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+# Analysis: Arena Physica and Atlas RF Studio
+
+## Company Overview
+
+Arena Physica positions itself as building "Electromagnetic Superintelligence" -- a foundation model trained directly on electromagnetic fields, one of the four fundamental forces of physics.
+
+**Website:** https://www.arenaphysica.com/
+**Key Product:** Atlas RF Studio (Beta)
+**Core Models:** Heaviside-0 (forward prediction), Marconi-0 (inverse design)
+
+## Technical Architecture
+
+### Heaviside-0: Forward Electromagnetic Model
+
+A transformer-based neural network that predicts S-parameters (scattering parameters) from circuit geometry.
+
+**Performance claims:**
+- Weighted MAE: < 1 dB
+- Speed: 13ms per design vs 4 minutes for traditional EM solvers
+- Speedup: 18,000x to 800,000x over commercial solvers (HFSS, CST)
+
+**Architecture insights:**
+- Transformer backbone (specific architecture undisclosed)
+- Trained on electromagnetic field data, not just input-output mappings
+- Field augmentation acts as a regularizer -- even 0.3% field coverage during training reduced OOD loss
+
+### Marconi-0: Inverse Design Model
+
+A diffusion-based generative model that produces physical RF geometries matching target S-parameter specifications.
+
+**Approach:**
+- Iterative refinement (diffusion process)
+- Generates "alien structures" -- non-intuitive geometries that meet specs
+- Trades compute time for quality (more diffusion steps = better designs)
+
+### Training Data
+
+**Simulated data:** 3 million designs across 25 expert templates with procedural variations, plus random organic structures to force learning in unexplored design space regions.
+
+**Measured data:** Fabricated designs tested with vector network analyzers to capture manufacturing tolerances, material variations, connector parasitics.
+
+**Total claimed:** 20M+ simulated designs in the broader training set.
+
+### Current Design Space
+
+- 2-layer PCB designs (8mm x 8mm)
+- 3 dielectric material choices
+- Ground vias
+- Filters and antennas
+
+## Key Technical Insight: Fields as Fundamental Quantities
+
+Arena Physica's central thesis is that Maxwell's equations govern electromagnetic fields, and models trained on field distributions learn the underlying physics rather than surface-level correlations between geometry and S-parameters.
+
+This is directly relevant to WiFi sensing because:
+
+1. **CSI IS an electromagnetic field measurement.** WiFi Channel State Information captures the complex transfer function H(f) between transmitter and receiver antennas across frequency subcarriers. This is a discrete sampling of the electromagnetic field in the propagation environment.
+
+2. **Human bodies perturb the electromagnetic field.** Pose estimation from WiFi works because the human body (70% water, high permittivity) creates measurable perturbations in the ambient electromagnetic field.
+
+3. **Foundation model approach could apply to sensing.** A model trained on electromagnetic field distributions in rooms with human bodies could potentially generalize across environments better than models trained on CSI-to-pose mappings directly.
+
+## Relevance to WiFi-DensePose Project
+
+### Direct Applicability: Moderate
+
+Arena Physica's current focus is RF component design (filters, antennas), not sensing. However, several concepts transfer directly:
+
+### 1. Physics-Informed Neural Architecture
+
+Arena Physica trains on the electromagnetic field itself, not just input-output pairs. We should adopt this principle:
+
+**Current approach in wifi-densepose:**
+```
+CSI amplitude/phase -> CNN/Transformer -> Keypoint coordinates
+```
+
+**Physics-informed approach inspired by Arena Physica:**
+```
+CSI amplitude/phase -> Field reconstruction -> Body perturbation extraction -> Pose estimation
+```
+
+Concretely, this means adding an intermediate field reconstruction stage that produces a spatial electromagnetic field map (similar to our existing `tomography.rs` module in RuvSense) and then extracting body perturbation from the field rather than going directly from CSI to pose.
+
+### 2. Forward Model for Data Augmentation
+
+Heaviside-0 predicts S-parameters from geometry. An analogous forward model for WiFi sensing would predict CSI from (room geometry + human pose). This enables:
+
+- **Synthetic training data generation:** Generate CSI samples for arbitrary room layouts and poses
+- **Domain adaptation:** Bridge the sim-to-real gap by training the forward model on measured data
+- **Physics-based data augmentation:** Perturb room geometry parameters to generate diverse training environments
+
+This directly addresses our MERIDIAN cross-environment generalization challenge (ADR-027).
+
+### 3. Diffusion-Based Inverse Models
+
+Marconi-0 uses diffusion to solve the inverse problem (S-parameters -> geometry). The analogous inverse problem for WiFi sensing is (CSI -> pose). Recent work on diffusion-based pose estimation could be adapted:
+
+- Generate multiple pose hypotheses from a single CSI observation
+- Score hypotheses by physical plausibility (bone length constraints, joint angle limits)
+- Select the highest-scoring hypothesis
+
+This is more robust than single-shot regression for ambiguous CSI measurements.
+
+### 4. Multi-Resolution Field Representation
+
+Arena Physica operates on 2-layer PCB designs at the mm scale. WiFi sensing operates at the wavelength scale (12.5 cm at 2.4 GHz). However, the principle of multi-resolution field representation applies:
+
+- **Coarse grid:** Room-level field structure (presence detection, zone occupancy)
+- **Medium grid:** Body-level perturbation (bounding box, silhouette)
+- **Fine grid:** Limb-level detail (keypoint localization)
+
+This maps to our existing RuvSense tomography module which implements RF tomography on a voxel grid, but suggests a multi-resolution approach would be more efficient.
+
+## Adaptation Strategy for ESP32 + Pi Zero Deployment
+
+### What to borrow from Arena Physica:
+
+1. **Field-augmented training:** During training (on GPU workstation), include an auxiliary loss that encourages the model to predict the electromagnetic field distribution, not just keypoints. This regularizes the model and improves OOD generalization. At inference time on Pi Zero, the field prediction head is pruned.
+
+2. **Lightweight forward model:** Train a small forward model (CSI predictor given room parameters) on the ESP32 side. This enables on-device anomaly detection: if observed CSI deviates significantly from the forward model prediction, flag the observation as potentially adversarial or corrupted.
+
+3. **Template-based design space:** Arena Physica uses 25 expert templates with procedural variations. We should define "room templates" (corridor, open office, bedroom, living room) and train specialized lightweight models per template, selected at deployment time.
+
+### What does NOT transfer:
+
+1. **Scale of training data:** 20M+ designs is infeasible for WiFi sensing. Real CSI data collection is expensive. Synthetic data (ray tracing simulation) partially addresses this but lacks the fidelity of Arena Physica's EM simulations.
+
+2. **Diffusion models on edge:** Marconi-0's diffusion approach is too computationally expensive for Pi Zero inference. We need single-shot architectures for real-time operation.
+
+3. **2D geometry inputs:** Arena Physica processes 2D PCB layouts. WiFi sensing requires processing time-series data with complex spatial structure. The input representations are fundamentally different.
+
+## Conclusions
+
+Arena Physica demonstrates that foundation models trained on electromagnetic field data achieve superior generalization compared to models trained on input-output mappings alone. The key transferable insights for WiFi-DensePose are:
+
+1. **Train on fields, not just observations** -- include field reconstruction as an auxiliary task
+2. **Use forward models for augmentation** -- predict CSI from room+pose for synthetic data
+3. **Multi-resolution representations** -- coarse-to-fine field reconstruction improves efficiency
+4. **Template-based specialization** -- room-type-specific models improve accuracy with lower compute
+
+These insights inform the implementation plan, particularly the training pipeline design and the novel "field-augmented" training approach proposed in the implementation plan.
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+# Arena Physica Studio Analysis
+
+Research document for wifi-densepose project.
+Date: 2026-04-02
+
+---
+
+## 1. What is Arena Physica?
+
+Arena Physica (trading as Arena, arena-ai.com / arenaphysica.com) is a startup pursuing "Electromagnetic Superintelligence" -- building AI foundation models that develop superhuman intuition for how geometry shapes electromagnetic fields.
+
+- **Founded**: 2019
+- **Founders**: Pratap Ranade (CEO), Arya Hezarkhani, Claire Pan, Michael Frei, Harish Krishnaswamy
+- **Funding**: $30M Series B (April 2025)
+- **Offices**: NYC (HQ), SF, LA
+- **Customers**: AMD, Anduril Industries, Sivers Semiconductors, Bausch & Lomb
+- **Impact claimed**: 35% reduction in engineering man-hours, multi-month acceleration in time-to-market, >3% improvement in product quality
+
+Arena does NOT do WiFi sensing. They build AI-driven tools for RF/electromagnetic hardware design -- antennas, PCBs, filters, RF components. Their relevance to our project is methodological: they demonstrate how to build neural surrogates for Maxwell's equations that run 18,000x to 800,000x faster than traditional solvers.
