理論THY-2026-0105v0.1
物理計算成本向量與計算時空
物理成本是向量 C_P =（分型的運算、按層級的記憶體流量、I/O、互連、記憶體駐留、裝置占用、wall time、能量），不是 FLOPs。計算時空首先是資源場的測度 V_CST = ∫ R(t) dt =（V_C、V_M、V_N、V_S）；未宣告正規化前各分量不可相加，體積相等（8 GPU × 10 s = 1 GPU × 80 s）不等於拓撲 Θ_CST =（T_wall、T_serial、P_parallel、D_peak、M_peak、B_peak、Γ_comm）相等。Roofline、memory wall 與資料搬移的結果解釋了為何相同 FLOPs 的工作在時間與能量上不同；峰值硬體占用是容量門檻；CST 等級從 D（規格推估）到 A+（因果資源歸因）。
定義
definitions- C_P = (O, B_M, B_I, B_N, M_R, D, T, E); O typed by precision; nominal vs executed vs useful operations.
- V_M = ∫ M_resident dt (byte·s), V_C = ∫ D(t) dt (device·s); MemoryTraffic ≠ MemoryResidency.
- Normalized scalar V*_CST(Reference, Weights, Boundary); topology Θ_CST; peak footprint H_peak.
- Measurement confidence bundle G_M = (Grade_μ, Grade_E, Grade_CST); P_compute = (C_P, V_CST, Θ_CST, H_peak, E, Boundary_P, G_M).
前提
assumptions- Attainable performance is bounded by min(P_peak, BW · arithmetic intensity) (Roofline).
主張
claims- FLOPs ≠ PhysicalComputationalCost; SameFLOPs ≠ SameLatency ≠ SameEnergy; SameDeviceTime ≠ SameEnergy.
- SameCSTVolume ≠ SameCSTTopology; TotalResource ≠ PeakCapacityRequirement; MoreDevices ⇏ LowerLatency.
- ScalarCST ⇒ DeclaredNormalization; CSTComparison ⇒ SameBoundaryOrExplicitConversion; LowUtilization ≠ BadSystem.
形式化
formalization- V_CST = ∫ R(t) dt with R = (r_C, r_M, r_N, r_S); V*_CST = ∫ Σ_j w_j r_j(t)/C_ref,j dt.
- Vector efficiency η_Q/CST = (Q/V_C, Q/V_M, Q/V_N, Q/V_S); Pareto dominance A ≻_P B.
預測
predictions- Controlling FLOPs will leave large independent variation in T, E, B_M, B_N and V_M across memory patterns and topologies (Falsifiable Claim 2).
證偽／失敗條件
falsification_conditions- If, FLOPs held fixed, time, energy, memory traffic and residency do not vary substantially across workloads, a single FLOPs cost model suffices.
已知限制
known_limitations- The pilot recorded wall time, device energy, peak VRAM, memory residency and utilization integrals for one GPU (CST-B); interconnect and memory traffic were not measured.
證據
| 來源 | 關係 | 目標 | 狀態 | ID |
|---|---|---|---|---|
EXP-2026-0103 XA-06 第一次真實模型 pilot——Qwythos-9B-v2 走 A0→A5 階梯（36 試驗，2026-09-03） | tests | THY-2026-0105 物理計算成本向量與計算時空 | ACTIVE | REL-2026-0482 |
EXP-2026-0106 Experiment D——物理軌跡對齊（已宣告） | tests | THY-2026-0105 物理計算成本向量與計算時空 | ACTIVE | REL-2026-0497 |
關係
| 來源 | 關係 | 目標 | 狀態 | ID |
|---|---|---|---|---|
THY-2026-0105 物理計算成本向量與計算時空 | extends | THY-2026-0104 能量帳本層級與熱力學型別安全 | ACTIVE | REL-2026-0371 |
RES-2026-0101 執行與物理線——一個答案在回合、語意工作、能量與計算時空上的代價 | develops | THY-2026-0105 物理計算成本向量與計算時空 | ACTIVE | REL-2026-0362 |
THY-2026-0109 鷹架能力紀錄：SSR、SDR、SCM 與消融階梯 | extends | THY-2026-0105 物理計算成本向量與計算時空 | ACTIVE | REL-2026-0375 |
THY-2026-0110 canonical intelligence event、Pareto 比較與不過早純量化 | extends | THY-2026-0105 物理計算成本向量與計算時空 | ACTIVE | REL-2026-0378 |
PAP-2026-0105 計算不是只有 FLOPs：記憶體、互連、硬體占用與計算時空體積 | formalizes | THY-2026-0105 物理計算成本向量與計算時空 | ACTIVE | REL-2026-0408 |
SYS-2026-0101 XA-03——遙測與執行記錄器（物理執行證據層） | implements | THY-2026-0105 物理計算成本向量與計算時空 | ACTIVE | REL-2026-0448 |
EXP-2026-0103 XA-06 第一次真實模型 pilot——Qwythos-9B-v2 走 A0→A5 階梯（36 試驗，2026-09-03） | tests | THY-2026-0105 物理計算成本向量與計算時空 | ACTIVE | REL-2026-0482 |
EXP-2026-0106 Experiment D——物理軌跡對齊（已宣告） | tests | THY-2026-0105 物理計算成本向量與計算時空 | ACTIVE | REL-2026-0497 |
歷史與來源歷程
- Canonical URL
- https://evemisslab.com/ai/theory/THY-2026-0105/
- 快照
AI-SNAPSHOT-v0.1-fe85b9694a45- 來源歷程
source- EveMissLab research collection: Intelligence Physical Metrology (真本體論13)
extracted_by- Splice (Claude Code), reading the canonical UTF-8 sources and each package's own reports
extracted_at- 2026-09-11
generator- tools/extract_all.py
claim_boundary- status, evidence level and result type follow the source artifact's own stated claim boundary; nothing is upgraded beyond what the report supports