Bone Fracture Detection from Radiograph (PWDR) L1-526

Medical ImagingCortical bone discontinuity recovery from X-ray with fracture categorical readoutδ=3 · standardL_DAG = 4.6📋 Stub — not mineable

📋

Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

Read the contribution guide →Open a claim issue →

Forward model E

S t a g e 1 (L 1 - 031) : r a d i o g r a p h \to cor t i c a l_{e} d g e_{m} a p, f r a g m e n t_{m} a s k s, d i s pl a ce m e n t_{v} ec t or s, j o in t_{s} u r f a ce . S t a g e 2 : se v er i t y = s t e p (cor t i c a l_{d} i sr u pt i o n_{w} i d t h, d i s pl a ce m e n t, f r a g m e n t_{c} o u n t); A O_{O} T A = d ec i s i o n_{t} r ee (ana t o mi c_{l} oc a t i o n, se v er i t y, a r t i c u l a r_{i} n v o l v e m e n t) .

Bone Fracture Detection (PWDR): wraps L1-031 with established orthopedic / emergency radiology grading rules. Stage 1 (analytical, from L1-031): from multi-view radiograph (AP, lateral, oblique), recover cortical bone edge map, fragment segmentation, displacement vectors, joint-surface relationships. Stage 2 (deterministic threshold): apply width / displacement / fragment-count thresholds; AO/OTA class overlay; severity bins. Difficulty tier delta = 3.

L-DAG

L.xray_source -> L.attenuation_projection -> L.cortical_edge_detection -> L.fragment_segmentation -> L.fracture_classifier -> int.spatial

L.xray_sourceL.attenuation_projectionL.cortical_edge_detectionL.fragment_segmentationL.fracture_classifierint.spatial

Well-posedness W

Existence:: true
Uniqueness:: conditional
Stability:: conditional
κ:: 60

Existence inherited from L1-031. Uniqueness conditional on adequate views. Stability dominated by overlapping_structures and growth_plate_confounder (pediatric). Joint Hadamard well-posedness established by Müller AO 1996 (foundational classification), Lindsey 2018 (deep learning fracture detection benchmark), Rajpurkar 2017 (CheXNet), Olczak 2017 (Stockholm fracture deep learning).

Solvability C

Solver class:: linear-operator + edge-detection [Canny / learned] + categorical-readout [AO/OTA classifier] | end-to-end deep neural [Aidoc Bone, Gleamer BoneView] with explicit physics-informed cortical-edge regularization
Convergence rate q:: 2
Complexity:: O(H * W * N_views) for stage 1; O(N_fragments) for stage 2

Specs (0)

No L2 specs registered yet for this principle.