L1 ⚛ L1-381 ⊙ Testnet

Type Ia Supernova Distance Standardization

Astrophysics · Cosmological distance ladder

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-381.md

# ⚛ L1 Principle — Type Ia Supernova Distance Standardization **ID:** `L1-381` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Cosmological distance ladder* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** distance modulus H0 > **📡 Carrier:** photon · **🌫 Noise:** observation gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555196 --- ## 🧠 1. Introduction **Type Ia Supernova Distance Standardization** is a **parameter-estimation problem** whose unknown lives in **distance modulus H0** space, within the **Cosmological distance ladder** sub-domain of **Astrophysics**. Measurements consist of photons collected by an optical detector via a **photometric sn standardization** sensing mechanism. The forward operator applies, in order: operator inherits structure from a graph (mesh, network); S · calibration · standardization operator; O · chi2 · hubble residual operator. Observations are corrupted by observation gaussian. Existence of the recovered distance_modulus_H0 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 ~= 15); Malmquist_bias dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Structured graph operator → S · calibration · standardization → O · chi2 · hubble residual → **y** (detector). ``` y = `O.chi2.hubble_residual` `S.calibration.standardization` G x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `G.structured` | Operator inherits structure from a graph (mesh, network) | | `S.calibration.standardization` | S · calibration · standardization operator | | `O.chi2.hubble_residual` | O · chi2 · hubble residual operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Cosmological distance ladder | | Carrier | photon | | Problem class | parameter_estimation | | Solution space | distance_modulus_H0 | | Noise model | observation_gaussian | | Integration axis | spectral_temporal | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 4. Measurement Model Existence of the recovered distance_modulus_H0 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 ~= 15); Malmquist_bias dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | H0_sigma_km_s_Mpc | | Secondary | sigma_int_mag | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `photometric_sn_standardization` **Center point:** | Parameter | Unit | Value | |---|---|---| | Median z | — | 0.3 | | Peculiar v kms | — | 200 | | N sn hubble flow | — | 500 | | Photometric noise mmag | — | 5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Median z | — | 0.02 – 2.0 | | Peculiar v kms | — | 100 – 600 | | N sn hubble flow | — | 50 – 2000 | | Photometric noise mmag | — | 1.0 – 50.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.8 H0_sigma_km_s_Mpc | Metric | Range | |---|---| | H0 sigma km s mpc | 0.2 – 3.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **H0_sigma_km_s_Mpc**, with κ = `300` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x2d1adb410d3fef6903be248b800dff7881b82e5dd6577a59a2763b0983fe0717` - **Chain tx hash:** `0x6f427f05ca4372b323a0ebba2994ed6310fa7d9bb15cf95d1cd3c5bc203dc728` - **Chain block:** `41555196` --- ## File Mapping This bundle consists of: `L1-381.md`, `L1-381.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-381.md` | Source of truth — edit this | Human or LLM | | `L1-381.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 `L1-381`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-381.md).
Regenerate L1-381.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-381-001 Type Ia Supernova Distance Standardization — Nominal + Mismatch Specs

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-381",
  "chain_block": 41555196,
  "chain_hash": "0x2d1adb410d3fef6903be248b800dff7881b82e5dd6577a59a2763b0983fe0717",
  "chain_tx_hash": "0x6f427f05ca4372b323a0ebba2994ed6310fa7d9bb15cf95d1cd3c5bc203dc728",
  "domain": "Astrophysics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 300,
    "metric": "H0_sigma_km_s_Mpc",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "H0_sigma_km_s_Mpc",
    "regime": "Existence of the recovered distance_modulus_H0 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 ~= 15); Malmquist_bias dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.",
    "secondary": "sigma_int_mag"
  },
  "physics_fingerprint": {
    "L_DAG": 2.8,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Astrophysics",
    "integration_axis": "spectral_temporal",
    "noise_model": "observation_gaussian",
    "primitives": [
      "G.structured",
      "S.calibration.standardization",
      "O.chi2.hubble_residual"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "photometric_sn_standardization",
    "solution_space": "distance_modulus_H0",
    "sub_domain": "Cosmological distance ladder",
    "title": "Type Ia Supernova Distance Standardization"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "photometric_sn_standardization"
    ],
    "allowed_omega_dimensions": [
      "N_SN_hubble_flow",
      "median_z",
      "photometric_noise_mmag",
      "peculiar_v_kms"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.8 H0_sigma_km_s_Mpc",
      "forward_operator": "photometric_sn_standardization",
      "input_format": "measurement_only",
      "omega": {
        "N_SN_hubble_flow": 500,
        "median_z": 0.3,
        "peculiar_v_kms": 200,
        "photometric_noise_mmag": 5.0
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "H0_sigma_km_s_Mpc": [
        0.2,
        3.0
      ]
    },
    "omega_bounds": {
      "N_SN_hubble_flow": [
        50,
        2000
      ],
      "median_z": [
        0.02,
        2.0
      ],
      "peculiar_v_kms": [
        100,
        600
      ],
      "photometric_noise_mmag": [
        1.0,
        50.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Cosmological distance ladder",
  "title": "Type Ia Supernova Distance Standardization"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.