+
+
+## 2. Atlas Platform and RF Studio
+
+### 2.1 Atlas (Main Platform)
+
+Atlas is Arena's "agentic platform" for hardware design workflows. It is deployed in production with Fortune 500 companies. Atlas encompasses:
+
+- AI-driven electromagnetic simulation
+- Design generation and optimization
+- Hardware verification workflows
+- Integration with existing engineering tools
+
+### 2.2 Atlas RF Studio (Public Beta)
+
+Atlas RF Studio (https://studio.arenaphysica.com/) is a lightweight public instance of the Atlas platform, released as an "interactive sandbox for AI-driven inverse RF design." It serves as a research preview of their electromagnetic foundation model.
+
+**Current capabilities (Beta):**
+- Two-layer RF structures
+- 8mm x 8mm maximum dimensions
+- Ground vias support
+- 3 dielectric material choices
+- AI-driven design generation from specifications
+- Real-time S-parameter prediction
+
+**Workflow:**
+1. User inputs electromagnetic specifications (target S-parameters)
+2. Marconi-0 (inverse model) generates candidate geometries via conditional diffusion
+3. Heaviside-0 (forward model) evaluates each candidate in 13ms
+4. System iterates: generate -> simulate -> refine
+5. User receives optimized RF component design
+
+### 2.3 Foundation Models
+
+**Heaviside-0 (Forward Model)**:
+- Named after Oliver Heaviside (reformulated Maxwell's equations into modern vector form)
+- Predicts: S-parameters (magnitude + phase) and electromagnetic field distributions
+- Speed: 13ms single design, 0.3ms batched
+- Traditional solver comparison: ~4 minutes (HFSS/FDTD)
+- Speedup: 18,000x - 800,000x
+- Trained on 3 million designs across 25 expert templates + random structures
+- Training data represents 20+ years of combined simulation time
+- Accuracy: < 1 dB magnitude-weighted MAE
+
+**Marconi-0 (Inverse Model)**:
+- Named after Guglielmo Marconi (radio pioneer)
+- Generates physical geometries from target S-parameter specifications
+- Uses conditional diffusion process (similar to Stable Diffusion / DALL-E architecture)
+- Can produce unconventional geometries that outperform human-designed solutions
+
+### 2.4 Roadmap
+
+Planned extensions include:
+- Multi-layer structures
+- Silicon integration (tapeout planned by end 2026)
+- Multiphysics integration (thermal, mechanical beyond EM)
+- Broader frequency ranges and design spaces
+
+
+## 3. Studio Technical Architecture
+
+### 3.1 Frontend Stack
+
+Based on runtime analysis of https://studio.arenaphysica.com/:
+
+| Component | Technology | Evidence |
+|---|---|---|
+| Framework | Next.js (App Router, server-side streaming) | `__next_f`, `__next_s` arrays, static chunk loading |
+| UI Library | Mantine | Responsive breakpoint utilities (xs, sm, md, lg, xl) |
+| Rendering | React (server components + client hydration) | React streaming, component loading |
+| Fonts | Custom: Rules (Regular/Medium/Bold), EditionNumericalXXIX, Geist Mono (Google Fonts) | Font declarations in page source |
+| Theme | Dark mode default for "rf" domain | `ATLAS_DOMAIN: "rf"` config triggers dark theme |
+
+### 3.2 Backend / API Infrastructure
+
+| Service | Detail |
+|---|---|
+| API Domain | `https://api.emfm.atlas.arena-ai.com` (Auth0 audience) |
+| Organization | `emfmprod` |
+| Authentication | Auth0 with custom organization ID |
+| Feature Flags | DevCycle SDK (A/B testing) |
+| Monitoring | Datadog RUM (Real User Monitoring) |
+| 3D Rendering | Unreal Engine server at `https://52.61.97.121` (AWS IP) |
+| Terms of Service | Required (`ATLAS_REQUIRE_TOS: true`) |
+
+### 3.3 Configuration Flags (from runtime config)
+
+```json
+{
+  "AUTH0_AUDIENCE": "https://api.emfm.atlas.arena-ai.com",
+  "ATLAS_DOMAIN": "rf",
+  "ATLAS_REQUIRE_TOS": true,
+  "POLL_FOR_MESSAGES": false,
+  "ENABLE_HOTJAR": false,
+  "SHOW_DEBUG_LOGS": false
+}
+```
+
+Key observations:
+- `POLL_FOR_MESSAGES: false` -- Messages likely use WebSocket/SSE push rather than polling
+- `ENABLE_HOTJAR: false` -- Session replay disabled in production
+- `SHOW_DEBUG_LOGS: false` -- Debug mode off
+- The `emfm` in the API domain likely stands for "ElectroMagnetic Field Model"
+
+### 3.4 3D Visualization via Unreal Engine
+
+The most technically interesting finding: Studio connects to an Unreal Engine server (IP: 52.61.97.121, AWS us-west region) for 3D electromagnetic field visualization.
+
+**Likely architecture:**
+1. User submits design geometry in the Next.js frontend
+2. Backend runs Heaviside-0/Marconi-0 inference
+3. S-parameter results and field distribution data sent to Unreal Engine instance
+4. Unreal Engine renders 3D field visualization (E-field, H-field, current distributions)
+5. Pixel streaming sends rendered frames back to browser via WebRTC/WebSocket
+6. Interactive controls (rotate, zoom, slice planes) forwarded to Unreal Engine
+
+This is consistent with Unreal Engine's Pixel Streaming technology, which renders on a remote GPU and streams video to a web browser. The `52.61.97.121` IP being hardcoded suggests a dedicated rendering server or fleet.
+
+**Unreal Engine WebSocket Protocol** (standard):
+- Signaling server negotiates WebRTC connection
+- Control messages: `{ type: "input", data: { ... } }` for mouse/keyboard
+- Video stream: H.264/VP8 encoded, streamed via WebRTC data channel
+- Bidirectional: user input -> Unreal, rendered frames -> browser
+
+### 3.5 Data Formats (Inferred)
+
+Based on the S-parameter focus:
+
+**Input (Design Specification):**
+- Target S-parameters: S11, S21, S12, S22 (magnitude + phase vs frequency)
+- Frequency range (likely GHz, given RF focus)
+- Material properties (dielectric constant, loss tangent)
+- Geometric constraints (layer count, max dimensions)
+
+**Output (Design Result):**
+- Geometry: likely a discretized grid (64x64 binary material map based on Not Boring article)
+- S-parameters: complex-valued frequency response curves
+- Field distributions: 2D/3D electromagnetic field maps
+- Performance metrics: return loss, insertion loss, bandwidth
+
+**Probable API format** (speculative, based on EM conventions):
+```json
+{
+  "design": {
+    "layers": [
+      {
+        "geometry": [[0,1,1,0,...], ...],  // Binary material grid
+        "material": "FR4",
+        "thickness_mm": 0.2
+      }
+    ],
+    "vias": [{"x": 3, "y": 5, "radius_mm": 0.15}],
+    "dielectric": "rogers_4003c"
+  },
+  "simulation": {
+    "s_parameters": {
+      "frequencies_ghz": [1.0, 1.1, ..., 40.0],
+      "s11_mag_db": [-5.2, -5.4, ...],
+      "s11_phase_deg": [45.2, 44.8, ...],
+      "s21_mag_db": [-0.3, -0.3, ...]
+    },
+    "field_data": {
+      "type": "near_field",
+      "grid_size": [64, 64],
+      "e_field_magnitude": [[...], ...]
+    }
+  }
+}
+```
+
+
+## 4. UI Components and Features
+
+### 4.1 Observed UI Elements
+
+Based on page source analysis:
+
+- **Dark theme** with custom fonts (Rules family -- geometric sans-serif)
+- **Icon system** ("IconMark" component -- likely a custom RF/EM icon set)
+- **Responsive design** via Mantine breakpoints
+- **ToS gate** requiring acceptance before use
+- **Organization-scoped access** (Auth0 org-based multi-tenancy)
+
+### 4.2 Likely Feature Set (inferred from product description and tech stack)
+
+| Feature | Description | UI Component |
+|---|---|---|
+| Specification Input | Enter target S-parameters, frequency range, constraints | Form with frequency sweep chart |
+| Design Canvas | View/edit 2D geometry layers | Interactive grid editor |
+| S-parameter Viewer | Plot S11/S21/S12/S22 vs frequency | Interactive chart (likely Recharts or D3) |
+| 3D Field Viewer | Visualize E/H field distributions | Unreal Engine pixel-streamed viewport |
+| Design History | Browse previous designs and iterations | List/card view with thumbnails |
+| Compare View | Side-by-side design comparison | Split-pane layout |
+| Export | Download design files (Gerber, GDSII, S-parameter Touchstone) | Download buttons |
+
+### 4.3 Agentic Workflow UI
+
+Atlas RF Studio describes "agentic workflows" that:
+1. Accept natural-language or parametric specifications
+2. Generate multiple candidate designs
+3. Simulate each candidate
+4. Present ranked results
+5. Allow iterative refinement
+
+This suggests an LLM chat interface (translating intent to specs) alongside the technical EM visualization. The pairing of LLM + LFM (Large Field Model) is explicitly described in their architecture.
