L1 ⚛ L1-367 ⊙ Testnet

CMB Gravitational Lensing Reconstruction

Astrophysics · CMB lensing

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Layer template

⬇ principle.md ⬇ principle.json

Fork L1-367

⬇ L1-367.md ⬇ L1-367.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-367 (CMB Gravitational Lensing Reconstruction) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-367.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-367.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.quadratic.estimator` `F.fourier.harmonic` x

world state x (2D lensing convergence)

→

F · fourier · harmonic `F.fourier.harmonic`

→

S · quadratic · estimator `S.quadratic.estimator`

→

observation y (photon detector)

Noise: thermally-driven Gaussian fluctuations

Solver / auxiliary components (1)

K.filter — K · filter operator

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-367.md

# ⚛ L1 Principle — CMB Gravitational Lensing Reconstruction **ID:** `L1-367` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *CMB lensing* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D lensing convergence > **📡 Carrier:** photon · **🌫 Noise:** thermal gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555176 --- ## 🧠 1. Introduction **CMB Gravitational Lensing Reconstruction** is a **nonlinear inverse problem** whose unknown lives in **2D lensing convergence** space, within the **CMB lensing** sub-domain of **Astrophysics**. Measurements consist of photons collected by an optical detector via a **quadratic lensing estimator** sensing mechanism. The forward operator applies, in order: F · fourier · harmonic operator; S · quadratic · estimator operator; K · filter operator. Observations are corrupted by thermally-driven Gaussian fluctuations. Existence of the recovered 2D_lensing_convergence 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 ~= 500); foreground_bias dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → F · fourier · harmonic → S · quadratic · estimator → **y** (detector). ``` y = `S.quadratic.estimator` `F.fourier.harmonic` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `F.fourier.harmonic` | F · fourier · harmonic operator | | `S.quadratic.estimator` | S · quadratic · estimator operator | **🛰 Estimator components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `K.filter` | K · filter operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | CMB lensing | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 2D_lensing_convergence | | Noise model | thermal_gaussian | | Integration axis | angular_multipole | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered 2D_lensing_convergence 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 ~= 500); foreground_bias dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | lensing_power_spectrum_C_kk_chi2 | | Secondary | reconstruction_SNR | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `quadratic_lensing_estimator` **Center point:** | Parameter | Unit | Value | |---|---|---| | N pix side | — | 2048 | | Noise uk arcmin | — | 5 | | Beam fwhm arcmin | — | 1.5 | | Survey area deg2 | — | 10000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N pix side | — | 512 – 8192 | | Noise uk arcmin | — | 1.0 – 50.0 | | Beam fwhm arcmin | — | 0.5 – 10.0 | | Survey area deg2 | — | 1000 – 40000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.05 lensing_power_spectrum_C_kk_chi2 | Metric | Range | |---|---| | Lensing power spectrum c kk chi2 | 0.9 – 2.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **lensing_power_spectrum_C_kk_chi2**, with κ = `100000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x3deb3f685300556ed7f8cfc9ca10983f283197b819c691782086109f0fe9ea25` - **Chain tx hash:** `0x759b9b0c9a8be2cf518b8a556f4d52b15ebd637238c7d290b7513bcc4b6743d8` - **Chain block:** `41555176` --- ## File Mapping This bundle consists of: `L1-367.md`, `L1-367.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-367.md` | Source of truth — edit this | Human or LLM | | `L1-367.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 `L1-367`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-367-001 CMB Gravitational Lensing Reconstruction — Nominal + Mismatch Specs

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📋 JSON metadata

{
  "artifact_id": "L1-367",
  "chain_block": 41555176,
  "chain_hash": "0x3deb3f685300556ed7f8cfc9ca10983f283197b819c691782086109f0fe9ea25",
  "chain_tx_hash": "0x759b9b0c9a8be2cf518b8a556f4d52b15ebd637238c7d290b7513bcc4b6743d8",
  "domain": "Astrophysics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 100000.0,
    "metric": "lensing_power_spectrum_C_kk_chi2",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "lensing_power_spectrum_C_kk_chi2",
    "regime": "Existence of the recovered 2D_lensing_convergence 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 ~= 500); foreground_bias dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor.",
    "secondary": "reconstruction_SNR"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Astrophysics",
    "integration_axis": "angular_multipole",
    "noise_model": "thermal_gaussian",
    "primitives": [
      "F.fourier.harmonic",
      "S.quadratic.estimator",
      "K.filter"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "quadratic_lensing_estimator",
    "solution_space": "2D_lensing_convergence",
    "sub_domain": "CMB lensing",
    "title": "CMB Gravitational Lensing Reconstruction"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "quadratic_lensing_estimator"
    ],
    "allowed_omega_dimensions": [
      "N_pix_side",
      "noise_uK_arcmin",
      "beam_FWHM_arcmin",
      "survey_area_deg2"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "1.05 lensing_power_spectrum_C_kk_chi2",
      "forward_operator": "quadratic_lensing_estimator",
      "input_format": "measurement_only",
      "omega": {
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        "beam_FWHM_arcmin": 1.5,
        "noise_uK_arcmin": 5.0,
        "survey_area_deg2": 10000
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "lensing_power_spectrum_C_kk_chi2": [
        0.9,
        2.0
      ]
    },
    "omega_bounds": {
      "N_pix_side": [
        512,
        8192
      ],
      "beam_FWHM_arcmin": [
        0.5,
        10.0
      ],
      "noise_uK_arcmin": [
        1.0,
        50.0
      ],
      "survey_area_deg2": [
        1000,
        40000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "CMB lensing",
  "title": "CMB Gravitational Lensing Reconstruction"
}

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