---
{
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"path": "/en/open-problems/gravity/orbital-discriminator",
"title": "Nondegenerate orbital observable and second-order review",
"title_en": "Nondegenerate orbital observable and second-order review",
"category": "Gravity",
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"en": "Deflection"
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"canonical_scope": "Research task from Chapter 2",
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"source_reference": "§IV.2—3 (2.27)—(2.42), end of §IV and chapter summary",
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"title": "各向异性空间动力学（最终合订稿）",
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"equations": [
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"Sources and collaboration"
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"mathematical_review": "OPEN REVIEW",
"review_path": "/en/theory/gravity#review-notes",
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"difficulty": "High",
"current_state": "The present static spherical action is equivalent to the Schwarzschild exterior expression; first-order precession is derived.",
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"deliverable": "A complete order expansion, parameter/coordinate mapping, degeneracy analysis and reproducible calculation. Record a null distinction if the difference vanishes."
},
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"Areal radius, actual spatial length and reference optical path are defined separately.",
"Weak-field perturbation, slow-rotation far field and boundary statistics each have separate conditions."
],
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"sha256": "125df9543371f89656a2c29d552e1166e5edcc9ff5f6ec1ef1e438c7688d6ec5",
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"title": "第二章-ASD理论-修订书稿 (2).pdf",
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---
## Task
An open research task extracted from the final Chapter 2 manuscript, not a new canonical derivation.
## Current state
The final manuscript specifies the full spherical action, canonical momenta and orbit equation; first-order results coincide under the mathematically matching Schwarzschild exterior construction. The next deliverable should first establish whether a nonzero difference survives the same references and parameter mapping. A zero difference is also a reproducible result.
## Required work
First determine whether the current model differs at all. If new independent constitutive inputs are needed, identify their physical origin. Match radius, coordinates, mass, distance and orbital parameters before testing second-order or other lowest-order nondegenerate observables.
## Deliverable and boundary
A complete order expansion, parameter/coordinate mapping, degeneracy analysis and reproducible calculation. Record a null distinction if the difference vanishes.
Re-expanding 2π/(1−κ) with truncated κ cannot supply a full second-order coefficient; a hoped-for distinction is not an existing prediction.
## Sources and collaboration
Final collected manuscript · Chapter 2 §四.2—3 (2.27)—(2.42)、§四末及小结
[Gravity](/en/theory/gravity) · [Tests](/en/tests/gravity)