+
+
+## 5. Lessons for Our Sensing Server UI
+
+### 5.1 Architecture Patterns to Adopt
+
+| Arena Physica Pattern | Application to wifi-densepose sensing-server |
+|---|---|
+| Dark theme default | Already appropriate for a sensing/monitoring dashboard |
+| Next.js + Mantine | Consider for our sensing-server UI (currently Axum + vanilla) |
+| Auth0 multi-tenancy | Overkill for local deployment; useful for cloud/multi-site |
+| Unreal Engine 3D | Too heavy; use Three.js/WebGL for 3D pose visualization |
+| WebSocket push (not polling) | Match our real-time CSI streaming needs |
+| Feature flags (DevCycle) | Useful for gradual feature rollout |
+| Datadog RUM | Consider lightweight alternative (e.g., self-hosted analytics) |
+
+### 5.2 Visualization Approaches
+
+**What Arena visualizes:**
+- S-parameters (frequency-domain complex response) -- charts
+- Electromagnetic field distributions -- 3D heatmaps
+- Design geometry -- 2D grid with material layers
+
+**What we need to visualize:**
+- CSI amplitude/phase across subcarriers -- frequency-domain charts (similar to S-parameters)
+- Person occupancy heatmap -- 2D/3D voxel grid (similar to field visualization)
+- Pose skeleton overlay -- 2D/3D joint rendering
+- Vital signs (HR, BR) -- time-series charts
+- Node mesh topology -- graph visualization
+- Signal quality metrics -- dashboard gauges
+
+**Shared patterns:**
+- Both need real-time frequency-domain data visualization
+- Both show spatial field/occupancy distributions
+- Both benefit from interactive 3D (but at different scales)
+- Both require low-latency streaming from computation backend
+
+### 5.3 Data Flow Architecture Comparison
+
+**Arena Physica:**
+```
+Browser (Next.js) -> API (inference) -> Heaviside-0/Marconi-0 -> Unreal Engine -> Pixel Stream -> Browser
+```
+
+**wifi-densepose (recommended):**
+```
+ESP32 nodes -> sensing-server (Axum) -> WebSocket -> Browser (React/Mantine)
+                    |
+                    v
+              RuvSense pipeline -> pose/vitals -> WebSocket -> Browser
+```
+
+Key difference: Arena renders 3D on the server (Unreal Engine) and streams pixels. We should render 3D on the client (Three.js/WebGL) and stream data, because:
+- Our 3D scenes are simpler (skeleton + voxels vs. full EM field)
+- Client-side rendering avoids GPU server costs
+- Lower latency for real-time sensing feedback
+- Works offline / on local network
+
+### 5.4 API Design Lessons
+
+**Arena's API pattern** (REST + WebSocket):
+- REST for design submission and retrieval
+- WebSocket/SSE for live simulation progress and results
+- Auth0 JWT for authentication
+- Organization-scoped resources
+
+**Recommended for sensing-server:**
+- REST endpoints for configuration, history, calibration
+- WebSocket for real-time CSI, pose, and vitals streaming
+- Optional: SSE as fallback for environments where WebSocket is blocked
+- API key or local-only access (no OAuth needed for embedded deployment)
+
+**Proposed WebSocket protocol for sensing-server:**
+```json
+// Server -> Client: CSI frame
+{
+  "type": "csi_frame",
+  "timestamp_us": 1712000000000,
+  "node_id": "esp32-node-1",
+  "subcarriers": 56,
+  "amplitude": [0.45, 0.52, ...],
+  "phase": [-1.23, 0.87, ...]
+}
+
+// Server -> Client: Pose update
+{
+  "type": "pose",
+  "timestamp_us": 1712000000000,
+  "persons": [
+    {
+      "id": 0,
+      "keypoints": [
+        {"name": "nose", "x": 2.3, "y": 1.5, "z": 1.7, "confidence": 0.92},
+        ...
+      ]
+    }
+  ]
+}
+
+// Server -> Client: Vitals update
+{
+  "type": "vitals",
+  "timestamp_us": 1712000000000,
+  "person_id": 0,
+  "heart_rate_bpm": 72.5,
+  "breathing_rate_rpm": 16.2,
+  "presence_score": 0.98
+}
+
+// Server -> Client: Occupancy grid
+{
+  "type": "occupancy",
+  "timestamp_us": 1712000000000,
+  "nx": 8, "ny": 8, "nz": 4,
+  "bounds": [0.0, 0.0, 0.0, 6.0, 6.0, 3.0],
+  "densities": [0.0, 0.0, 0.12, ...]
+}
+
+// Client -> Server: Configuration
+{
+  "type": "config",
+  "action": "set",
+  "key": "tomography.lambda",
+  "value": 0.15
+}
+```
+
+### 5.5 Specific UI Components to Build
+
+Based on Arena Physica's approach and our sensing needs:
+
+**Priority 1 (Core Dashboard):**
+1. **Real-time CSI waterfall** -- Subcarrier amplitude over time, color-mapped (similar to spectrogram)
+2. **Pose skeleton view** -- 2D/3D rendering of detected keypoints with skeleton connections
+3. **Node topology map** -- Show ESP32 mesh with RSSI-colored edges
+4. **Vitals panel** -- Heart rate and breathing rate with time-series charts
+
+**Priority 2 (Advanced Visualization):**
+5. **Occupancy heatmap** -- 2D top-down view of tomographic voxel grid
+6. **Phase coherence indicator** -- Per-link coherence scores (green/yellow/red)
+7. **Fresnel zone overlay** -- Show first Fresnel zone on room floor plan per link
+
+**Priority 3 (Configuration/Debug):**
+8. **Calibration wizard** -- Guide through empty-room calibration for field_model
+9. **Link quality matrix** -- NxN grid showing per-link signal metrics
+10. **Raw CSI inspector** -- Select individual link, view amplitude + phase per subcarrier
+
+
+## 6. Public API Endpoints and Protocols
+
+### 6.1 Confirmed Endpoints
+
+| Endpoint | Protocol | Purpose |
+|---|---|---|
+| `https://studio.arenaphysica.com` | HTTPS | Main web application (Next.js SSR) |
+| `https://api.emfm.atlas.arena-ai.com` | HTTPS | Backend API (Auth0 audience) |
+| `https://52.61.97.121` | HTTPS/WSS | Unreal Engine rendering server |
+
+### 6.2 Authentication
+
+- Auth0-based with organization scoping
+- Custom audience: `https://api.emfm.atlas.arena-ai.com`
+- Organization: `emfmprod`
+- Terms of Service required before access
+
+### 6.3 Feature Flags
+
+DevCycle SDK integrated for A/B testing and feature gating. This suggests gradual rollout of new capabilities.
+
+### 6.4 Monitoring
+
+Datadog RUM (Real User Monitoring) for performance tracking. Session replay (Hotjar) is available but disabled in production.
+
+### 6.5 What is NOT Publicly Documented
+
+- REST API endpoints (no public API docs found)
+- WebSocket message schemas
+- S-parameter data format
+- Geometry encoding format
+- Rate limits or usage quotas
+- Pricing model
+
+Arena Physica appears to operate as a closed platform without public API access. The Studio beta is a controlled preview, not an open API.
+
+
+## 7. Summary of Findings
+
+### What Arena Physica Is
+A $30M-funded startup building neural surrogates for electromagnetic simulation. Their AI predicts S-parameters and field distributions 18,000-800,000x faster than traditional solvers. They serve Fortune 500 hardware companies (AMD, Anduril) for RF component design.
+
+### What Arena Physica Is NOT
+They are not a WiFi sensing company. They do not do human pose estimation, CSI analysis, or IoT sensing. The relevance to our project is purely methodological.
+
+### Key Technical Takeaways for wifi-densepose
+
+1. **Neural surrogates for Maxwell's equations work** -- Arena proves that training on millions of simulation examples produces models accurate to < 1 dB MAE running in milliseconds. We could apply the same approach to CSI prediction.
+
+2. **Inverse design via conditional diffusion** -- Marconi-0's approach (generating geometry from target specs) parallels our inverse problem (generating pose from CSI). Conditional diffusion is a viable architecture.
+
+3. **Bidirectional search** -- The generate-evaluate-refine loop is more effective than direct inversion. For real-time sensing, the evaluator (forward model) must be fast.
+
+4. **Domain-specific models beat general LLMs** -- For electromagnetic tasks, specialized architectures substantially outperform GPT-4 / Claude. This validates our approach of building specialized CSI processing rather than relying on general-purpose models.
