L1 ⚛ L1-509 ⊙ Testnet

Photoacoustic-Ultrasound Dual-mode Imaging (PAUS)

Medical Imaging · Concurrent functional + anatomical imaging via dual-contrast acquisition (multi-physics joint inverse)

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You are helping me submit a MODIFICATION of L1-509 (Photoacoustic-Ultrasound Dual-mode Imaging (PAUS)) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-509.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-509.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.

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[PASTE THE .md HERE]

⚙ Forward Model

y = `int.spectral_temporal_spatial` `L.transducer_detection_dual` `L.us_pulse_echo` `L.us_transmit_beam` `L.acoustic_wave_propagation` `L.thermoelastic_grueneisen` exp(-∫µ dl) `L.optical_diffusion` `L.optical_source` x + n,    n ~ 𝒩(0, σ²)

world state x (4D dual contrast functional anatomical)

→

L · optical source `L.optical_source`

→

L · optical diffusion `L.optical_diffusion`

→

Beer-Lambert attenuation exp(-∫µ dl)

→

L · thermoelastic grueneisen `L.thermoelastic_grueneisen`

→

L · acoustic wave propagation `L.acoustic_wave_propagation`

→

L · us transmit beam `L.us_transmit_beam`

→

L · us pulse echo `L.us_pulse_echo`

→

L · transducer detection dual `L.transducer_detection_dual`

→

int · spectral temporal spatial `int.spectral_temporal_spatial`

→

observation y (photon acoustic dual detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-509.md

