# Phase Canon Consolidated Audit Report v1.0
## Five-Batch Canonical Consolidation of the EveMissLab Phase-Theory Genealogy

**日期：** 2026-08-14  
**狀態：** FINAL CONSOLIDATED AUDIT  
**上游：** Phase Canon v1.0；Audit Batches 01–05；GPC-CS；PCPRT  
**下游：** EveMissLab Phase Canon v1.1  
**總 claim 數：** 238

---

# 0. Executive Closure

Phase Canon Audit Batches 01–05 已完成。

總計審核：

$$
\boxed{238\ \text{claim-level judgments}}
$$

粗分類結果：

| Canonical category | Count | Share |
|---|---:|---:|
| KEEP | 80 | 33.61% |
| REPAIR/REFRAME | 29 | 12.18% |
| CONJECTURE/BENCHMARK | 33 | 13.87% |
| RETIRE | 91 | 38.24% |
| HISTORICAL/OPEN | 5 | 2.10% |

這個結果不代表：

$$
\boxed{
\text{old phase theory}
\rightarrow
\text{mostly false}
}
$$

更準確是：

$$
\boxed{
\text{old phase theory}
\rightarrow
\text{structure extraction}
+
\text{type correction}
+
\text{evidence calibration}.
}
$$

---

# 1. Five-Batch Coverage

| Batch | Scope | Claims | KEEP | REPAIR | CONJECTURE / BENCHMARK | RETIRE | HISTORICAL / OPEN |
|---|---|---:|---:|---:|---:|---:|---:|
| Batch 01 | G1 Strong Ontology | 28 | 3 | 4 | 4 | 15 | 2 |
| Batch 02 | G2 Mathematics / Topology | 43 | 10 | 13 | 7 | 12 | 1 |
| Batch 03 | G3 Cognitive / Time / Semantic | 57 | 20 | 6 | 5 | 25 | 1 |
| Batch 04 | G4 AI / Search / Cross-Carrier | 62 | 30 | 2 | 9 | 21 | 0 |
| Batch 05 | Biological / Body / Engineering | 48 | 17 | 4 | 8 | 18 | 1 |

五批形成一條理論成熟路徑：

$$
\boxed{
G1\ \text{Ontology}
\rightarrow
G2\ \text{Mathematics}
\rightarrow
G3\ \text{Generalized Relation}
\rightarrow
G4\ \text{Executable AI / Search}
\rightarrow
\text{Bio / Engineering Evidence Boundary}.
}
$$

---

# 2. What Survived

Audit 後真正跨世代存活的不是單一「宇宙相位場」，而是下列結構。

## 2.1 Physical phase

$$
\theta\in S^1
$$

以及 phase difference、phase response、synchronization、entrainment、coherence、oscillator computing 與 engineering multiphase timing。

## 2.2 Regime / order-parameter structure

包括 material / dynamical phase、bifurcation、metastable repertoire、phase boundary 與 order parameter。

## 2.3 Typed relational difference

G3/G4 中存活的是：

$$
\boxed{
\Delta_\Phi
=
(
d_1,\ldots,d_m
)
}
$$

而不是把所有 cognitive / semantic variables 強迫壓成一個 $S^1$ angle。

## 2.4 Realization maps

最重要的物理回接條件：

$$
\boxed{
\Pi\circ\Phi_{\mathrm{phys}}
\approx
\Gamma\circ\Pi.
}
$$

## 2.5 Fiber / closure tests

若：

$$
\Pi(z_1)=\Pi(z_2)
$$

卻：

$$
P(z_1)\neq P(z_2),
$$

則 coarse state 對 $P$ 不充分。

## 2.6 Plasticity / adaptive carrier

$$
q=(\theta,a,\lambda,\mu)
$$

或更一般：

$$
q=(z,\lambda,\mu).
$$

interaction 不只改 state，也能改 coupling / update rule。

## 2.7 Cross-carrier transduction

$$
\boxed{
H_A
\xrightarrow{E_A}
Z
\xrightarrow{T_{AB}}
U_B
\xrightarrow{D_B}
H'_B.
}
$$

## 2.8 Active epistemic control

GIPE 的核心存活為：

$$
\boxed{
X_t
\rightarrow
a_t
\rightarrow
o_t
\rightarrow
v_t
\rightarrow
X_{t+1}.
}
$$

phase 在此最多是 typed epistemic discrepancy，不是 physical oscillator。

---

# 3. What Was Retired

91 條 RETIRE 主要分成八類：

1. **Type jump**：semantic/generalized phase 無映射升格為 PH-0。
2. **Representation → ontology jump**：可表示不等於本體身份。
3. **Analogy → isomorphism jump**：mapping table 不等於同構。
4. **Frequency coincidence → coupling jump**：頻率接近不等於相互作用。
5. **Correlation / efficacy → mechanism jump**：效果不證明指定機制。
6. **Hidden computation → O(1)**：前處理／索引／拓樸計算不能被藏掉。
7. **Continuous space → hypercomputation**：不可數 state space 不等於 exact real input access。
8. **Engineering phase → quantum phase**：多相、PLL、resonance 不等於量子相位。

