L1 ⚛ L1-409 ⊙ Testnet

Phylogenetic Likelihood Inference

Computational Biology · Molecular evolution

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⬇ L1-409.md

# ⚛ L1 Principle — Phylogenetic Likelihood Inference **ID:** `L1-409` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Molecular evolution* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** phylogenetic tree topology > **📡 Carrier:** N/A · **🌫 Noise:** multinomial > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555219 --- ## 🧠 1. Introduction **Phylogenetic Likelihood Inference** is a **nonlinear inverse problem** whose unknown lives in **phylogenetic tree topology** space, within the **Molecular evolution** sub-domain of **Computational Biology**. Measurements consist of N/A via a **molecular sequence alignment** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; S · mcmc · tree space bayesian operator; O · atr · total tree likelihood operator. Observations are corrupted by multinomial counting noise across categories. Existence of the recovered phylogenetic_tree_topology is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 2000); model_misspecification_substitution dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Multinomial sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Pointwise nonlinearity → S · mcmc · tree space bayesian → O · atr · total tree likelihood → **y** (detector). ``` y = `O.atr.total_tree_likelihood` `S.mcmc.tree_space_bayesian` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `S.mcmc.tree_space_bayesian` | S · mcmc · tree space bayesian operator | | `O.atr.total_tree_likelihood` | O · atr · total tree likelihood operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Molecular evolution | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | phylogenetic_tree_topology | | Noise model | multinomial | | Integration axis | phylogenetic_tree | | Difficulty delta | 5 | | L dag | 4.5 | ## 📡 4. Measurement Model Existence of the recovered phylogenetic_tree_topology is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 2000); model_misspecification_substitution dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Multinomial sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | Robinson_Foulds_distance | | Secondary | branch_length_RMSE | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `molecular_sequence_alignment` **Center point:** | Parameter | Unit | Value | |---|---|---| | N taxa | — | 50 | | N sites | — | 5000 | | Divergence time my | — | 100 | | Mutation rate per site yr | — | 1e-09 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N taxa | — | 4 – 10000 | | N sites | — | 100 – 100000 | | Divergence time my | — | 1 – 1000 | | Mutation rate per site yr | — | 1e-10 – 1e-07 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 5 Robinson_Foulds_distance | Metric | Range | |---|---| | Robinson foulds distance | 0 – 20 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **Robinson_Foulds_distance**, with κ = `100000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x89d3fb6cb7267412f3fd12ba45b4705b67200fc24e7b93d4c5cde61fbfa2b4e3` - **Chain tx hash:** `0x820f0c2cd9fc9212901c8779f0a5ac0601dd802d9870bd446a567b786268b0f9` - **Chain block:** `41555219` --- ## File Mapping This bundle consists of: `L1-409.md`, `L1-409.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-409.md` | Source of truth — edit this | Human or LLM | | `L1-409.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 `L1-409`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-409-001 Phylogenetic Likelihood Inference — Nominal + Mismatch Specs

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📋 JSON metadata

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    "title": "Phylogenetic Likelihood Inference"
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  "status": "testnet",
  "sub_domain": "Molecular evolution",
  "title": "Phylogenetic Likelihood Inference"
}

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