+
+5. **Studio UI is Next.js + Mantine + Unreal Engine** -- A modern stack, but the Unreal Engine component is overkill for our visualization needs. Three.js/WebGL on the client is more appropriate for our real-time sensing dashboard.
+
+6. **WebSocket push over polling** -- Confirmed by their `POLL_FOR_MESSAGES: false` configuration. Our sensing-server should use WebSocket push for real-time data streaming.
+
+
+## References
+
+- Arena Physica Homepage: https://www.arenaphysica.com/
+- Atlas RF Studio Beta: https://studio.arenaphysica.com/
+- Introducing Atlas RF Studio (publication): https://www.arenaphysica.com/publications/rf-studio
+- Electromagnetism Secretly Runs the World (Not Boring essay): https://www.notboring.co/p/electromagnetism-secretly-runs-the
+- Arena Launches Atlas (press release): https://www.prnewswire.com/news-releases/arena-launches-atlas-to-accelerate-humanitys-rate-of-hardware-innovation-302423412.html
+- Arena AI raises $30M (SiliconANGLE): https://siliconangle.com/2025/04/08/arena-ai-raises-30m-accelerate-innovation-hardware-testing-atlas/
+- Artificial Intuition (CDFAM presentation): https://www.designforam.com/p/artificial-intuition-building-an
+- Pratap Ranade LinkedIn announcement: https://www.linkedin.com/posts/pratap-ranade-7272829_today-im-excited-to-introduce-arena-physica-activity-7442204772725723137-RRtE
+- Mantine UI: https://mantine.dev/
+- Unreal Engine Pixel Streaming: https://dev.epicgames.com/documentation/en-us/unreal-engine/remote-control-api-websocket-reference-for-unreal-engine
@@ -0,0 +1,141 @@
+# Deep Analysis: arXiv 2505.15472 -- PhysicsArena
+
+**Date:** 2026-04-02
+**Analyst:** GOAP Planning Agent
+**Relevance to wifi-densepose:** Indirect (physics reasoning benchmark, not WiFi sensing)
+
+---
+
+## 1. Paper Identity
+
+- **Title:** PhysicsArena: The First Multimodal Physics Reasoning Benchmark Exploring Variable, Process, and Solution Dimensions
+- **Authors:** Song Dai, Yibo Yan, Jiamin Su, Dongfang Zihao, Yubo Gao, Yonghua Hei, Jungang Li, Junyan Zhang, Sicheng Tao, Zhuoran Gao, Xuming Hu
+- **Submitted:** 2025-05-21, revised 2025-05-22
+- **Category:** cs.CL (Computation and Language)
+- **arXiv ID:** 2505.15472v2
+
+## 2. Core Contribution
+
+PhysicsArena introduces a multimodal benchmark for evaluating how Large Language Models (MLLMs) reason about physics problems. The benchmark assesses three dimensions:
+
+1. **Variable Identification** -- Can the model correctly identify physical variables from multimodal inputs (diagrams, text, equations)?
+2. **Physical Process Formulation** -- Can the model select and chain the correct physical laws and processes?
+3. **Solution Derivation** -- Can the model produce correct numerical/symbolic solutions?
+
+This is the first benchmark to decompose physics reasoning into these three granular dimensions rather than only evaluating final answers.
+
+## 3. Technical Approach
+
+### 3.1 Benchmark Structure
+
+The benchmark presents physics problems with multimodal inputs (text descriptions accompanied by diagrams, graphs, and physical setups). Problems span classical mechanics, electromagnetism, thermodynamics, optics, and modern physics.
+
+### 3.2 Evaluation Protocol
+
+Unlike prior benchmarks that score only final answers, PhysicsArena evaluates intermediate reasoning:
+
+- **Variable extraction accuracy:** Does the model identify all relevant physical quantities (mass, velocity, charge, field strength, etc.)?
+- **Process correctness:** Does the model apply the right sequence of physical laws (Newton's laws, Maxwell's equations, conservation laws)?
+- **Solution accuracy:** Does the final numerical answer match the ground truth within tolerance?
+
+### 3.3 Key Finding
+
+Current MLLMs (GPT-4V, Claude, Gemini) perform significantly worse on variable identification and process formulation than on final solution derivation when provided with correct intermediate steps. This reveals that models often arrive at correct answers through pattern matching rather than genuine physics reasoning.
+
+## 4. Relevance to WiFi-DensePose
+
+### 4.1 Direct Relevance: Low
+
+This paper is not about WiFi sensing, CSI processing, pose estimation, or edge deployment. It benchmarks LLM reasoning about physics problems.
+
+### 4.2 Indirect Relevance: Moderate
+
+Several concepts transfer to our domain:
+
+#### 4.2.1 Physics-Informed Reasoning for Signal Processing
+
+The paper's decomposition of physics reasoning into (variables, process, solution) maps onto WiFi sensing:
+
+| PhysicsArena Dimension | WiFi-DensePose Analog |
+|------------------------|----------------------|
+| Variable identification | CSI feature extraction (amplitude, phase, subcarrier indices, antenna config) |
+| Process formulation | Signal processing pipeline selection (phase alignment, coherence gating, multiband fusion) |
+| Solution derivation | Pose/activity estimation output |
+
+This suggests a potential architecture where intermediate representations are explicitly supervised -- not just end-to-end loss on final pose, but also losses on intermediate physical quantities (estimated path lengths, Doppler shifts, angle-of-arrival).
+
+#### 4.2.2 Multimodal Grounding
+
+PhysicsArena's core challenge is grounding abstract reasoning in physical reality from multimodal inputs. WiFi-DensePose faces the same challenge: grounding neural network predictions in the actual physics of electromagnetic wave propagation through space containing human bodies.
+
+#### 4.2.3 Decomposed Evaluation
+
+The three-dimension evaluation framework suggests we should evaluate our pipeline at multiple stages:
+
+1. **CSI quality metrics** (SNR, coherence, phase stability) -- analogous to variable identification
+2. **Feature extraction quality** (does the modality translator preserve physically meaningful information?) -- analogous to process formulation
+3. **Pose accuracy** (PCK@50, MPJPE) -- analogous to solution derivation
+
+This would help diagnose whether failures in pose estimation originate from poor CSI capture, lossy feature translation, or incorrect pose regression.
+
+### 4.3 Transferable Insight: Intermediate Supervision
+
+The paper's key insight -- that evaluating only final outputs masks fundamental reasoning failures -- argues for adding intermediate supervision signals to the wifi-densepose training pipeline:
+
+```
+L_total = lambda_pose * L_pose 
+        + lambda_physics * L_physics_consistency
+        + lambda_intermediate * L_intermediate_features
+```
+
+Where `L_physics_consistency` penalizes predictions that violate known electromagnetic propagation physics (e.g., predicted person positions that are inconsistent with observed CSI phase relationships).
+
+## 5. Applicable Techniques for Implementation Plan
+
+### 5.1 Physics-Constrained Loss Functions
+
+Add a physics consistency loss that enforces:
+
+- **Fresnel zone consistency:** Predicted body positions must be consistent with the Fresnel zones that would produce the observed CSI perturbations
+- **Multipath geometry:** The number of strong multipath components should be consistent with the predicted scene geometry
+- **Doppler-velocity consistency:** If temporal CSI changes indicate Doppler shift, the predicted keypoint velocities must match
+
+### 5.2 Hierarchical Evaluation Pipeline
+
+Implement three-stage evaluation matching PhysicsArena's decomposition:
+
+```rust
+pub struct HierarchicalEvaluation {
+    /// Stage 1: CSI quality assessment
+    pub csi_quality: CsiQualityMetrics,
+    /// Stage 2: Feature translation fidelity
+    pub translation_fidelity: TranslationMetrics, 
+    /// Stage 3: Pose estimation accuracy
+    pub pose_accuracy: PoseMetrics,
+}
+```
+
+### 5.3 Structured Intermediate Representations
+
+Rather than a single encoder-decoder, structure the network to produce interpretable intermediate outputs:
+
+```
+CSI input -> [Physics Encoder] -> physical_features (AoA, ToF, Doppler)
+          -> [Geometry Decoder] -> spatial_occupancy_map
+          -> [Pose Regressor]   -> keypoint_coordinates
+```
+
+Each intermediate output can be supervised independently where ground truth is available.
+
+## 6. Conclusion
+
+While arXiv 2505.15472 is not directly about WiFi sensing, its framework for decomposing physics reasoning into interpretable stages provides a valuable architectural pattern. The key takeaway for wifi-densepose is: **do not rely solely on end-to-end training; add intermediate physics-grounded supervision signals to improve robustness and interpretability.**
+
+This aligns with the existing RuvSense architecture which already has explicit stages (multiband fusion, phase alignment, coherence scoring, coherence gating, pose tracking) -- the paper's framework validates this design choice and argues for adding supervision at each stage boundary.
