain intermittency / active-volume collapse。

free Seven-Point Q cancellation已刪除：

$$
\boxed{Q\text{-cancellation}\Rightarrow\mathsf G.}
$$

---

# 6. Residual Class P — Pressure Compensation / Provenance

$$
\boxed{\mathsf P}
$$

包含：

- mean-rotation compensation；
- pressure concentration；
- far-pressure signature $(-,+,+)$ / $(-,-,+)$；
- det-zero signature boundary；
- pressure-source fragmentation / turnover；
- compressive-axis pressure locking。

C5-D/F 已得到有限維 incompatibilities，但未消除所有 pressure provenance routes。

---

# 7. Residual Class H — High-Order Harmonic / Theorem-Window Defect

$$
\boxed{\mathsf H}
$$

包含：

- fixed-$k$ direct gate failure；
- Window-Persistent Sign Defect；
- harmonic-temporal critical saturation；
- persistent bad derivative clusters；
- theorem setup合法但 harmonic window永遠不 pass。

已刪除：

- SHELLFULL；
- COMPSIGN；
- generic Type switching；
- generic theorem-time mismatch；
- line fragmentation as independent motif。

---

# 8. Residual Class F — Forcing / Order-Variation Debt

$$
\boxed{\mathsf F}
$$

包含：

- viscous $D^{k+2}u$ turnover toll；
- projected nonlinear turnover；
- order curvature；
- chain-clock variation；
- root-order variation；
- theorem/factorial normalization drift。

generic root turnover與 generic clock mismatch均已刪除：

$$
\boxed{\text{TURNOVER/CLOCK}\Rightarrow\mathsf F.}
$$

---

# 9. Final six-class residual alphabet

$$
\boxed{
\mathfrak D_{C5}
=
\{\mathsf A,\mathsf T,\mathsf G,\mathsf P,\mathsf H,\mathsf F\}.
}
$$

| Class | Meaning |
|---|---|
| $\mathsf A$ | legality / ancestry / theorem setup |
| $\mathsf T$ | temporal phase oscillation / concentration |
| $\mathsf G$ | strain/vorticity field geometry |
| $\mathsf P$ | pressure compensation / signature / provenance |
| $\mathsf H$ | high-order harmonic / theorem-window defect |
| $\mathsf F$ | forcing / order variation debt |

---

# 10. Pseudo-defect deletion audit

以下不再保留為 independent node：

1. free Seven-Point Q cancellation；
2. generic line fragmentation；
3. generic Type-A/B switching；
4. generic root turnover；
5. generic clock mismatch；
6. amplitude-level carrier relay；
7. large operator norm alone；
8. vorticity constraint complement alone；
9. static all-order effective-volume escalation。

它們都已被 route 到：

$$
\mathsf T,\mathsf G,\mathsf P,\mathsf H,\mathsf F
$$

或 external regularity gate。

---

# 11. Certified compatibility graph

定義：

$$
\mathcal G_{C5}=(V,E),
$$

$$
V=
\{\mathsf A,\mathsf T,\mathsf G,\mathsf P,\mathsf H,\mathsf F,\mathrm{REG}\}.
$$

edges標記：

- `U` = unconditional identity/routing；
- `C` = conditional on extra/localization/ancestry gate；
- `E` = external theorem closure。

---

# 12. Temporal routing

### $\mathsf T\to\mathsf T$

scalar temporal data允許 recurrent oscillation / concentration。

### $\mathsf T\to\mathsf G/\mathsf P$

需要 shared-source/localization bridge。

狀態：

$$
\boxed{\mathrm{CONDITIONAL}.}
$$

---

# 13. Geometry routing

### $\mathsf G\to\mathsf H$

derivative fluctuation / cubic intermittency會進 derivative theorem interfaces。

### $\mathsf G\to\mathsf P$

strong-middle coherence + local quadratic forcing + mean-rotation depletion會逼 pressure re-entry。

### $\mathsf G\to\mathsf G$

gap degeneration / direction dispersion本身可 recurrent。

---

# 14. Pressure routing

### $\mathsf P\to\mathrm{REG}$

pressure regularity gate若閉合。

### $\mathsf P\to\mathsf G$

pressure axis/signature restrictions回饋 strain/compressive-axis geometry。

### $\mathsf P\to\mathsf P$

mean rotation / signature boundary / provenance fragmentation仍可 recurrent。

---

# 15. High-order routing

### $\mathsf H\to\mathrm{REG}$

- Grujić–Xu Theorem 3.5；
- Grujić–Xu Theorem 3.14。

### $\mathsf H\to\mathsf F$

persistent bad windows / line roughness / root turnover / clock defects支付 forcing/order debt。

