Open Problems: Find Work You Can Advance

Stable Finite-Energy Electron Solution

• PDE
• Topology
• Numerical physics

Current state

ASD describes the electron as a closed orientation structure in the minimal negative-charge sector. Chapter 4 supplies the orientation field, finite-energy boundary, topological current and charge matching. Chapter 5 supplies the unique positive stationary radius and radial second-derivative check of a one-parameter energy model. The scale-stabilization mechanism is analytic; the next task is the full three-dimensional electron configuration.

Reviewable deliverable

First deliver a reproducible electron-sector solution with equation residuals, boundary/grid convergence, vacuum-subtracted energy, topological integrals and perturbation spectra. Calculate charge, mass and rotational response from that same core–surrounding-field system, identifying calibrated parameters.

Dynamical Origin of Born Statistics

• Quantum foundations
• Statistical inference
• PDE

Current state

A linearly driven detector’s mean absorbed power is proportional to the envelope modulus squared. Fixed energy per event and negligible leakage, dead time and saturation give an event rate and a conditional position distribution after time/thickness integration. The manuscript also supplies phase-flow equivariance and a nonlinear detector-response expansion. These are established results within their stated conditions.

Reviewable deliverable

First deliver a complete response model, conservation accounting, event definition and calibration for one detector. Provide a proof, numerical result or counterexample for single-record exclusivity and initial-state convergence, without using the target probability as a preset sampling rule.

First complete device-level quantitative discriminator

• Metrology
• Atomic clocks
• Accelerator physics
• Statistical inference

Current state

The three workbenches define clear comparison problems, but ASD clock responses, the muon statistical map and the joint high-speed source–probe model remain open. The registry has no QUANTITATIVE DISCRIMINATOR. This is a cross-module research deliverable, not a new physical result.

Reviewable deliverable

Choose a fixed apparatus, observable, theory version and parameter domain. Independently calculate $O_{\rm ASD}$ and $O_{\rm comparison}$ for the same readout, obtaining $\Delta O$. Supply errors, correlations, identifiability, calibration and a rejection region. Separate independent inputs, derived outputs and fitted parameters. Release code, data, expected outputs and checksums. If results coincide or nuisance parameters absorb the difference, deliver a non-discrimination result. If closure fails, identify the missing equation.

Topological Classification

• Topology

Current state

The manuscript distinguishes compact phase, 3D SU(2) degree and internal winding; classification of the complete field space remains open.

Reviewable deliverable

A definition of full configuration space, relevant homotopy or relative classification, conservation conditions and counterexamples; enumerate physical identification inputs rather than using drawings as proofs.

Mass Generation

• PDE
• Numerical physics

Current state

The final manuscript separately defines rest-energy mass, translational inertia, active gravitational source and passive response, and states the source-coupling and normalization matching needed for equality. Local divergence coupling has zero exterior density response; an independent frame-stretch extension supplies an integrable 1/r far field.

Reviewable deliverable

Deliver integrals or response calculations for all four definitions, units, convergence checks and differences; identify which of G and the source coefficients are inputs and which are independently calculated.

Spin and Statistics

• Topology
• Quantum foundations

Current state

Collective rotation and a conditional FR sign choice exist; the joint derivation of half-integer spin and exchange statistics is incomplete.

Reviewable deliverable

Rotation/exchange homotopy proof, constrained quantum state space, ground-state/statistics selection and explicit missing ingredients for the g-factor calculation.

Proton Structure

• Topology
• Numerical physics

Current state

ASD organizes the proton as one closed structure with three internal twists, distinguishing N_int=3 from global charge N_em=+1. Chapter 4 gives topological-current conservation, charge coupling and a three-channel fractional-response representation with additional conditions; the scale-stabilization mechanism has an analytic expression.

Reviewable deliverable

Deliver a proton candidate solution with explicit fields and boundaries, or a localized failure result; provide energy, topological number, stability spectrum and at least one probe response, with input/output parameter roles.

Particle Mass Spectrum

• Numerical physics

Current state

Energy functionals and mass definitions exist; electron/proton masses have not been independently output from shared inputs.

Reviewable deliverable

An input/output parameter ledger, mass and ratio calculations, convergence and sensitivity analysis separating predictions, fits and dimensional estimates.

Creation and Annihilation Dynamics

• PDE
• Numerical physics

Current state

Charge/energy–momentum accounting and conditional thresholds are available; core formation/unlocking and rates are unsolved.

Reviewable deliverable

Reproducible time evolution, conservation errors, threshold/recoil checks, normalized rates or cross sections, detector response and the energy budget of any extra longitudinal branch.

Unified spatial dynamics

• PDE
• Numerical physics

Current state

The local two-field parent action, both variations, reciprocal sources and energy-square completion are established. The manuscript also gives an independent frame-stretch extension for the gravitational far field, the coupled vacuum spectrum and an analytic radius for the scale model. The task is joint closure of these existing ingredients, not finding an entirely unwritten master equation.

Reviewable deliverable

Deliver the full variation, conserved quantities, vacuum spectrum and parameter domain of one explicit truncation; map it to the static far field, stable localization and accompanying-field envelope, recording incompatible conditions.

