L1 ⚛ L1-083 ⊙ Testnet

3D Gaussian Splatting (3DGS) — explicit real-time rendering

Computational Optics · Explicit primitive-based 3D reconstruction

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⬇ L1-083.md

# ⚛ L1 Principle — 3D Gaussian Splatting (3DGS) — explicit real-time rendering **ID:** `L1-083` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Optics — *Explicit primitive-based 3D reconstruction* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D explicit primitives > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554183 --- ## 🧠 1. Introduction **3D Gaussian Splatting (3DGS) — explicit real-time rendering** is a **nonlinear inverse problem** whose unknown lives in **3D explicit primitives** space, within the **Explicit primitive-based 3D reconstruction** sub-domain of **Computational Optics**. Measurements consist of photons collected by an optical detector via a **multi view photogrammetry** sensing mechanism. The forward operator applies, in order: S · scan · view operator; L · project · gaussian operator; L · alpha composite operator; int · depth operator. Observations are corrupted by additive Gaussian noise. Non-convex parameter fitting. Unique 3D Gaussian cloud only up to primitive-reparameterization (splitting one Gaussian into two overlapping ones yields identical rendering). Stability risks: pose error introduces baked-in floaters; aggressive densification produces over-opaque pancake Gaussians (mitigated by Mip-Splatting / 2DGS). ## ⚙ 2. Forward Model Physical chain: **x** → S · scan · view → L · project · gaussian → L · alpha composite → int · depth → **y** (detector). ``` y = `int.depth` `L.alpha_composite` `L.project.gaussian` `S.scan.view` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.scan.view` | S · scan · view operator | | `L.project.gaussian` | L · project · gaussian operator | | `L.alpha_composite` | L · alpha composite operator | | `int.depth` | Int · depth operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Optics | | Sub domain | Explicit primitive-based 3D reconstruction | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 3D_explicit_primitives | | Noise model | gaussian | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Non-convex parameter fitting. Unique 3D Gaussian cloud only up to primitive-reparameterization (splitting one Gaussian into two overlapping ones yields identical rendering). Stability risks: pose error introduces baked-in floaters; aggressive densification produces over-opaque pancake Gaussians (mitigated by Mip-Splatting / 2DGS). | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `gaussian_splatting_novel_view` · **Forward operator:** `gaussian_splat_rasterize` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1080 | | W | px | 1920 | | L sh | — | 3 | | K views | — | 200 | | N gaussians | — | 1000000 | | Photon count | — | 2000 | | Non lambertian | — | 0 | | Pose error rad | rad | 0 | | Per frame exposure variation | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 400 – 4000 | | W | px | 400 – 4000 | | L sh | — | 0 – 4 | | K views | — | 10 – 1000 | | N gaussians | — | 100000 – 10000000 | | Photon count | — | 100 – 10000 | | Non lambertian | — | 0.0 – 0.5 | | Pose error rad | rad | 0.0 – 0.1 | | N budget too small | — | 0.0 – 0.8 | | Motion blur per frame | — | 0.0 – 0.1 | | Per frame exposure variation | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 31.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 18.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `4000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x129e3a3a772e37f0a0a226bb79566e255da24be9cc182ba6c339adf3894b0ad7` - **Chain tx hash:** `0xdd1929f81145c7971c11e75b579dc2ab281677a4da64a899749fe9aa1c081723` - **Chain block:** `41554183` --- ## File Mapping This bundle consists of: `L1-083.md`, `L1-083.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-083.md` | Source of truth — edit this | Human or LLM | | `L1-083.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-083`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-083.md).
Regenerate L1-083.json so every field matches the Markdown.
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L2-083-001 3DGS Novel-View Synthesis Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Computational Optics",
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    "title": "3D Gaussian Splatting (3DGS) \u2014 explicit real-time rendering"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Explicit primitive-based 3D reconstruction",
  "title": "3D Gaussian Splatting (3DGS) \u2014 explicit real-time rendering"
}

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