### $\mathsf H\to\mathsf H$

bounded compact bad-window root profiles仍可 recurrent。

---

# 16. Forcing routing

### $\mathsf F\to\mathsf H$

viscous $D^{k+2}u$ congestion把 activity推向 higher derivative levels。

### $\mathsf F\to\mathsf G/\mathsf P$

projected nonlinear forcing包含 full N–S nonlinear source，但 C5尚未證 universal deterministic destination。

### $\mathsf F\to\mathsf F$

forcing / root-order / clock variation本身可 recurrent。

---

# 17. Legality routing

$\mathsf A$ 是 theorem-entry / proof-route state。

若 legality建立，route才進 physical graph：

$$
\{\mathsf T,\mathsf G,\mathsf P,\mathsf H,\mathsf F\}.
$$

若 legality持續失敗，它表示目前 proof interface不完整，不應偷當成 physical singularity mechanism。

---

# 18. Finite recurrence principle

對任意 infinite hypothetical survivor labels：

$$
D_1,D_2,\ldots,
\qquad
D_n\in\mathfrak D_{C5},
$$

因 residual alphabet有限，至少一個 class出現無限多次。

所以：

$$
\boxed{\textbf{every infinite survivor has a recurrent residual class}.}
$$

---

# 19. SCC reduction

若 certified routing graph對該 survivor path是 complete，

其 SCC condensation graph有限且 acyclic。

因此 infinite path經 transient之後必在某 sink SCC中 recurrent。

所以：

$$
\boxed{
\textbf{C6 的真正 object 是 recurrent sink SCC / minimal defect cycle，
不是新的 isolated defect node。}
}
$$

---

# 20. Candidate recurrent cycle I — High-order forcing loop

$$
\boxed{
\mathsf H\longrightarrow\mathsf F\longrightarrow\mathsf H.
}
$$

interpretation：

1. persistent bad theorem window；
2. derivative descent/load；
3. high-order viscous / projected nonlinear / clock debt；
4. activity轉到 higher derivative level；
5. new theorem window again bad。

C5 尚無 finite all-order budget排除此 loop。

---

# 21. Candidate recurrent cycle II — Geometry–Pressure loop

$$
\boxed{
\mathsf G\leftrightarrow\mathsf P.
}
$$

possible compensation：

- strong-middle coherence逼 pressure / mean rotation；
- pressure axis/signature回饋 strain geometry；
- gap collapse / two-negative pressure / source fragmentation避開有限維 obstruction。

C5 已大幅限制但未消除所有 routes。

---

# 22. Candidate recurrent class III — Temporal loop

$$
\boxed{\mathsf T}
$$

可在 scalar temporal層自我 recurrent：

- oscillation；
- concentration；
- separated compensation。

要移除此 candidate SCC，需要 universal：

$$
\boxed{\mathsf T\to\mathsf G/\mathsf P/\mathsf H}
$$

shared-source theorem。

目前 open。

---

# 23. Legality class A

$\mathsf A$ 不是 physical SCC。

C6 必先分清：

- actual PDE survivor；
- theorem-entry / proof-route setup failure。

---

# 24. Finite Defect Recurrence Theorem

在 current certified C5 graph內：

任何 infinite hypothetical survivor path avoiding `REG` 都有 recurrent residual subsequence。

若 graph representation對該 path complete，則 eventual recurrence被支撐在某 sink SCC。

狀態：

$$
\boxed{
\mathrm{PROVED\ AS\ FINITE\ GRAPH\ THEORY}
}
$$

但 graph completeness本身仍是 C6 edge-audit 問題。

---

# 25. Why finite graph is not regularity

finite graph可能有 directed cycles。

compactness不消滅 cycle。

debt-routing若沒有 finite summability theorem，也不形成 contradiction。

所以：

$$
\boxed{
\text{finite defect graph}
\not\Rightarrow
\text{global regularity}.
}
$$

---

# 26. Final temporal status

C5 已完成：

- colored Young state；
- concentration defect；
- phase covariance；
- cumulative scalar ledgers。

仍剩：

$$
\boxed{
\mathsf T:
\ \mathrm{COMPACT\ BUT\ NOT\ ELIMINATED}.
}
$$

---

# 27. Final spatial–matrix status

C5 已完成：

- Q cancellation finite-dimensionalization；
- strong-middle/Q incompatibility；
- Q→gap/derivative/vorticity；
- middle-gap→cubic intermittency；
- compressive-axis pressure incompatibility。

