spark/context/equations-and-bounds.md

id	title	status	source_sections	related_topics	key_equations	key_terms	images	examples	open_questions
equations-and-bounds	Equations and Bounds	established	Derived from context files and official specifications	[gb10-superchip memory-and-storage ai-workloads connectivity]	[flops-fp4 memory-bandwidth model-memory-estimate nvlink-c2c-bandwidth storage-throughput]	[tflops pflop bandwidth throughput fp4 fp8 fp16 fp32]	[]	[llm-memory-estimation.md]	[Sustained vs. peak TFLOPS under real workloads Actual memory bandwidth under mixed CPU+GPU access patterns]

Equations and Bounds

Reference for all quantitative specifications, formulas, and validation ranges for the Dell Pro Max GB10.

1. Compute Performance

Peak TFLOPS by Precision

Precision	Peak TFLOPS	Source	Notes
FP4	1,000	T0 Spec	Headline figure, 1 PFLOP
FP8	~500	T3 Infer	Typical 2:1 ratio from FP4
FP16	~250	T3 Infer	Typical 4:1 ratio from FP4
FP32	~125	T3 Infer	Typical 8:1 ratio from FP4

Note: FP8/FP16/FP32 values are inferred from typical Blackwell architecture ratios. Actual values not yet independently confirmed.

GPU Cores

• CUDA cores: 6,144 (T0 Spec)
• Tensor Cores: 5th generation (count TBD)

2. Memory

Bandwidth

• Memory bandwidth: 273 GB/s (T0 Spec, LPDDR5X at 9,400 MT/s)
• NVLink-C2C bandwidth: 600 GB/s bidirectional (T0 Spec, CPU-GPU interconnect)

Capacity

• Total unified memory: 128 GB LPDDR5X (T0 Spec)
• Usable for models: ~109-115 GB (T3 Infer, after OS/framework/KV cache overhead)

3. Model Memory Estimation

Formula: Memory Required for Model Weights

Memory (GB) = Parameters (billions) × Bytes_per_parameter

Precision	Bytes/Param	Formula
FP4	0.5	Params_B × 0.5
FP8/INT8	1.0	Params_B × 1.0
FP16	2.0	Params_B × 2.0
FP32	4.0	Params_B × 4.0

Total Inference Memory (approximate)

Total Memory ≈ Model_Weights + KV_Cache + Activation_Memory + Framework_Overhead

Rule of thumb: budget 1.2-1.5x the raw model weight size for total inference memory.

Maximum Model Sizes (single unit, 128 GB)

Precision	Max Params (raw)	Max Params (practical, ~110 GB usable)
FP4	256B	~200B
FP8/INT8	128B	~100B
FP16	64B	~55B
FP32	32B	~27B

4. Networking Bounds

Interface	Bandwidth	Direction
NVLink-C2C	600 GB/s	Bidirectional
LPDDR5X memory	273 GB/s	System memory
QSFP (per port)	200 Gbps (25 GB/s)	Network
QSFP (total)	400 Gbps (50 GB/s)	2 ports combined
10 GbE Ethernet	10 Gbps (1.25 GB/s)	Network
USB-C (per port)	20 Gbps (2.5 GB/s)	I/O

5. Power Bounds

Parameter	Value
PSU rating	280W
System TDP	~140W
Power delivery	USB-C PD

6. Physical Bounds

Parameter	Value
Volume	~1.15 L
Weight	1.31 kg
Footprint	150 × 150 mm
Height	51 mm

7. Validation Rules

When checking calculations:

• Model size estimates should not exceed 128 GB (single) or 256 GB (stacked)
• TFLOPS claims must specify precision — reject unqualified "1 PFLOP" statements
• Memory bandwidth (273 GB/s) is the system memory bus, NOT the NVLink-C2C (600 GB/s)
• Network bandwidth (QSFP) is in Gbps, not GB/s — divide by 8 for bytes