+
+## 7. Cross-References
+
+- **Arena Physica (arena-physica-analysis.md):** Their thesis that "fields are the fundamental quantities" reinforces the physics-first approach recommended here. Training on electromagnetic field distributions rather than end-to-end CSI-to-pose would constitute the WiFi sensing analog of PhysicsArena's decomposed evaluation.
+- **WiFlow (sota-wifi-sensing-2025.md, Section 1.1):** WiFlow's bone constraint loss is a concrete implementation of physics-informed intermediate supervision -- the skeleton must obey anatomical constraints at every prediction step.
+- **MultiFormer (sota-wifi-sensing-2025.md, Section 1.2):** MultiFormer's dual-token (time + frequency) tokenization is analogous to PhysicsArena's variable identification -- it explicitly separates the physical dimensions of the CSI measurement before reasoning about them.
+- **Implementation plan (implementation-plan.md):** The hierarchical evaluation pipeline in Section 5.2 directly implements the three-stage evaluation framework recommended here.
@@ -0,0 +1,615 @@
+# Maxwell's Equations in WiFi/RF Sensing
+
+Research document for wifi-densepose project.
+Date: 2026-04-02
+
+---
+
+## 1. Maxwell's Equations and CSI Extraction
+
+### 1.1 Foundational Electromagnetic Theory
+
+All WiFi-based sensing ultimately derives from Maxwell's four partial differential equations governing electromagnetic field behavior:
+
+```
+(1) Gauss's Law (Electric):       nabla . E = rho / epsilon_0
+(2) Gauss's Law (Magnetic):       nabla . B = 0
+(3) Faraday's Law:                nabla x E = -dB/dt
+(4) Ampere-Maxwell Law:           nabla x B = mu_0 * J + mu_0 * epsilon_0 * dE/dt
+```
+
+In free space with no charges or currents (the indoor propagation case), these simplify to the wave equation:
+
+```
+nabla^2 E - mu_0 * epsilon_0 * d^2 E / dt^2 = 0
+```
+
+yielding plane wave solutions `E(r, t) = E_0 * exp(j(k . r - omega * t))` where `k = 2*pi / lambda` is the wavenumber. At 2.4 GHz WiFi, `lambda ~ 12.5 cm`; at 5 GHz, `lambda ~ 6 cm`.
+
+### 1.2 From Maxwell to Channel State Information
+
+Channel State Information (CSI) is the frequency-domain representation of the wireless channel's impulse response. The derivation from Maxwell's equations proceeds through several simplification layers:
+
+**Layer 1: Full Maxwell's equations** -- Exact but computationally intractable for room-scale environments at GHz frequencies.
+
+**Layer 2: High-frequency ray optics (Geometrical Optics / Uniform Theory of Diffraction)** -- When object dimensions >> lambda (walls, furniture), Maxwell's equations reduce to ray tracing. Each ray follows Snell's law at interfaces, with Fresnel reflection/transmission coefficients computed from the dielectric contrast.
+
+**Layer 3: Multipath channel model** -- The channel impulse response aggregates all propagation paths:
+
+```
+h(t) = sum_{n=1}^{N} alpha_n * exp(-j * phi_n) * delta(t - tau_n)
+```
+
+where for each path n:
+- `alpha_n` = complex attenuation (from free-space path loss, reflection, diffraction)
+- `phi_n = 2*pi*f*tau_n` = phase shift
+- `tau_n = d_n / c` = propagation delay (distance / speed of light)
+
+**Layer 4: Channel Frequency Response (CFR) = CSI** -- The Fourier transform of h(t):
+
+```
+H(f_k) = sum_{n=1}^{N} alpha_n * exp(-j * 2*pi * f_k * tau_n)
+```
+
+Each OFDM subcarrier k at frequency f_k provides one complex CSI measurement:
+
+```
+H(f_k) = |H(f_k)| * exp(j * angle(H(f_k)))
+```
+
+With 802.11n/ac providing 56-256 subcarriers and 802.11ax up to 512 subcarriers across 160 MHz bandwidth, CSI captures a frequency-sampled version of the channel's multipath structure.
+
+**Key insight for sensing**: When a human moves in the environment, paths reflecting off the body change their `alpha_n`, `tau_n`, and `phi_n`, modulating the CSI. The sensing problem is to invert this relationship -- recover body state from CSI changes.
+
+### 1.3 The Two CSI Models
+
+The Tsinghua WiFi Sensing Tutorial (tns.thss.tsinghua.edu.cn) identifies two mainstream models:
+
+**Ray-Tracing Model**: Establishes explicit geometric relationships between signal paths and CSI. The received signal is:
+
+```
+V = sum_{n=1}^{N} |V_n| * exp(-j * phi_n)
+```
+
+This model enables extraction of geometric parameters (distances, reflection points, angles of arrival) from CSI data. It underpins localization and tracking applications.
+
+**Scattering Model**: Decomposes CSI into static and dynamic contributions:
+
+```
+H(f,t) = sum_{o in Omega_s} H_o(f,t) + sum_{p in Omega_d} H_p(f,t)
+```
+
+Dynamic scatterers (moving bodies) contribute through angular integration:
+
+```
+H_p(f,t) = integral_0^{2pi} integral_0^{pi} h_p(alpha, beta, f, t) * exp(-j*k*v_p*cos(alpha)*t) d_alpha d_beta
+```
+
+The scattering model yields the CSI autocorrelation:
+
+```
+rho_H(f, tau) ~ sinc(k * v * tau)
+```
+
+enabling speed extraction from autocorrelation peak analysis:
+
+```
+v = x_0 * lambda / (2 * pi * tau_0)
+```
+
+where `x_0` is the first sinc extremum location and `tau_0` is the corresponding time lag.
+
+### 1.4 Practical Simplifications Used in WiFi Sensing
+
+| Approximation | Physical Basis | Used When | Accuracy |
+|---|---|---|---|
+| Ray tracing (GO/UTD) | High-frequency limit of Maxwell | Objects >> lambda | Good for LOS + major reflections |
+| Fresnel zone model | Wave diffraction | Target near TX-RX line | Excellent for presence/respiration |
+| Born approximation | Weak scattering (small perturbation) | Low-contrast objects | Breaks down for human body |
+| Rytov approximation | Phase perturbation expansion | Moderate scattering | Better for lossy media |
+| Free-space path loss | 1/r^2 power decay | Coarse attenuation models | Adequate for RSSI-based sensing |
+
+**Relevance to wifi-densepose**: Our `field_model.rs` implements the eigenstructure approach (Layer 2.5 -- between full ray tracing and statistical models), decomposing the channel covariance via SVD to separate environmental modes from body perturbation. Our `tomography.rs` implements the voxel-based inverse at Layer 3 using L1-regularized least squares.
+
+
+## 2. Physics-Informed Neural Networks (PINNs) for RF Sensing
+
+### 2.1 PINN Architecture for Wireless Channels
+
+Physics-Informed Neural Networks embed physical laws as constraints in the loss function or network architecture. For RF sensing, PINNs encode electromagnetic propagation principles:
+
+**Standard PINN loss for RF propagation:**
+
+```
+L_total = L_data + lambda_physics * L_physics + lambda_boundary * L_boundary
+
+where:
+  L_data = (1/N) * sum |H_pred(f_k) - H_meas(f_k)|^2     (CSI measurement fit)
+  L_physics = (1/M) * sum |nabla^2 E + k^2 * E|^2          (Helmholtz equation residual)
+  L_boundary = (1/B) * sum |E_pred - E_bc|^2                (boundary conditions)
+```
+
+The Helmholtz equation `nabla^2 E + k^2 * n^2(r) * E = 0` (time-harmonic Maxwell) constrains the solution space, where `n(r)` is the spatially varying refractive index.