仍剩：

$$
\boxed{
\mathsf G:
\ \mathrm{HIGHLY\ COMPRESSED,\ NOT\ ELIMINATED}.
}
$$

---

# 28. Final pressure status

C5 已完成：

- local pressure re-entry；
- pressure oscillation；
- signature compactification；
- det-zero switching boundary；
- axis lock；
- pressure-Poisson vorticity re-entry；
- constraint-complement routing。

仍剩：

$$
\boxed{
\mathsf P:
\ \mathrm{GEOMETRICALLY\ CONSTRAINED,\ NOT\ ELIMINATED}.
}
$$

---

# 29. Final high-order status

C5 已完成：

- fixed-$k$ theorem-ready direct gate；
- all-order volume no-go；
- sign failure→descent；
- fragmentation→upper roughness；
- order-sandwich；
- published Type-switch stitching audit；
- window-persistent sign defect；
- root-turnover PDE forcing；
- clock defect measure。

仍剩：

$$
\boxed{
\mathsf H+\mathsf F:
\ \mathrm{THEOREM\mbox{-}READY\ INTERFACES\ EXIST,
BUT\ RECURRENT\ LOOP\ REMAINS}.
}
$$

---

# 30. Final ancestry/setup status

UV ancestry / local-source dominance與 Theorem 3.14 setup仍有 conditional/open interfaces。

因此：

$$
\boxed{
\mathsf A
}
$$

必明確保存。

---

# 31. Six-Class Closure Theorem

在 current C3/C4/C5 guards與 conditional ancestry framework下，

所有 C5-A–L encountered recurrent survivor states都可 encode為：

$$
\boxed{
\mathfrak D_{C5}
=
\{\mathsf A,\mathsf T,\mathsf G,\mathsf P,\mathsf H,\mathsf F\}
}
$$

加各 class內 compact metadata。

沒有 C5-A–L mechanism需要新增第七個 independent residual class。

所以：

$$
\boxed{
\textbf{C5 defect-state classification is structurally closed}.
}
$$

這是 research-program closure，不是 PDE proof closure。

---

# 32. Compact metadata inventory

### $\mathsf T$

- temporal Young measures；
- concentration masses；
- phase covariance；
- cumulative temporal ledgers。

### $\mathsf G$

- strain-direction/gap measures；
- compressive-axis measures；
- derivative/vorticity stocks；
- effective active-volume。

### $\mathsf P$

- pressure oscillation；
- pressure spatial probability；
- far-matrix signature；
- det-zero distance；
- axis locking；
- pressure heredity。

### $\mathsf H$

- fixed-$k$ gate ratio；
- window sign score；
- bad-window line profile；
- root-load domination；
- theorem setup flag。

### $\mathsf F$

- viscous/nonlinear turnover toll；
- root BV path；
- order curvature；
- chain-clock defect measure；
- synchronized cluster count。

### $\mathsf A$

- ancestry legality；
- theorem-entry/setup status。

---

# 33. C5 Phase Closure Theorem

C5-A–L 已提供所有 recurrent motif families的 compact state representations，並把主要 pseudo-defects route 到 finite residual alphabet或 external regularity gate。

因此：

$$
\boxed{
\textbf{C5 — Recurrent Motif Limits,
Defect Measures, and Compensation Compactness}
}
$$

formal status：

$$
\boxed{
\mathrm{PHASE\ CLOSED}.
}
$$

PDE status：

$$
\boxed{
\mathrm{GLOBAL\ REGULARITY\ OPEN}.
}
$$

---

# 34. C5 / C6 boundary

## C5

$$
\boxed{
\text{state construction}
+
\text{compactification}
+
\text{debt routing}.
}
$$

## C6

$$
\boxed{
\text{cycle extraction}
+
\text{SCC elimination}
+
\text{global recurrence compatibility}.
}
$$

---

# 35. Proposed C6

$$
\boxed{
\textbf{C6 — Minimal Recurrent Defect Cycles,
Sink-SCC Extraction, and Cross-Domain Closure}.
}
$$

第一篇：

$$
\boxed{
\textbf{C6-A — Certified Defect Graph,
Sink-SCC Extraction, and Minimal Survivor Cycles}.
}
$$

---

# 36. C6-A obligations

1. Edge completeness audit；
2. certified SCC extraction；
3. sink SCC identification；
4. cycle debt vector；
5. finite-budget tests；
6. critical-saturation cycle compactification；
7. temporal class $T$ cross-domain coupling；
8. minimal survivor theorem。

