L1 ⚛ L1-406 ⊙ Testnet

SEIR Epidemic with Exposed Compartment

Computational Biology · Epidemiology

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⬇ L1-406.md

# ⚛ L1 Principle — SEIR Epidemic with Exposed Compartment **ID:** `L1-406` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Epidemiology* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** SEIR parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** negative binomial > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555218 --- ## 🧠 1. Introduction **SEIR Epidemic with Exposed Compartment** is a **parameter-estimation problem** whose unknown lives in **SEIR parameter vector** space, within the **Epidemiology** sub-domain of **Computational Biology**. Measurements consist of N/A via a **seir incubation tracking** sensing mechanism. The forward operator applies, in order: time evolution of the state; O · likelihood · seir incidence operator; S · mcmc · seir posterior operator. Observations are corrupted by negative-binomial over-dispersed counts. Existence of the recovered SEIR_parameter_vector 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 ~= 80); age_structure_neglect dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Negative binomial sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Time derivative → O · likelihood · seir incidence → S · mcmc · seir posterior → **y** (detector). ``` y = `S.mcmc.seir_posterior` `O.likelihood.seir_incidence` ∂_t x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `O.likelihood.seir_incidence` | O · likelihood · seir incidence operator | | `S.mcmc.seir_posterior` | S · mcmc · seir posterior operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Epidemiology | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | SEIR_parameter_vector | | Noise model | negative_binomial | | Integration axis | time | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 4. Measurement Model Existence of the recovered SEIR_parameter_vector 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 ~= 80); age_structure_neglect dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Negative binomial sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | peak_incidence_RMSE_percent | | Secondary | timing_error_days | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `seir_incubation_tracking` **Center point:** | Parameter | Unit | Value | |---|---|---| | N days | — | 150 | | R0 true | — | 2.5 | | Detection rate | — | 0.5 | | Incubation period days | — | 5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N days | — | 20 – 730 | | R0 true | — | 1.0 – 10.0 | | Detection rate | — | 0.05 – 1.0 | | Incubation period days | — | 1 – 20 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20 peak_incidence_RMSE_percent | Metric | Range | |---|---| | Peak incidence rmse percent | 3 – 100 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **peak_incidence_RMSE_percent**, with κ = `2000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5bbf4fd3eca97926dd6b8f9356fa1d09acae91ea77773c6f99e5361932751a49` - **Chain tx hash:** `0xebf46c98d7fb57895cfb5c9c31a18acf60350d10a3f7d0adc77bc1be6d2ebddd` - **Chain block:** `41555218` --- ## File Mapping This bundle consists of: `L1-406.md`, `L1-406.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-406.md` | Source of truth — edit this | Human or LLM | | `L1-406.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 `L1-406`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-406.md).
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L2-406-001 SEIR Epidemic with Exposed Compartment — Nominal + Mismatch Specs

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📋 JSON metadata

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  "artifact_id": "L1-406",
  "chain_block": 41555218,
  "chain_hash": "0x5bbf4fd3eca97926dd6b8f9356fa1d09acae91ea77773c6f99e5361932751a49",
  "chain_tx_hash": "0xebf46c98d7fb57895cfb5c9c31a18acf60350d10a3f7d0adc77bc1be6d2ebddd",
  "domain": "Computational Biology",
  "hardness_fn": {
    "delta": 3,
    "kappa": 2000,
    "metric": "peak_incidence_RMSE_percent",
    "type": "epsilon_fn"
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  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "peak_incidence_RMSE_percent",
    "regime": "Existence of the recovered SEIR_parameter_vector 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 ~= 80); age_structure_neglect dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Negative binomial sets the irreducible data-fidelity floor.",
    "secondary": "timing_error_days"
  },
  "physics_fingerprint": {
    "L_DAG": 2.8,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Computational Biology",
    "integration_axis": "time",
    "noise_model": "negative_binomial",
    "primitives": [
      "D.time",
      "O.likelihood.seir_incidence",
      "S.mcmc.seir_posterior"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "seir_incubation_tracking",
    "solution_space": "SEIR_parameter_vector",
    "sub_domain": "Epidemiology",
    "title": "SEIR Epidemic with Exposed Compartment"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "seir_incubation_tracking"
    ],
    "allowed_omega_dimensions": [
      "N_days",
      "R0_true",
      "incubation_period_days",
      "detection_rate"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "20 peak_incidence_RMSE_percent",
      "forward_operator": "seir_incubation_tracking",
      "input_format": "measurement_only",
      "omega": {
        "N_days": 150,
        "R0_true": 2.5,
        "detection_rate": 0.5,
        "incubation_period_days": 5
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "peak_incidence_RMSE_percent": [
        3,
        100
      ]
    },
    "omega_bounds": {
      "N_days": [
        20,
        730
      ],
      "R0_true": [
        1.0,
        10.0
      ],
      "detection_rate": [
        0.05,
        1.0
      ],
      "incubation_period_days": [
        1,
        20
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Epidemiology",
  "title": "SEIR Epidemic with Exposed Compartment"
}

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