+
+### 2.2 Key Papers and Approaches
+
+**PINN + GNN for RF Map Construction** (arXiv 2507.22513):
+- Combines Physics-Informed Neural Networks with Graph Neural Networks
+- Physical constraints from EM propagation laws guide learning
+- Parameterizes multipath signals into received power, delay, and angle of arrival
+- Integrates spatial dependencies for accurate prediction
+
+**PINN for Wireless Channel Estimation** (NeurIPS 2025, OpenReview r3plaU6DvW):
+- Synergistically combines model-based channel estimation with deep network
+- Exploits prior information about environmental propagation
+- Critical for next-gen wireless systems: precoding, interference reduction, sensing
+
+**ReVeal: High-Fidelity Radio Propagation** (DySPAN 2025):
+- Physics-informed approach for radio environment mapping
+- Achieves high fidelity with limited measurement data
+
+**Physics-Informed Generative Model for Passive RF Sensing** (arXiv 2310.04173, Savazzi et al.):
+- Variational Auto-Encoder integrating EM body diffraction
+- Forward model: predicts CSI perturbation from body position/pose
+- Validated against classical diffraction-based EM tools AND real RF measurements
+- Enables real-time processing where traditional EM is too slow
+
+**Multi-Modal Foundational Model** (arXiv 2602.04016, February 2026):
+- Foundation model for AI-driven physical-layer wireless systems
+- Physics-guided pretraining grounded in EM propagation principles
+- Treats wireless as inherently multimodal physical system
+
+**Generative AI for Wireless Sensing** (arXiv 2509.15258, September 2025):
+- Physics-informed diffusion models for data augmentation
+- Channel prediction and environment modeling
+- Conditional mechanisms constrained by EM laws
+
+### 2.3 PINN Architecture for CSI-Based Sensing
+
+```
+Algorithm: Physics-Informed CSI Sensing Network
+
+Input: CSI tensor H[time, subcarrier, antenna] of shape (T, K, M)
+Output: Body state estimate (pose, position, or occupancy)
+
+1. PREPROCESSING (physics-guided):
+   a. Remove carrier frequency offset (CFO): H_clean = H * exp(-j*2*pi*delta_f*t)
+   b. Conjugate multiply across antenna pairs to cancel common phase noise
+   c. Compute CSI-ratio: H_ratio(f,t) = H_dynamic(f,t) / H_static(f,t)
+
+2. PHYSICS ENCODER:
+   a. Embed Fresnel zone geometry as positional encoding
+   b. Apply multi-head attention with frequency-aware kernels
+   c. Enforce causality: attention mask respects propagation delay ordering
+
+3. PHYSICS-CONSTRAINED DECODER:
+   a. Predict body state x_hat
+   b. Forward-simulate expected CSI from x_hat using ray-tracing differentiable renderer
+   c. Compute physics loss: L_phys = ||H_simulated(x_hat) - H_measured||^2
+
+4. TRAINING LOSS:
+   L = L_pose_supervision + alpha * L_phys + beta * L_temporal_smoothness
+```
+
+### 2.4 Relevance to wifi-densepose
+
+Our RuvSense pipeline already implements physics-guided preprocessing (phase alignment, coherence gating, Fresnel zone awareness). The next step would be to:
+
+1. Add a differentiable ray-tracing forward model as a physics constraint during NN training
+2. Use the field model eigenstructure (from `field_model.rs`) as an informed prior
+3. Embed Fresnel zone geometry from link topology as architectural bias
+
+
+## 3. Inverse Electromagnetic Scattering for Body Reconstruction
+
+### 3.1 The Inverse Problem
+
+The forward problem: given a known body position/shape and room geometry, predict the CSI.
+
+```
+Forward:  body_state -> Maxwell/ray-tracing -> H(f,t)     [well-posed]
+Inverse:  H(f,t) -> ??? -> body_state                     [ill-posed]
+```
+
+WiFi sensing is fundamentally an inverse scattering problem. A WiFi antenna receives signal as 1D amplitude/phase -- the spatial information of the 3D scene is collapsed to a single CSI complex number per subcarrier per antenna pair. Reconstructing fine-grained spatial information from this compressed observation is severely ill-posed.
+
+### 3.2 Linearized Inverse Scattering: Born and Rytov Approximations
+
+**Helmholtz equation with scatterer:**
+
+```
+nabla^2 E(r) + k^2 * (1 + O(r)) * E(r) = 0
+```
+
+where `O(r) = epsilon_r(r) - 1` is the object function (dielectric contrast of the body relative to free space).
+
+**Born approximation** (first-order): Assumes the field inside the scatterer equals the incident field:
+
+```
+E_scattered(r) ~ k^2 * integral O(r') * E_incident(r') * G(r, r') dr'
+```
+
+where `G(r, r')` is the free-space Green's function. This is valid when `O(r)` is small and the object is electrically small. For the human body at 2.4 GHz (`epsilon_r ~ 40-60` for muscle tissue), the Born approximation is grossly violated.
+
+**Rytov approximation**: Expands the complex phase rather than the field:
+
+```
+E_total(r) = E_incident(r) * exp(psi(r))
+
+psi(r) ~ (k^2 / E_incident(r)) * integral O(r') * E_incident(r') * G(r, r') dr'
+```
+
+The Rytov approximation handles larger phase accumulation than Born but still assumes weak scattering. It works better for lossy media where absorption limits multiple scattering.
+
+**Extended Phaseless Rytov Approximation (xPRA-LM)** (Dubey et al., arXiv 2110.03211):
+- First linear phaseless inverse scattering approximation with large validity range
+- Demonstrated with 2.4 GHz WiFi nodes for indoor imaging
+- Handles objects with `epsilon_r` up to 15+j1.5 (20x wavelength size)
+- At `epsilon_r = 77+j7` (water/tissue), shape reconstruction still accurate
+
+### 3.3 Iterative Nonlinear Methods
+
+For high-contrast scatterers like the human body, iterative methods are required:
+
+**Distorted Born Iterative Method (DBIM):**
+
+```
+Algorithm: DBIM for WiFi Body Imaging
+
+Input: Measured scattered field E_s at receiver locations
+Output: Object function O(r) (dielectric map of scene)
+
+1. Initialize: O_0(r) = 0 (empty room)
+2. For iteration i = 0, 1, 2, ...:
+   a. Solve forward problem: compute total field E_i(r) in medium with O_i(r)
+   b. Compute Green's function G_i(r, r') for medium O_i(r)
+   c. Linearize: delta_E_s = K_i * delta_O   (Frechet derivative)
+   d. Solve: delta_O = K_i^+ * (E_s_measured - E_s_computed(O_i))
+   e. Update: O_{i+1} = O_i + delta_O
+   f. Check convergence: ||E_s_measured - E_s_computed(O_{i+1})|| < epsilon
+```
+
+**Challenges for WiFi sensing:**
+- WiFi provides sparse spatial sampling (few antenna pairs vs. full aperture)
+- Phase is often unavailable (RSSI-only) or corrupted by hardware imperfections
+- Real-time requirement conflicts with iterative forward solves
+- Human body is a strong, moving scatterer
+
+### 3.4 Radio Tomographic Imaging (RTI)
+
+RTI (Wilson & Patwari, 2010) simplifies the inverse scattering problem by:
+1. Using only RSS (received signal strength) -- phaseless
+2. Assuming a voxelized scene with additive attenuation model
+3. Linearizing: measured attenuation = sum of voxel attenuations along path
+
+**Forward model:**
+
+```
+y = W * x + n
+
+where:
+  y = [y_1, ..., y_L]^T   attenuation measurements (L links)
+  x = [x_1, ..., x_V]^T   voxel occupancy values (V voxels)
+  W = [w_{l,v}]             weight matrix (link-voxel intersection)
+  n = measurement noise
+```
+
+**Weight model (elliptical):**
+
+```
+w_{l,v} = { 1 / sqrt(d_l)   if d_{l,v}^tx + d_{l,v}^rx < d_l + lambda_w
+           { 0               otherwise
+
+where:
+  d_l = distance between TX_l and RX_l
+  d_{l,v}^tx = distance from TX_l to voxel v center
+  d_{l,v}^rx = distance from RX_l to voxel v center
+  lambda_w = excess path length parameter (typically ~lambda/4)
+```
+
+**Inverse solution (Tikhonov-regularized):**
+
+```
+x_hat = (W^T W + alpha * C^{-1})^{-1} * W^T * y
+```
+
+where `C` is the spatial covariance matrix and `alpha` controls regularization.