# ⚛ L1 Principle — Photoacoustic-Ultrasound Dual-mode Imaging (PAUS) **ID:** `L1-509` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Concurrent functional + anatomical imaging via dual-contrast acquisition (multi-physics joint inverse)* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 4D dual contrast functional anatomical > **📡 Carrier:** photon_acoustic_dual · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553387 --- ## 🧠 1. Introduction **Photoacoustic-Ultrasound Dual-mode Imaging (PAUS)** is a **nonlinear inverse problem** whose unknown lives in **4D dual contrast functional anatomical** space, within the **Concurrent functional + anatomical imaging via dual-contrast acquisition (multi-physics joint inverse)** sub-domain of **Medical Imaging**. Measurements consist of photon acoustic dual via a **joint thermoelastic and pulse echo** sensing mechanism. The forward operator applies, in order: L · optical source operator; L · optical diffusion operator; exponential attenuation along the propagation path; L · thermoelastic grueneisen operator; L · acoustic wave propagation operator; L · us transmit beam operator; L · us pulse echo operator; L · transducer detection dual operator; int · spectral temporal spatial operator. Observations are corrupted by additive Gaussian noise. Existence of recovered joint state (mu_a, Z, c, rho) is guaranteed within the declared Omega bounds. Uniqueness holds under multi-illumination + multi-wavelength PA acquisition combined with US transmit-receive at adequate SNR; single-wavelength single-illumination PAUS suffers the same multiplicative non-uniqueness as single-wavelength qPAT (excluded from the spec range). Stability is moderately conditioned (kappa_eff ~ 40 after joint model-based reconstruction) — pa_us_synchronization_jitter dominates registration error; fluence_inhomogeneity dominates qPAT-class chromophore bias; acoustic_attenuation dominates US-class deep-tissue contrast; transducer_bandwidth_difference_pa_vs_us contributes a frequency-dependent reconstruction artifact (PA typically lower-frequency band 0.5-10 MHz, US higher 5-20 MHz). Joint Hadamard well-posedness for the coupled qPAT + US Born forward is established by the qPAT references (Bal-Uhlmann 2010, Bal-Ren 2011) plus the dual-mode literature: Niederhauser et al. 2005 (combined OAT/US), Beard 2011 (review), Wang LV 2008 (multiscale photoacoustic), Mehrmohammadi et al. 2013 (PA-US clinical), Park et al. 2017 (PAUS guided interventions). ## ⚙ 2. Forward Model Physical chain: **x** → L · optical source → L · optical diffusion → Beer-Lambert attenuation → L · thermoelastic grueneisen → L · acoustic wave propagation → L · us transmit beam → L · us pulse echo → L · transducer detection dual → int · spectral temporal spatial → **y** (detector). ``` y = `int.spectral_temporal_spatial` `L.transducer_detection_dual` `L.us_pulse_echo` `L.us_transmit_beam` `L.acoustic_wave_propagation` `L.thermoelastic_grueneisen` exp(-∫µ dl) `L.optical_diffusion` `L.optical_source` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.optical_source` | L · optical source operator | | `L.optical_diffusion` | L · optical diffusion operator | | `L.beer_lambert` | Exponential attenuation along the propagation path | | `L.thermoelastic_grueneisen` | L · thermoelastic grueneisen operator | | `L.acoustic_wave_propagation` | L · acoustic wave propagation operator | | `L.us_transmit_beam` | L · us transmit beam operator | | `L.us_pulse_echo` | L · us pulse echo operator | | `L.transducer_detection_dual` | L · transducer detection dual operator | | `int.spectral_temporal_spatial` | Int · spectral temporal spatial operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Concurrent functional + anatomical imaging via dual-contrast acquisition (multi-physics joint inverse) | | Carrier | photon_acoustic_dual | | Problem class | nonlinear_inverse | | Solution space | 4D_dual_contrast_functional_anatomical | | Noise model | gaussian | | Integration axis | spectral_temporal_spatial | | Difficulty delta | 5 | | L dag | 9.5 | ## 📡 4. Measurement Model Existence of recovered joint state (mu_a, Z, c, rho) is guaranteed within the declared Omega bounds. Uniqueness holds under multi-illumination + multi-wavelength PA acquisition combined with US transmit-receive at adequate SNR; single-wavelength single-illumination PAUS suffers the same multiplicative non-uniqueness as single-wavelength qPAT (excluded from the spec range). Stability is moderately conditioned (kappa_eff ~ 40 after joint model-based reconstruction) — pa_us_synchronization_jitter dominates registration error; fluence_inhomogeneity dominates qPAT-class chromophore bias; acoustic_attenuation dominates US-class deep-tissue contrast; transducer_bandwidth_difference_pa_vs_us contributes a frequency-dependent reconstruction artifact (PA typically lower-frequency band 0.5-10 MHz, US higher 5-20 MHz). Joint Hadamard well-posedness for the coupled qPAT + US Born forward is established by the qPAT references (Bal-Uhlmann 2010, Bal-Ren 2011) plus the dual-mode literature: Niederhauser et al. 2005 (combined OAT/US), Beard 2011 (review), Wang LV 2008 (multiscale photoacoustic), Mehrmohammadi et al. 2013 (PA-US clinical), Park et al. 2017 (PAUS guided interventions). | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | RMSE_per_modality | ## 📏 5. Operating Range (Ω) **Center problem class:** `paus_dual_contrast` · **Forward operator:** `paus_joint_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 64 | | Snr pa db | dB | 22 | | Snr us db | dB | 28 | | N us modes | — | 2 | | Voxel size mm | mm | 0.2 | | Lambda range nm | nm | 700 – 1064 | | N pa wavelengths | — | 5 | | Us bandwidth mhz | MHz | 5 | | Speed of sound mps | — | 1500 | | Acoustic attenuation | — | 0 | | Fluence inhomogeneity | — | 0 | | Us center frequency mhz | MHz | 7.5 | | Motion during acquisition | — | 0 | | Acoustic speed heterogeneity | — | 0 | | Pa us synchronization jitter | — | 0 | | Transducer bandwidth difference pa vs us | µs | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 512 | | W | px | 128 – 512 | | Z | — | 32 – 256 | | Snr pa db | dB | 5 – 40 | | Snr us db | dB | 5 – 45 | | N us modes | — | 1 – 5 | | Voxel size mm | mm | 0.05 – 1.0 | | N pa wavelengths | — | 2 – 16 | | Us bandwidth mhz | MHz | 1 – 20 | | Speed of sound mps | — | 1400 – 1600 | | Acoustic attenuation | — | 0.0 – 0.4 | | Fluence inhomogeneity | — | 0.0 – 0.4 | | Us center frequency mhz | MHz | 1 – 30 | | Motion during acquisition | — | 0.0 – 0.3 | | Acoustic speed heterogeneity | — | 0.0 – 0.1 | | Pa us synchronization jitter | — | 0.0 – 0.3 | | Transducer bandwidth difference pa vs us | µs | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 8.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `280` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xedc6787d7a57c3ffbe0fcc816d4c1b47dd38ddfa2914b2392b57b48d19033e1d` - **Chain tx hash:** `0x6d485b3261bc469ae58032e3f62431adb715c465c744d975ddc8ec63b9b20fc0` - **Chain block:** `41553387` --- ## File Mapping This bundle consists of: `L1-509.md`, `L1-509.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-509.md` | Source of truth — edit this | Human or LLM | | `L1-509.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 `L1-509`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-509-001 Photoacoustic-Ultrasound Dual-mode Imaging (PAUS) — Spec Skeleton