---

# 37. C6 likely target I — Can T remain isolated?

如果 temporal phase defect必 universal feed into geometry/pressure/high-order forcing：

$$
\mathsf T\to\mathsf G/\mathsf P/\mathsf H,
$$

isolated temporal SCC消失。

目前 open。

---

# 38. C6 likely target II — Can G/P close?

C5 已得到兩個 finite-dimensional incompatibilities，但 gap collapse、two-negative pressure、mean rotation、source fragmentation仍可能形成 compensation loop。

C6要判斷它是否必累積 derivative/high-order debt。

---

# 39. C6 likely target III — Can H/F close?

persistent bad windows → forcing/order debt → higher derivative activity → new bad windows。

目前沒有 finite all-order budget排除：

$$
\boxed{
\mathsf H\leftrightarrow\mathsf F.
}
$$

這可能是最硬的 sink-SCC candidate。

---

# 40. C6 likely target IV — Do pressure/high-order loops merge?

Projected nonlinear forcing與 pressure complement來自同一 full N–S nonlinearity。

若能證 universal：

$$
\mathsf F\to\mathsf G/\mathsf P,
$$

candidate SCC可能合併成一個更小的 minimal recurrent cycle。

---

# 41. Major no-go audit

### NG-M1

compact residual state space ⇒ regularity：FALSE。

### NG-M2

finite defect graph ⇒ no infinite survivor：FALSE。

### NG-M3

pseudo-defects routed ⇒ all residuals eliminated：FALSE。

### NG-M4

external theorem gate exists ⇒ antecedents automatic：FALSE。

### NG-M5

C5 phase closure = Millennium problem closure：FALSE。

---

# 42. X-Integration guards

- C5 closure永遠標 research-program closure；
- 六類 $A,T,G,P,H,F$ 保持不同；
- 已刪除 pseudo-defect不要無理由復活；
- graph edge保存 `U/C/E` proof status；
- 未證 reverse edge不得宣稱 SCC；
- external theorem kill state不列 residual node；
- $A$ 不得偷當 physical singularity mechanism。

---

# 43. True ETN transition

C5 final state：

$$
\boxed{
\mathfrak T^{C5}_{final}
=
(
\text{residual class},
\text{compact metadata},
\text{edge status},
\text{debt vector},
\text{external kill gates}
).
}
$$

C6 state：

$$
\boxed{
\mathfrak T^{C6}
=
(
\text{SCC},
\text{cycle},
\text{cycle debt},
\text{recurrence frequency},
\text{cycle incompatibility}
).
}
$$

---

# 44. Formal C5 closeout map

$$
\boxed{
\begin{aligned}
\text{C5-A}&:\ \text{motif compactness},\\
\text{C5-B}&:\ \text{temporal Young defects},\\
\text{C5-C}&:\ \text{temporal cross-curvature},\\
\text{C5-D}&:\ \text{spatial-matrix incompatibility},\\
\text{C5-E}&:\ Q\to\text{gap/derivative/vorticity},\\
\text{C5-F}&:\ \text{axis-pressure / derivative escalation},\\
\text{C5-G}&:\ \text{fixed-order theorem-ready gate},\\
\text{C5-H}&:\ \text{static all-order volume no-go},\\
\text{C5-I}&:\ \text{sign geometry}\to\text{root descent},\\
\text{C5-J}&:\ \text{fragmentation}\to\text{upper toll/order curvature},\\
\text{C5-K}&:\ \text{dynamic theorem-time/switch audit},\\
\text{C5-L}&:\ \text{persistent-window / turnover / clock compression},\\
\text{C5-M}&:\ \boxed{\text{six-class defect graph closure}}.
\end{aligned}
}
$$

---

# 45. 正式狀態

$$
\boxed{
\begin{aligned}
\text{C5 pseudo-defect deletion audit}
&:\ \mathrm{COMPLETED},\\
\text{six residual classes}
&:\ \mathrm{DEFINED},\\
\text{finite compatibility graph}
&:\ \mathrm{DEFINED},\\
\text{compact metadata for all six classes}
&:\ \mathrm{AVAILABLE},\\
\text{finite recurrence principle}
&:\ \mathrm{PROVED},\\
\text{sink-SCC principle}
&:\ \mathrm{PROVED\ CONDITIONALLY\ ON\ GRAPH\ COMPLETENESS},\\
\text{unique sink SCC}
&:\ \mathrm{NOT\ PROVED},\\
\text{all recurrent cycles impossible}
&:\ \mathrm{NOT\ PROVED},\\
\text{C5 research phase}
&:\ \mathrm{CLOSED},\\
\text{Navier--Stokes global regularity}
&:\ \mathrm{OPEN}.
\end{aligned}
}
$$