+
+**Our implementation** (`tomography.rs`) uses ISTA (Iterative Shrinkage-Thresholding Algorithm) with L1 regularization for sparsity:
+
+```
+Algorithm: ISTA for RF Tomography (as in tomography.rs)
+
+Input: Weight matrix W, observations y, lambda (L1 weight)
+Output: Sparse voxel densities x
+
+1. Initialize x = 0
+2. step_size = 1 / ||W^T * W||_spectral
+3. For iter = 1 to max_iterations:
+   a. gradient = W^T * (W * x - y)
+   b. x_candidate = x - step_size * gradient
+   c. x = soft_threshold(x_candidate, lambda * step_size)
+      where soft_threshold(z, t) = sign(z) * max(|z| - t, 0)
+   d. residual = ||W * x - y||
+   e. if residual < tolerance: break
+```
+
+### 3.5 Reconciling RTI with Inverse Scattering
+
+Dubey, Li & Murch (arXiv 2311.09633) reconciled empirical RTI with formal inverse scattering theory:
+- RTI's additive attenuation model corresponds to a first-order Born approximation of the scattered field amplitude
+- Their enhanced method reconstructs both shape AND material properties
+- Validated at 2.4 GHz with WiFi transceivers indoors
+
+### 3.6 State-of-the-Art: Deep Learning Approaches
+
+**DensePose From WiFi** (Geng, Huang, De la Torre, arXiv 2301.00250, CMU):
+- Maps WiFi CSI amplitude+phase to UV coordinates across 24 body regions
+- Uses 3 TX + 3 RX antennas, 56 subcarriers per link
+- Teacher-student training: camera-based DensePose provides labels
+- Performance comparable to image-based approaches
+- Works through walls and in darkness
+
+**RF-Pose** (Zhao et al., CVPR 2018, MIT CSAIL):
+- Through-wall human pose estimation using radio signals
+- Cross-modal supervision: vision model trains RF model
+- Generalizes to through-wall scenarios with no through-wall training data
+
+**Person-in-WiFi** (Wang et al., ICCV 2019, CMU):
+- End-to-end body segmentation and pose from WiFi
+- Standard 802.11n signals, off-the-shelf hardware
+
+**3D WiFi Pose Estimation** (arXiv 2204.07878):
+- Free-form and moving activities
+- 3D joint position estimation from CSI
+
+**HoloCSI** (2025-2026):
+- Holographic tomography pipeline coupling physics-guided projection with adaptive top-k sparse transformer
+- Preprocesses: CFO rectification, Doppler compensation, antenna-pair normalization
+- Sparse multi-head attention prunes low-magnitude query-key pairs (quadratic -> near-linear complexity)
+- Results: +2.9 dB PSNR, +3.6% SSIM, +12.4% mesh IoU vs baselines
+- 25 fps on RTX-4070-mobile at 5% sparsity; 7 fps on Raspberry Pi 5 with attention-GRU variant
+
+
+## 4. Computational Electromagnetics for WiFi Sensing
+
+### 4.1 FDTD (Finite-Difference Time-Domain)
+
+FDTD discretizes Maxwell's curl equations on a Yee grid and marches forward in time:
+
+```
+Algorithm: FDTD Update (2D TM mode, simplified)
+
+Grid: dx = dy = lambda/20 (minimum 10 cells per wavelength)
+Time step: dt = dx / (c * sqrt(2))  [Courant condition]
+
+For each time step n:
+  1. Update H fields:
+     H_z^{n+1/2}(i,j) = H_z^{n-1/2}(i,j) + (dt/mu_0) * [
+       (E_x^n(i,j+1) - E_x^n(i,j)) / dy -
+       (E_y^n(i+1,j) - E_y^n(i,j)) / dx
+     ]
+
+  2. Update E fields:
+     E_x^{n+1}(i,j) = E_x^n(i,j) + (dt / epsilon(i,j)) * [
+       (H_z^{n+1/2}(i,j) - H_z^{n+1/2}(i,j-1)) / dy
+     ]
+```
+
+**For WiFi at 2.4 GHz:**
+- Wavelength: 12.5 cm
+- Grid cell: ~6 mm (20 cells/lambda)
+- Room 6m x 6m x 3m: 1000 x 1000 x 500 = 500M cells
+- Memory: ~24 GB (6 field components * 4 bytes * 500M)
+- Time steps: ~10,000 for steady state
+
+**Key references for WiFi FDTD:**
+- Lauer & Ertel (2003), "Using Large-Scale FDTD for Indoor WLAN" -- Full FDTD at 2.45 GHz in office environments
+- Lui et al. (2018), "Human Body Shadowing" -- FDTD human body model for ray-tracing calibration (Hindawi IJAP 9084830)
+- Martinez-Gonzalez et al. (2008), "FDTD Assessment Human Exposure WiFi/Bluetooth" -- SAR computation with anatomical body models
+
+**Practical limitations**: FDTD is too slow for real-time sensing but valuable for:
+- Generating training data for neural networks
+- Validating approximate models
+- Understanding near-field body-wave interaction
+
+### 4.2 Method of Moments (MoM)
+
+MoM converts Maxwell's integral equations into matrix equations by expanding fields in basis functions:
+
+```
+[Z] * [I] = [V]
+
+where:
+  Z_{mn} = integral integral G(r_m, r_n) * f_m(r) * f_n(r') dS dS'
+  I_n = unknown current coefficients
+  V_m = incident field excitation
+```
+
+**Application**: MoM excels for antenna analysis and is used to model WiFi antenna patterns. Less practical for full room simulation due to O(N^2) memory and O(N^3) solve time.
+
+### 4.3 FEM (Finite Element Method)
+
+FEM handles complex geometries and material interfaces more naturally than FDTD:
+
+```
+Weak form of Helmholtz equation:
+integral nabla x E_test . (1/mu_r * nabla x E) dV - k_0^2 * integral E_test . epsilon_r * E dV
+= -j * omega * integral E_test . J_s dV
+```
+
+**Application**: HFSS (Ansys) and COMSOL use FEM for electromagnetic simulation. Arena Physica's Heaviside-0 model was trained against such commercial FEM solvers.
+
+### 4.4 Comparison for WiFi Sensing Applications
+
+| Method | Speed | Accuracy | Body Modeling | Room Scale | Real-Time |
+|---|---|---|---|---|---|
+| FDTD | Hours | Full-wave exact | Excellent | Feasible (GPU) | No |
+| MoM | Hours | Exact for surfaces | Good (surface) | Impractical | No |
+| FEM | Hours | Exact | Excellent | Feasible | No |
+| Ray tracing | Seconds | GO/UTD approximation | Coarse | Easy | Near real-time |
+| RTI (ISTA) | Milliseconds | Linear approximation | Voxelized | Easy | Yes |
+| Neural surrogate | Milliseconds | Trained accuracy | Implicit | Trained domain | Yes |
+
+### 4.5 Hybrid Approaches: Neural Surrogates Trained on CEM
+
+The most promising direction combines full-wave accuracy with real-time speed:
+
+1. **Offline**: Run thousands of FDTD/FEM simulations with different body positions
+2. **Train**: Neural network learns the mapping from body state to CSI
+3. **Deploy**: Neural surrogate runs in milliseconds for real-time inference
+
+This is exactly Arena Physica's approach (Section 5), applied to RF component design rather than sensing. The same methodology applies to WiFi sensing: train a neural forward model on FDTD data, then use it as a differentiable physics constraint during inverse model training.
+
+
+## 5. Arena Physica's Approach
+
+### 5.1 Company Overview
+
+Arena Physica (arena-ai.com / arenaphysica.com) pursues "Electromagnetic Superintelligence" -- building foundation models that develop superhuman intuition for how geometry shapes electromagnetic fields. Founded by Pratap Ranade (CEO), Arya Hezarkhani, Claire Pan, Michael Frei, and Harish Krishnaswamy. Offices in NYC (HQ), SF, LA.
+
+Raised $30M Series B (April 2025). Deployed with AMD, Anduril Industries, Sivers Semiconductors, Bausch & Lomb. Claims 35% reduction in engineering man-hours and multi-month acceleration in time-to-market.
+
+### 5.2 Technical Architecture
+
+Arena's Atlas platform uses two foundation models:
+
+**Heaviside-0 (Forward Model)**:
+- Input: PCB/RF geometry (discretized as grid)
+- Output: S-parameters (magnitude + phase) and field distributions
+- Speed: 13ms per design (single), 0.3ms batched
+- Comparison: Traditional solver (HFSS/FDTD) takes ~4 minutes
+- Speedup: 18,000x to 800,000x
+
+**Marconi-0 (Inverse Model)**:
+- Input: Target S-parameter specification
+- Output: Physical geometry that achieves the specification
+- Method: Conditional diffusion process (similar to image generation)
+- Generates unconventional geometries no human designer would conceive
+
+**Training data**: 3 million simulated designs across 25 expert templates + random structures, totaling 20+ years of combined simulation time. Incorporates both S-parameter data and electromagnetic field distributions.
+
+**Validation**: Predictions validated against commercial numerical field solvers (likely HFSS). Internal testing shows < 1 dB magnitude-weighted MAE (RF engineers operate in 20-30 dB ranges).
+
+### 5.3 Relationship to Maxwell's Equations
+
+Arena does NOT solve Maxwell's equations directly. Instead:
+
+1. **Training phase**: Maxwell's equations are solved by conventional solvers (FDTD/FEM/MoM) millions of times to generate training data
+2. **Inference phase**: Neural surrogate approximates Maxwell's solutions in milliseconds
+3. **Design loop**: Generator proposes geometry -> Evaluator predicts EM behavior -> Iterate
+
+As Pratap Ranade states: the model "learns the syntax of physics" inductively from examples, rather than deductively from equations. This trades precision for speed -- acceptable when searching design space where "speed and direction matter more than precision."
