# ⚛  L1 Principle — RNA-seq Cell-Type Classification (PWDR)

**ID:** `L1-520` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Biology — *Single-cell / bulk RNA-seq transcript quantification with marker-gene-panel cell-type categorical readout*
> **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D celltype label
> **📡 Carrier:** rna_molecules_with_sequencing · **🌫 Noise:** negative binomial
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555318

---

## 🧠 1. Introduction

**RNA-seq Cell-Type Classification (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D celltype label** space, within the **Single-cell / bulk RNA-seq transcript quantification with marker-gene-panel cell-type categorical readout** sub-domain of **Computational Biology**.

Measurements consist of rna molecules with sequencing via a **rnaseq with marker panel classifier** sensing mechanism.

The forward operator applies, in order: L · poly a capture operator; L · reverse transcription operator; L · pcr amplification operator; L · sequencing operator; L · transcriptome alignment operator; L · transcript quantification operator; L · normalization operator; L · marker panel classifier operator; int · cell operator.

Observations are corrupted by negative-binomial over-dispersed counts. Existence guaranteed within Omega bounds. Uniqueness conditional on adequate sequencing depth (typically >30k reads per cell for 3' chemistry) and adequate marker-panel coverage. Stability conditional with dropout_rate dominant for low-expressing markers; batch_effect dominant cross-sample; doublet_contamination dominant for high cell densities. Joint Hadamard well-posedness for the coupled RNA-seq + marker-panel-classifier forward established by Trapnell 2014 (foundational scRNA-seq), Macosko 2015 (Drop-seq), Stuart-Butler 2019 (Seurat v3 integration), Tabula Sapiens Consortium 2022, Zhang 2019 (CellMarker), Franzen 2019 (PanglaoDB).

## ⚙ 2. Forward Model

Physical chain: **x** → L · poly a capture → L · reverse transcription → L · pcr amplification → L · sequencing → L · transcriptome alignment → L · transcript quantification → L · normalization → L · marker panel classifier → int · cell → **y** (detector).

```
y = `int.cell` `L.marker_panel_classifier` `L.normalization` `L.transcript_quantification` `L.transcriptome_alignment` `L.sequencing` `L.pcr_amplification` `L.reverse_transcription` `L.poly_a_capture` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.poly_a_capture` | L · poly a capture operator |
| `L.reverse_transcription` | L · reverse transcription operator |
| `L.pcr_amplification` | L · pcr amplification operator |
| `L.sequencing` | L · sequencing operator |
| `L.transcriptome_alignment` | L · transcriptome alignment operator |
| `L.transcript_quantification` | L · transcript quantification operator |
| `L.normalization` | L · normalization operator |
| `L.marker_panel_classifier` | L · marker panel classifier operator |
| `int.cell` | Int · cell operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Biology |
| Sub domain | Single-cell / bulk RNA-seq transcript quantification with marker-gene-panel cell-type categorical readout |
| Carrier | rna_molecules_with_sequencing |
| Problem class | linear_inverse_with_categorical_readout |
| Solution space | 1D_celltype_label |
| Noise model | negative_binomial |
| Integration axis | molecular_cellular |
| Difficulty delta | 5 |
| L dag | 8.3 |

## 📡 4. Measurement Model

Existence guaranteed within Omega bounds. Uniqueness conditional on adequate sequencing depth (typically >30k reads per cell for 3' chemistry) and adequate marker-panel coverage. Stability conditional with dropout_rate dominant for low-expressing markers; batch_effect dominant cross-sample; doublet_contamination dominant for high cell densities. Joint Hadamard well-posedness for the coupled RNA-seq + marker-panel-classifier forward established by Trapnell 2014 (foundational scRNA-seq), Macosko 2015 (Drop-seq), Stuart-Butler 2019 (Seurat v3 integration), Tabula Sapiens Consortium 2022, Zhang 2019 (CellMarker), Franzen 2019 (PanglaoDB).

| Metric | Value |
|---|---|
| Metric | categorical_accuracy |
| Secondary | macro_F1_per_celltype |

## 📏 5. Operating Range (Ω)

**Center problem class:** `scrnaseq_celltype_pwdr` · **Forward operator:** `scrnaseq_celltype_pwdr_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N cells | — | 5000 |
| N genes | — | 20000 |
| Batch effect | — | 0 |
| Dropout rate | — | 0 |
| Reads per cell | — | 50000 |
| Sequencing depth | — | 50000 |
| Library complexity | — | 0.85 |
| Doublet contamination | — | 0 |
| Taxonomy disagreement | — | 0 |
| Ambient rna contamination | — | 0 |
| Marker panel coverage uncertainty | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N cells | — | 100 – 1000000 |
| N genes | — | 1000 – 60000 |
| Dropout rate | — | 0.0 – 0.5 |
| Reads per cell | — | 1000 – 1000000 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.85_accuracy

| Metric | Range |
|---|---|
| Categorical accuracy | 0.4 – 0.99 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **categorical_accuracy**, with κ = `200` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0x673b55bb788633e2b747d4088754fce2dd908b8e80fb87a580eae551bba1a5d1`
- **Chain tx hash:** `0xc076736d4f2f15c82c65bb5a3b13c16628e630d165c72e056fb413fb169ed1eb`
- **Chain block:** `41555318`

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## File Mapping

This bundle consists of: `L1-520.md`, `L1-520.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-520.md` | Source of truth — edit this | Human or LLM |
| `L1-520.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 `L1-520`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._