---

# 46. 結論

C5 從：

$$
\boxed{
T,O,M,Q,P,D
}
$$

的 compensation motifs出發。

經過 A–L 的 compactification與 debt-routing後，真正 residual alphabet並沒有膨脹，反而收斂成：

$$
\boxed{
\mathfrak D_{C5}
=
\{A,T,G,P,H,F\}.
}
$$

- $A$：legality / ancestry / theorem setup；
- $T$：temporal phase；
- $G$：field geometry；
- $P$：pressure compensation/provenance；
- $H$：high-order harmonic/theorem-window；
- $F$：forcing/order variation。

generic turnover、fragmentation、Type switch、carrier relay、free Q cancellation、generic clock mismatch、large operator norm alone、vorticity complement alone，都已經不再是 free independent motifs。

所以：

$$
\boxed{
\textbf{C5 的 state-space / motif-compactification任務已完成。}
}
$$

但 finite graph仍可能有 cycle。

目前 candidate：

$$
\boxed{
H\leftrightarrow F,
}
$$

$$
\boxed{
G\leftrightarrow P,
}
$$

以及可能 isolated：

$$
\boxed{
T.
}
$$

C6 的工作因此不是再增加一個 local criterion，而是：

> 找出真正的 sink SCC／minimal recurrent defect cycle，
> 再問它的 debt能不能無限支付。

正式下一階：

$$
\boxed{
\textbf{C6 — Minimal Recurrent Defect Cycles,
Sink-SCC Extraction, and Cross-Domain Closure}.
}
$$

第一篇：

$$
\boxed{
\textbf{C6-A — Certified Defect Graph,
Sink-SCC Extraction, and Minimal Survivor Cycles}.
}
$$

---

# References

1. Clay Mathematics Institute, *Navier–Stokes Equation*, Millennium Prize Problem status page.
2. Z. Grujić, L. Xu, *Asymptotic Criticality of the Navier–Stokes Regularity Problem*, Journal of Mathematical Fluid Mechanics 26, Article 53 (2024), DOI: 10.1007/s00021-024-00888-x.
3. E. Miller, *On the interaction of strain and vorticity for solutions of the Navier–Stokes equation*, arXiv:2407.02691; Pure and Applied Analysis 8 (2026).
4. E. Miller, *A regularity criterion for the Navier–Stokes equation involving only the middle eigenvalue of the strain tensor*, arXiv:1710.05569; Arch. Rational Mech. Anal. 235 (2020).
5. Z. Bradshaw, T.-P. Tsai, *On the local pressure expansion for the Navier–Stokes equations*, arXiv:2001.11526.
6. P. Constantin, *Pressure, Intermittency, Singularity*, arXiv:2301.04489.

# Internal dependencies

- `NS_C5L_PersistentBadWindow_ClockDefect_RootTurnoverCompression_v0.1.md`
- `NS_C5K_ChainTime_WindowPersistent_DynamicInterpolationAudit_v0.1.md`
- `NS_C5J_LineSection_OrderSandwich_HarmonicSaturation_v0.1.md`
- `NS_C5I_SignGeometry_Chain_HarmonicCompatibility_v0.1.md`
- `NS_C5H_AllOrder_EffectiveVolume_AsymptoticCriticality_v0.1.md`
- `NS_C5G_PressureSignature_VorticityComplement_FixedOrderGate_v0.1.md`
- `NS_C5F_AxisPressureSignature_DerivativeGateEscalation_v0.1.md`
- `NS_C5E_StrainDirection_MiddleGap_DerivativeIntermittency_v0.1.md`
- `NS_C5D_SpatialMatrix_StrongMiddleQuadraticPressureObstruction_v0.1.md`
- `NS_C5C_TemporalCorrelation_CrossCurvatureOrdering_v0.1.md`
- `NS_C5B_TemporalYoung_PulsePhaseCompatibility_v0.1.md`
- `NS_C5A_RecordWindow_MotifCompactness_v0.1.md`
- `NS_C4J_CompensationRigidity_FinalSynchronizationAudit_v0.1.md`
- `True ETN / 無限維張力場`
- `X_Integral_Unified_Program_v0.2.md`