---

# 4. Five Core Audit Principles

## Principle A — Type Before Transfer

$$
\boxed{
\text{same word}
\neq
\text{same mathematical object}.
}
$$

## Principle B — Map Before Ontology

高層 phase claim 若要回接物理：

$$
\boxed{
x=\Pi(z)
}
$$

與：

$$
\boxed{
\Pi\Phi_{\mathrm{phys}}
\approx
\Gamma\Pi
}
$$

必須可定義、可測、可反證。

## Principle C — Benchmark Before Novelty

對 PH-5 / PH-6：

$$
\boxed{
\Delta S_\phi
=
S(M_\phi)-S(M_{\mathrm{typed}}).
}
$$

若無增益，phase 只是 nomenclature。

## Principle D — Mechanism Before Medical Inference

$$
\boxed{
B0\ \text{periodicity}
\not\Rightarrow
B1\ \text{phase}
\not\Rightarrow
B2\ \text{coupling}
\not\Rightarrow
B3\ \text{clinical relevance}.
}
$$

## Principle E — Preserve Provenance, Retire Claims

舊文件不刪除。退出的是 claim 的 current-canonical status，不是歷史紀錄。

---

# 5. Canonical Migration by Generation

## G1 — Strong Ontology

$$
\text{universal phase ontology}
\rightarrow
\boxed{
\text{substrate-specific physical phase}
+
\text{effective realization}
+
\text{typed conjectures}.
}
$$

## G2 — Mathematics / Topology

$$
\text{topology = phase}
\rightarrow
\boxed{
\text{phase-coherence TDA}
+
\text{weighted oscillators}
+
H^1_{\mathrm{persistent}}\to S^1
+
\text{topology-aware computing}.
}
$$

## G3 — Cognitive / Semantic / Time

$$
\text{semantic quantum phase}
\rightarrow
\boxed{
\text{typed relational difference}
+
\text{comparison base}
+
\text{internal time}
+
\text{receiver-dependent reconstruction}.
}
$$

## G4 — AI / Search / Cross-Carrier

$$
\text{global phase metaphor}
\rightarrow
\boxed{
\text{open-world retrieval}
+
\text{active epistemic control}
+
\text{grounded verification}
+
\text{cross-carrier transduction}.
}
$$

## Bio / Engineering

生物：

$$
\boxed{
\text{endogenous oscillator}
+
\text{Zeitgeber}
+
\text{phase response}
+
\text{evidence ladder}.
}
$$

工程：

$$
\boxed{
\text{multiphase}
+
\text{resonance}
+
\text{PDN}
+
\text{predictive control}.
}
$$

---

# 6. Current Canonical Successor Graph

$$
\boxed{
\text{Phase Taxonomy}
\rightarrow
\text{Phase Canon}
\rightarrow
\begin{cases}
\text{GPC-CS}\\
\text{PCPRT}
\end{cases}
}
$$

數學延伸：

$$
\boxed{
\text{PCH}
+
\text{Weighted Infinite Oscillators}
+
\text{Persistent Cohomology Circular Coordinates}.
}
$$

AI／認知延伸：

$$
\boxed{
\text{GIPSS / GIPE}
\rightarrow
\text{GPC effective relation}.
}
$$

---

# 7. v1.1 Mandatory Amendments

1. **No type jump without a map.**
2. **Renaming a state as phase does not create phase mechanics.**
3. **Frequency coincidence is not coupling.**
4. **Semantic alignment is not grounded validity.**
5. **Representation is not automatically language.**
6. **Algorithmic phase novelty requires ablation against a typed non-phase baseline.**
7. **Persistent topology is informative but generally incomplete.**
8. **Biological phase is not medical efficacy.**
9. **Engineering phase is not quantum phase.**
10. **Retired claims remain in provenance but cannot be cited as current Canon.**

---

# 8. Research Stack After Audit

1. Physical Phase Realization
2. Phase-Coherence TDA
3. Weighted Infinite Oscillators
4. Persistent-Cohomology Circular Coordinates
5. Typed Relational Difference
6. GPC Cross-Carrier Safety
7. GIPSS Open-World Discovery
8. GIPE Active Epistemic Control
9. Cross-Carrier Semantic Transduction
10. Biological Oscillator / Entrainment Science
11. Multiscale Physiological Monitoring
12. Classical Power-Phase Engineering

---

# 9. Audit Cycle Closure

從強本體論到 2026-08-14 的 Canonization，phase research 的成熟不是：

$$
\boxed{
\text{phase becomes more universal}.
}
$$

而是：

$$
\boxed{
\text{phase becomes more typed, more mapped, more falsifiable, and more executable}.
}
$$

現行最高版本：

$$
\boxed{
\text{Phase Canon}
=
\text{Typed Structures}
+
\text{Maps}
+
\text{Dynamics}
+
\text{Evidence}
+
\text{Ablation}
+
\text{Falsification}.
}
$$

**Phase Canon Consolidated Audit Cycle — CLOSED.**