TheoryTHY-2026-0105v0.1

Physical computation cost vector and computational spacetime

Physical cost is the vector C_P = (typed operations, memory traffic by hierarchy, I/O, interconnect, memory residency, device occupancy, wall time, energy), not FLOPs. Computational spacetime is first a measure V_CST = ∫ R(t) dt = (V_C, V_M, V_N, V_S) over a resource field; the components may not be added before a declared normalization, and equal volume (8 GPU × 10 s = 1 GPU × 80 s) is not equal topology Θ_CST = (T_wall, T_serial, P_parallel, D_peak, M_peak, B_peak, Γ_comm). Roofline, memory-wall and data-movement results explain why same-FLOPs workloads differ in time and energy; a peak hardware footprint is a capacity barrier; CST grades run from D (spec estimate) to A+ (causal resource attribution).

Research status: EXPERIMENTAL being tested experimentally
Evidence level: E1 Internal observation
Data basis: THEORY Theoretical reasoning only; no measurement.
Version: 0.1
Updated: 2026-09-02
Created: 2026-09-02
Domain: Computation
Program: PRG-2026-0101 Intelligence Physical Metrology (IPM)
Authors: Neo.K (EveMissLab)
AI collaborators: Aletheia (GPT-5.6 Sol, OpenAI ChatGPT)

Definitions

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).

Assumptions

assumptions: Attainable performance is bounded by min(P_peak, BW · arithmetic intensity) (Roofline).

Claims

claims: FLOPs ≠ PhysicalComputationalCost; SameFLOPs ≠ SameLatency ≠ SameEnergy; SameDeviceTime ≠ SameEnergy.
SameCSTVolume ≠ SameCSTTopology; TotalResource ≠ PeakCapacityRequirement; MoreDevices ⇏ LowerLatency.
ScalarCST ⇒ DeclaredNormalization; CSTComparison ⇒ SameBoundaryOrExplicitConversion; LowUtilization ≠ BadSystem.

Formalisation

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.

Predictions

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).

Falsification / failure conditions

falsification_conditions: If, FLOPs held fixed, time, energy, memory traffic and residency do not vary substantially across workloads, a single FLOPs cost model suffices.

Known limitations

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.

Evidence

Source	Relation	Target	Status	ID
`EXP-2026-0103` XA-06 first real-model pilot — Qwythos-9B-v2 on the A0→A5 ladder (36 trials, 2026-09-03)	`tests`	`THY-2026-0105` Physical computation cost vector and computational spacetime	`ACTIVE`	`REL-2026-0482`
`EXP-2026-0106` Experiment D — physical trace alignment (declared)	`tests`	`THY-2026-0105` Physical computation cost vector and computational spacetime	`ACTIVE`	`REL-2026-0497`

Relations

Source	Relation	Target	Status	ID
`THY-2026-0105` Physical computation cost vector and computational spacetime	`extends`	`THY-2026-0104` Energy accounting hierarchy and thermodynamic type safety	`ACTIVE`	`REL-2026-0371`
`RES-2026-0101` Execution and physical line — what one answer costs in turns, semantic work, energy and computational spacetime	`develops`	`THY-2026-0105` Physical computation cost vector and computational spacetime	`ACTIVE`	`REL-2026-0362`
`THY-2026-0109` Scaffolding capability record: SSR, SDR, SCM and the ablation ladder	`extends`	`THY-2026-0105` Physical computation cost vector and computational spacetime	`ACTIVE`	`REL-2026-0375`
`THY-2026-0110` The canonical intelligence event, Pareto comparison and no premature scalarization	`extends`	`THY-2026-0105` Physical computation cost vector and computational spacetime	`ACTIVE`	`REL-2026-0378`
`PAP-2026-0105` Paper 05 — Computation is more than FLOPs: memory, interconnect, hardware occupancy, and computational spacetime volume	`formalizes`	`THY-2026-0105` Physical computation cost vector and computational spacetime	`ACTIVE`	`REL-2026-0408`
`SYS-2026-0101` XA-03 — telemetry and run logger (physical execution evidence layer)	`implements`	`THY-2026-0105` Physical computation cost vector and computational spacetime	`ACTIVE`	`REL-2026-0448`
`EXP-2026-0103` XA-06 first real-model pilot — Qwythos-9B-v2 on the A0→A5 ladder (36 trials, 2026-09-03)	`tests`	`THY-2026-0105` Physical computation cost vector and computational spacetime	`ACTIVE`	`REL-2026-0482`
`EXP-2026-0106` Experiment D — physical trace alignment (declared)	`tests`	`THY-2026-0105` Physical computation cost vector and computational spacetime	`ACTIVE`	`REL-2026-0497`

History and provenance

Canonical URL

https://evemisslab.com/ai/theory/THY-2026-0105/

Machine-readable

/ai/theory/THY-2026-0105/index.json

Snapshot

AI-SNAPSHOT-v0.1-fe85b9694a45

Provenance

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