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📋 JSON metadata

{
  "artifact_id": "L1-509",
  "chain_block": 41553387,
  "chain_hash": "0xedc6787d7a57c3ffbe0fcc816d4c1b47dd38ddfa2914b2392b57b48d19033e1d",
  "chain_tx_hash": "0x6d485b3261bc469ae58032e3f62431adb715c465c744d975ddc8ec63b9b20fc0",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 5,
    "kappa": 280,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of recovered joint state (mu_a, Z, c, rho) is guaranteed within the declared Omega bounds. Uniqueness holds under multi-illumination + multi-wavelength PA acquisition combined with US transmit-receive at adequate SNR; single-wavelength single-illumination PAUS suffers the same multiplicative non-uniqueness as single-wavelength qPAT (excluded from the spec range). Stability is moderately conditioned (kappa_eff ~ 40 after joint model-based reconstruction) \u2014 pa_us_synchronization_jitter dominates registration error; fluence_inhomogeneity dominates qPAT-class chromophore bias; acoustic_attenuation dominates US-class deep-tissue contrast; transducer_bandwidth_difference_pa_vs_us contributes a frequency-dependent reconstruction artifact (PA typically lower-frequency band 0.5-10 MHz, US higher 5-20 MHz). Joint Hadamard well-posedness for the coupled qPAT + US Born forward is established by the qPAT references (Bal-Uhlmann 2010, Bal-Ren 2011) plus the dual-mode literature: Niederhauser et al. 2005 (combined OAT/US), Beard 2011 (review), Wang LV 2008 (multiscale photoacoustic), Mehrmohammadi et al. 2013 (PA-US clinical), Park et al. 2017 (PAUS guided interventions).",
    "secondary": "RMSE_per_modality"
  },
  "physics_fingerprint": {
    "L_DAG": 9.5,
    "carrier": "photon_acoustic_dual",
    "difficulty_delta": 5,
    "domain": "Medical Imaging",
    "integration_axis": "spectral_temporal_spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.optical_source",
      "L.optical_diffusion",
      "L.beer_lambert",
      "L.thermoelastic_grueneisen",
      "L.acoustic_wave_propagation",
      "L.us_transmit_beam",
      "L.us_pulse_echo",
      "L.transducer_detection_dual",
      "int.spectral_temporal_spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "joint_thermoelastic_and_pulse_echo",
    "solution_space": "4D_dual_contrast_functional_anatomical",
    "sub_domain": "Concurrent functional + anatomical imaging via dual-contrast acquisition (multi-physics joint inverse)",
    "title": "Photoacoustic-Ultrasound Dual-mode Imaging (PAUS)"
  },
  "size_tiers": {
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      "paus_joint_forward",
      "paus_alternating_pa_us_forward",
      "paus_with_shared_tissue_model",
      "paus_with_co_estimated_speed_of_sound"
    ],
    "allowed_omega_dimensions": [
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      "W",
      "Z",
      "N_PA_wavelengths",
      "lambda_range_nm",
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      "us_bandwidth_MHz",
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      "speed_of_sound_mps",
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      "motion_during_acquisition"
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    "allowed_problem_classes": [
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      "paus_with_shear_wave"
    ],
    "center_spec": {
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      "forward_operator": "paus_joint_forward",
      "input_format": "synchronized_dual_contrast_time_resolved",
      "omega": {
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        "N_PA_wavelengths": 5,
        "N_US_modes": 2,
        "SNR_PA_dB": 22,
        "SNR_US_dB": 28,
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        "Z": 64,
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        "acoustic_speed_heterogeneity": 0.0,
        "fluence_inhomogeneity": 0.0,
        "lambda_range_nm": [
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          1064
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        "motion_during_acquisition": 0.0,
        "pa_us_synchronization_jitter": 0.0,
        "speed_of_sound_mps": 1500.0,
        "transducer_bandwidth_difference_pa_vs_us": 0.0,
        "us_bandwidth_MHz": 5.0,
        "us_center_frequency_MHz": 7.5,
        "voxel_size_mm": 0.2
      },
      "problem_class": "paus_dual_contrast"
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    "epsilon_bounds": {
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        42.0
      ]
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        512
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      "N_PA_wavelengths": [
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        16
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      "N_US_modes": [
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        5
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      "W": [
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      "Z": [
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      "acoustic_attenuation": [
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        0.4
      ],
      "acoustic_speed_heterogeneity": [
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        0.1
      ],
      "fluence_inhomogeneity": [
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      ],
      "motion_during_acquisition": [
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        0.3
      ],
      "pa_us_synchronization_jitter": [
        0.0,
        0.3
      ],
      "speed_of_sound_mps": [
        1400,
        1600
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      "transducer_bandwidth_difference_pa_vs_us": [
        0.0,
        0.5
      ],
      "us_bandwidth_MHz": [
        1,
        20
      ],
      "us_center_frequency_MHz": [
        1,
        30
      ],
      "voxel_size_mm": [
        0.05,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Concurrent functional + anatomical imaging via dual-contrast acquisition (multi-physics joint inverse)",
  "title": "Photoacoustic-Ultrasound Dual-mode Imaging (PAUS)"
}

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