L1 ⚛ L1-405 ⊙ Testnet

SIR Epidemic Parameter Estimation

Computational Biology · Epidemiology

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⬇ principle.md ⬇ principle.json

Fork L1-405

⬇ L1-405.md ⬇ L1-405.json

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You are helping me submit a MODIFICATION of L1-405 (SIR Epidemic Parameter Estimation) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-405.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-405.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = `S.mcmc.epidemic_posterior` `O.likelihood.incidence_nb` ∂_t x

world state x (SIR parameter vector)

→

Time derivative ∂_t

→

O · likelihood · incidence nb `O.likelihood.incidence_nb`

→

S · mcmc · epidemic posterior `S.mcmc.epidemic_posterior`

→

observation y (N/A detector)

Noise: negative-binomial over-dispersed counts

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-405.md

# ⚛ L1 Principle — SIR Epidemic Parameter Estimation **ID:** `L1-405` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Epidemiology* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** SIR parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** negative binomial > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555218 --- ## 🧠 1. Introduction **SIR Epidemic Parameter Estimation** is a **parameter-estimation problem** whose unknown lives in **SIR parameter vector** space, within the **Epidemiology** sub-domain of **Computational Biology**. Measurements consist of N/A via a **incidence case surveillance** sensing mechanism. The forward operator applies, in order: time evolution of the state; O · likelihood · incidence nb operator; S · mcmc · epidemic posterior operator. Observations are corrupted by negative-binomial over-dispersed counts. Existence of the recovered SIR_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 ~= 50); under_reporting_factor 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 · incidence nb → S · mcmc · epidemic posterior → **y** (detector). ``` y = `S.mcmc.epidemic_posterior` `O.likelihood.incidence_nb` ∂_t x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `O.likelihood.incidence_nb` | O · likelihood · incidence nb operator | | `S.mcmc.epidemic_posterior` | S · mcmc · epidemic posterior operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Epidemiology | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | SIR_parameter_vector | | Noise model | negative_binomial | | Integration axis | time | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered SIR_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 ~= 50); under_reporting_factor dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Negative binomial sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | R0_estimation_RMSE | | Secondary | incidence_prediction_RMSE | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `incidence_case_surveillance` **Center point:** | Parameter | Unit | Value | |---|---|---| | R0 true | — | 2.5 | | Detection rate | — | 0.5 | | N incidence days | — | 100 | | Overdispersion k | — | 10 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | R0 true | — | 1.0 – 10.0 | | Detection rate | — | 0.05 – 1.0 | | N incidence days | — | 10 – 500 | | Overdispersion k | — | 1 – 100 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.2 R0_estimation_RMSE | Metric | Range | |---|---| | R0 estimation rmse | 0.05 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **R0_estimation_RMSE**, with κ = `1000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4d92422c8c3788c9c3d985065862fc4d9515767c7738699528c989f329842e4c` - **Chain tx hash:** `0x395004fb80e2a73bc39abc039c5bd894b87130fdc19cbfbedda6f2aa2d99083b` - **Chain block:** `41555218` --- ## File Mapping This bundle consists of: `L1-405.md`, `L1-405.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-405.md` | Source of truth — edit this | Human or LLM | | `L1-405.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 `L1-405`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "artifact_id": "L1-405",
  "chain_block": 41555218,
  "chain_hash": "0x4d92422c8c3788c9c3d985065862fc4d9515767c7738699528c989f329842e4c",
  "chain_tx_hash": "0x395004fb80e2a73bc39abc039c5bd894b87130fdc19cbfbedda6f2aa2d99083b",
  "domain": "Computational Biology",
  "hardness_fn": {
    "delta": 3,
    "kappa": 1000,
    "metric": "R0_estimation_RMSE",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
      "name": "primary",
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    }
  ],
  "layer": "L1",
  "observable_profile": {
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    "regime": "Existence of the recovered SIR_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 ~= 50); under_reporting_factor dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Negative binomial sets the irreducible data-fidelity floor.",
    "secondary": "incidence_prediction_RMSE"
  },
  "physics_fingerprint": {
    "L_DAG": 2.5,
    "carrier": "N/A",
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    "integration_axis": "time",
    "noise_model": "negative_binomial",
    "primitives": [
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      "O.likelihood.incidence_nb",
      "S.mcmc.epidemic_posterior"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "incidence_case_surveillance",
    "solution_space": "SIR_parameter_vector",
    "sub_domain": "Epidemiology",
    "title": "SIR Epidemic Parameter Estimation"
  },
  "size_tiers": {
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    "allowed_omega_dimensions": [
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    "allowed_problem_classes": [
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    "center_spec": {
      "epsilon_fn_center": "0.2 R0_estimation_RMSE",
      "forward_operator": "incidence_case_surveillance",
      "input_format": "measurement_only",
      "omega": {
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        1.0
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    "omega_bounds": {
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        500
      ],
      "R0_true": [
        1.0,
        10.0
      ],
      "detection_rate": [
        0.05,
        1.0
      ],
      "overdispersion_k": [
        1,
        100
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Epidemiology",
  "title": "SIR Epidemic Parameter Estimation"
}

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