+
+### 5.4 The "Large Field Model" (LFM) Concept
+
+Arena's LFM is distinct from Large Language Models:
+- LLMs learn linguistic patterns from text
+- LFMs learn electromagnetic field patterns from simulation data
+- The input is geometry (not text); the output is field distributions (not tokens)
+- Domain-specific architecture substantially outperforms general LLMs on EM tasks
+
+### 5.5 Relevance to WiFi Sensing
+
+Arena Physica focuses on RF component design (antennas, PCBs, filters), not WiFi sensing. However, their approach is directly transferable:
+
+| Arena Physica (Design) | WiFi Sensing (Our Case) |
+|---|---|
+| Forward: geometry -> S-parameters | Forward: body pose -> CSI |
+| Inverse: S-parameters -> geometry | Inverse: CSI -> body pose |
+| Train on FDTD/FEM simulations | Train on ray-tracing / FDTD simulations |
+| 13ms inference | Real-time CSI inference |
+| Conditional diffusion for generation | Conditional generation for pose prediction |
+
+**Key lesson for wifi-densepose**: Building a neural forward model (body_pose -> expected_CSI) trained on electromagnetic simulation data, then using it as a differentiable physics constraint during inverse model training, could significantly improve our pose estimation accuracy and generalization. This is the "physics-informed" approach with the computational burden shifted to offline training.
+
+
+## 6. Connections to wifi-densepose Codebase
+
+### 6.1 Existing Physics-Based Modules
+
+| Module | Physical Model | Maxwell Connection |
+|---|---|---|
+| `field_model.rs` | SVD eigenstructure decomposition | Eigenmode basis of room's EM field |
+| `tomography.rs` | L1-regularized RTI (ISTA solver) | Linearized inverse scattering |
+| `multistatic.rs` | Attention-weighted cross-node fusion | Exploits geometric diversity of multiple TX/RX |
+| `phase_align.rs` | LO phase offset estimation | Corrects hardware-induced phase corruption |
+| `coherence.rs` | Z-score coherence scoring | Statistical test on EM field stability |
+| `coherence_gate.rs` | Accept/Reject decisions | Quality control on EM measurements |
+| `adversarial.rs` | Physical impossibility detection | Enforces EM consistency constraints |
+
+### 6.2 Potential Enhancements Based on This Research
+
+1. **Differentiable ray-tracing forward model**: Train a neural surrogate on ray-tracing simulations of CSI for various body poses in the deployment room. Use as physics constraint in pose estimation.
+
+2. **Fresnel zone integration**: Augment the attention mechanism in `multistatic.rs` with Fresnel zone geometry -- links where the body falls within the first Fresnel zone should receive higher attention weight.
+
+3. **xPRA-LM inverse scattering**: For higher-resolution body imaging than RTI, implement the Extended Phaseless Rytov Approximation. Our tomography module currently uses the simpler additive attenuation model.
+
+4. **HoloCSI-style sparse transformer**: Replace the dense attention in cross-viewpoint fusion with top-k sparse attention for efficiency on ESP32-constrained deployments.
+
+5. **Physics-informed training loss**: When training the DensePose model, add a loss term penalizing physically impossible CSI patterns (e.g., signals that would require faster-than-light propagation or negative attenuation).
+
+
+## 7. References
+
+### Core WiFi Sensing Surveys
+- WiFi Sensing with Channel State Information: A Survey. ACM Computing Surveys, 2019. https://dl.acm.org/doi/fullHtml/10.1145/3310194
+- Cross-Domain WiFi Sensing with Channel State Information: A Survey. ACM Computing Surveys, 2022. https://dl.acm.org/doi/10.1145/3570325
+- Wireless sensing applications with Wi-Fi CSI, preprocessing techniques, and detection algorithms: A survey. Computer Communications, 2024. https://www.sciencedirect.com/science/article/abs/pii/S0140366424002214
+- Understanding CSI (Tsinghua Tutorial). https://tns.thss.tsinghua.edu.cn/wst/docs/pre/
+
+### Physics-Informed Neural Networks for RF
+- PINN and GNN-based RF Map Construction. arXiv 2507.22513
+- Physics-Informed Neural Networks for Wireless Channel Estimation. NeurIPS 2025, OpenReview r3plaU6DvW
+- ReVeal: High-Fidelity Radio Propagation. DySPAN 2025. https://wici.iastate.edu/wp-content/uploads/2025/03/ReVeal-DySPAN25.pdf
+- Physics-informed generative model for passive RF sensing. Savazzi et al., arXiv 2310.04173
+- Multi-Modal Foundational Model for Wireless Communication and Sensing. arXiv 2602.04016
+- Generative AI Meets Wireless Sensing: Towards Wireless Foundation Model. arXiv 2509.15258
+- Physics-Informed Neural Networks for Sensing Radio Spectrum. IJRTE v14i3, 2025
+
+### Inverse Scattering and Body Reconstruction
+- DensePose From WiFi. Geng, Huang, De la Torre. arXiv 2301.00250
+- Through-Wall Human Pose Estimation Using Radio Signals. Zhao et al., CVPR 2018. https://rfpose.csail.mit.edu/
+- Person-in-WiFi: Fine-grained Person Perception. Wang et al., ICCV 2019
+- 3D Human Pose Estimation for Free-from Activities Using WiFi. arXiv 2204.07878
+- EM-POSE: 3D Human Pose from Sparse Electromagnetic Trackers. ICCV 2021
+- Reconciling Radio Tomographic Imaging with Phaseless Inverse Scattering. Dubey, Li, Murch. arXiv 2311.09633
+- Accurate Indoor RF Imaging using Extended Rytov Approximation. Dubey et al., arXiv 2110.03211
+- Phaseless Extended Rytov Approximation for Strongly Scattering Low-Loss Media. IEEE, 2022. https://ieeexplore.ieee.org/document/9766313/
+- Distorted Wave Extended Phaseless Rytov Iterative Method. arXiv 2205.12578
+- 3D Full Convolution Electromagnetic Reconstruction Neural Network (3D-FCERNN). PMC 9689780
+
+### Radio Tomographic Imaging
+- Radio Tomographic Imaging with Wireless Networks. Wilson & Patwari, 2010. https://span.ece.utah.edu/uploads/RTI_version_3.pdf
+- Compressive Sensing Based Radio Tomographic Imaging with Spatial Diversity. PMC 6386865
+- Passive Localization Based on Radio Tomography Images with CNN. Nature Scientific Reports, 2025
+- Enhancing Accuracy of WiFi Tomographic Imaging Using Human-Interference Model. 2018
+
+### Fresnel Zone Models
+- WiFi CSI-based device-free sensing: from Fresnel zone model to CSI-ratio model. CCF Trans. Pervasive Computing, 2021. https://link.springer.com/article/10.1007/s42486-021-00077-z
+- Towards a Dynamic Fresnel Zone Model for WiFi-based Human Activity Recognition. ACM IMWUT, 2023. https://dl.acm.org/doi/10.1145/3596270
+- CSI-based human sensing using model-based approaches: a survey. JCDE, 2021. https://academic.oup.com/jcde/article/8/2/510/6137731
+
+### Computational Electromagnetics
+- Using Large-Scale FDTD for Indoor WLAN. ResearchGate. https://www.researchgate.net/publication/42637096
+- Human Body Shadowing -- FDTD and UTD. Hindawi IJAP, 2018. https://www.hindawi.com/journals/ijap/2018/9084830/
+- FDTD Assessment Human Exposure WiFi/Bluetooth. ResearchGate. https://www.researchgate.net/publication/23400115
+- Simulation of Wireless LAN Indoor Propagation Using FDTD. IEEE, 2007. https://ieeexplore.ieee.org/document/4396450
+- Waveguide Models of Indoor Channels: FDTD Insights. ResearchGate. https://www.researchgate.net/publication/4368711
+- XFdtd 3D EM Simulation Software. Remcom. https://www.remcom.com/xfdtd-3d-em-simulation-software
+- Wireless InSite Ray Tracing. Remcom. https://www.remcom.com/wireless-insite-em-propagation-software/
+
+### Arena Physica
+- Introducing Atlas RF Studio. https://www.arenaphysica.com/publications/rf-studio
+- Electromagnetism Secretly Runs the World. Not Boring (Packy McCormick). https://www.notboring.co/p/electromagnetism-secretly-runs-the
+- Arena Launches Atlas (Press Release). https://www.prnewswire.com/news-releases/arena-launches-atlas-to-accelerate-humanitys-rate-of-hardware-innovation-302423412.html
+- Arena AI raises $30M. SiliconANGLE. https://siliconangle.com/2025/04/08/arena-ai-raises-30m-accelerate-innovation-hardware-testing-atlas/
+- Artificial Intuition: Building an AI Mind for EM Design. CDFAM NYC 2025. https://www.designforam.com/p/artificial-intuition-building-an
+
+### Holographic / Advanced
+- HoloCSI: Holographic tomography pipeline with physics-guided projection and sparse transformer. 2025-2026
+- CSI-Bench: Large-Scale In-the-Wild Dataset for Multi-task WiFi Sensing. arXiv 2505.21866
+- RFBoost: Understanding and Boosting Deep WiFi Sensing via Physical Data Augmentation. arXiv 2410.07230
+- Vision Reimagined: AI-Powered Breakthroughs in WiFi Indoor Imaging. arXiv 2401.04317
+- Electromagnetic Information Theory for 6G. arXiv 2401.08921