STANDARDIZED CLAIM CARD: CLAIM-01-DRAM

Document ID: CLAIM-01-DRAM
Version: 1.0.0-gold (Pre-Registered)
Parent Paper: The 4x Working Set Multiplier: Defeating the Memory Wall Without Buying More Silicon
Date: Tuesday, September 22, 2026
Status: FORMULA. NOT A CHIP MEASUREMENT.
SHA-256 (Locked Paper): e435686a5d9da80ef3c9edf5f569b457a688619aa55ae10211896b5e3349d2f1

1. Exact Claim

The 4.14× figure below is the formula W = 4.1445. It is not a memory-chip measurement. The dollar figures are not invoices. Earlier drafts named two different machines. This card does not report a measurement from either. ATESO binary arena architecture describes a 4.14× Working Set Multiplier ($W = 4.1445$, conservatively clamped to $4.14\times$) against ordinary managed-heap object graphs. The sizes below are arithmetic on that formula. They are not a reading from a 36 GB machine, a 16 GB machine, or a 128 GB machine. The formula talks about a 42 GB resident arena and an information equivalent of 174.1 GB of managed V8 heap ($3.35\times$ system-level effective multiplier including OS reserves; $215.5\text{ GB}$ zero-reserve theoretical ceiling). The same arithmetic, not a server measurement, puts a 1,027.8 GB managed-heap equivalent next to a 248 GB arena. The $286/GB to $69/GB figures follow that formula. They are not invoices.

2. Scope & Target Architecture

• In-Scope: Persistent structured state, graph databases, multi-agent workspaces, and real-time physics vectors on 64-bit architectures (Apple Silicon M-Series, x86-64, ARM64).
• Out-of-Scope: Compressed RAM page swapping (zswap, zram), lossy vector quantization, or static read-only mmap archives.

3. Baseline & Adversarial Controls

• Primary Baseline: Google V8 (Node.js v22.x) object graph representation with measured expansion factor $\beta = 3.500$ (Map pointer, prototype link, hidden class descriptors, pointer alignment).
• Secondary Controls:
  • Float64Array / Uint8Array typed buffers (dense, but lack dynamic polymorphic schema mutation).
  • FlatBuffers / Cap’n Proto (zero-copy serialization, but static schema without resident graph mutation).
  • OpenJDK HotSpot JVM (CompressedOOPs enabled, 16-byte object header).

4. Fundamental Equation & Constants

$$W = \frac{\beta}{(1 - \alpha_{\text{GC}})(\gamma + f)}$$ - $\beta = 3.500$ (Measured V8 object-to-payload bloat ratio, Appendix A). - $\alpha_{\text{GC}} = 0.250$ (25% collector headroom buffer to prevent GC thrashing). - $\gamma = 1.000$ (Direct Mode: 1 packed 64-byte granule per slot; fallback Siege Mode $\gamma = 2.000$). - $f = 0.12598 \approx 0.126$ (Directory and Merkle metadata per payload byte, $8.06\text{ B} / 64\text{ B}$). - Calculated direct Multiplier: $W = \frac{3.500}{(1 - 0.250)(1.000 + 0.126)} = \frac{3.500}{0.8445} = \mathbf{4.1445\times \approx 4.14\times}$. - Fallback Siege Multiplier: $W = \frac{3.500}{(1 - 0.250)(2.000 + 0.126)} = \frac{3.500}{1.5945} = \mathbf{2.195\times \approx 2.20\times}$.

5. Environment & Raw Data

• Machines named in earlier drafts, and they are not one rig: One line said Apple M5 Max 36 GB plus M1 Pro 16 GB. Another said Apple M5 Max with 128 GB unified memory. This card does not report a measurement from either.
• Benchmark Suite: 41-check automated harness (STAGE5-BETA-BENCHMARK/).
• Reproducibility Repository: manymoats-kpf/engines/arena-multiplier/ (un-gated script).

6. Falsification Criterion

The claim is falsified if an adversary can construct an ordinary V8 or JVM managed-heap object graph that holds identical relational state with an expansion ratio $\beta \le 1.200$ while maintaining sub-millisecond continuous mutation without triggering garbage collection pauses $>1.0\text{ ms}$.

7. Known Failure Modes & Limitations

• Workloads consisting purely of opaque large binary blobs (e.g., MP4 video streams, pre-compressed JPEG) experience $W \approx 1.0\times$ because V8 does not wrap raw blobs in fine-grained object wrappers.
• Memory arenas must be pre-allocated; resizing an arena under full capacity requires contiguous address reservation.