FCC continuum consistency

• Numerical physics
• PDE

Current state

The equal-connection FCC scalar model has a full-wave-number cosine dispersion, second moment and long-wave expansion. Continuous-time lattice propagation, the full multicomponent field and feedback-renormalized speeds are different checks. This review finds that Eq. (5.1.11), its following half-angle form and fourth-order expansion cannot all be identical with their printed coefficients; the FCC page records the specific difference.

Reviewable deliverable

Deliver a reproducible neighbour table, dynamical matrix, inter-equation coefficient check and reviewable correction options; only then provide coefficient-dependent dispersion plots, domains and directional experimental response.

High-energy electromagnetism · Chinese original

• Accelerator physics
• Metrology

The detailed task brief is currently available in Chinese.

Current state

同速平行横向构型的 LVE 磁力代数可复算；一般场与探针映射尚需完成。

Reviewable deliverable

闭合的构型定义、场与力表达、守恒检查及同一装置下的实验预测。

Detecting longitudinal waves

• Metrology

Current state

There is an effective-equation target for a free longitudinal mode; detector coupling and signal strength remain undetermined.

Reviewable deliverable

Source and detector models, transfer function, polarization or direction features, sensitivity and systematics.

Muon survival under the LVE path interpretation · Chinese original

• Numerical physics
• Statistical inference

The detailed task brief is currently available in Chinese.

Current state

第一章的路径关系与示例已复算；尚无 ASD 能谱、通量或存活分布的装置级拟合。

Reviewable deliverable

同输入的 ASD 与标准理论存活分布、可复算代码、数据来源、残差和误差预算。

Experimental sequence: P2

Operational mapping from true length to instrument readings · Chinese original

• Metrology

The detailed task brief is currently available in Chinese.

Current state

SI 定义和操作路径关系已明确；LVE 的运动构造仍保留独立前提。

Reviewable deliverable

被测量定义表、事件图、路径与读数关系、参考传递流程及不确定度项目。

Scale–frequency response of specific clocks · Chinese original

• Atomic clocks
• Metrology

The detailed task brief is currently available in Chinese.

Current state

过程计量关系与第二章尺度耦合已整理；跨钟种统一性和运钟映射尚未闭合。

Reviewable deliverable

钟种模型、响应函数、信号传递协议、同输入的理论比较、残差或明确的未闭合项。

Experimental sequence: P1

Inertial closure and common energy–mass normalization · Chinese original

• PDE
• Numerical physics

The detailed task brief is currently available in Chinese.

Current state

式（2.11）的构成输入下角积分给出动量；功积分给出动能，总能量另需归一化。

Reviewable deliverable

有限核心质量积分、惯性角分布、能量泛函、普适耦合条件及全部匹配假设。

Nondegenerate orbital observable and second-order review

• Astrophysics
• Numerical physics

Current state

The present static spherical action is equivalent to the Schwarzschild exterior expression; first-order precession is derived.

Reviewable deliverable

A complete order expansion, parameter/coordinate mapping, degeneracy analysis and reproducible calculation. Record a null distinction if the difference vanishes.

Complete spatial structure of rotating compact objects

• Astrophysics
• PDE

Current state

The manuscript contains a first-order weak-field far-zone azimuthal field and directed optical path; ζ=4 is reference matching.

Reviewable deliverable

Causal field equations, domain, weak-field matching, boundary conditions and ray calculations including source and detector models.

Microscopic source and macroscopic longitudinal structure

• PDE
• Astrophysics

Current state

Finite near-core density deficit, far-field mass flux and universal mass normalization have distinct roles; a microscopic source solution remains open.

Reviewable deliverable

A convergent near-core integral, exterior flux solution, energy/inertial/active/passive mass matching and coupling-coefficient calculation.

Strong-field closure

• Astrophysics
• PDE

Current state

An exterior X, radial length and optical constitutive law exist, alongside weak static source equations.

Reviewable deliverable

A reviewable action, field equations, exterior solution, weak-field matching and stability analysis, with adopted inputs distinguished from outputs.

Full Moving-Charge Spatial Field

• PDE
• Accelerator physics

Current state

The common-velocity transverse law is specified; radial-candidate flux and potential-gradient derivatives have been checked. Total flux does not uniquely determine the local field.

Reviewable deliverable

Field equations and boundaries; at least one reproducible finite-source solution; flux, static-limit and common-transverse checks; a list of undetermined parameters.

Field Representation from LVE

• PDE
• Metrology

Current state

The LVE correction, free material action, slow-source quasistatic potential and chosen minimal coupling are available. The free transverse sector has the representation A_T=N_Tu_T.

Reviewable deliverable

Source–field map and action; conservation checks for different velocities; conditions deriving the slow-source coupling; recovery of the common-transverse true interaction law.

Maxwell Effective Limit and Source Extension

• PDE

Current state

Free Maxwell equations are derived given the quadratic action, transverse constraint and matching. Sourced variation also closes after an effective source coupling is chosen.

Reviewable deliverable

Conditions of free-sector equivalence; source-coupling derivation; gauge, continuity and positive-energy checks; a definite beyond-domain correction or explicitly undetermined parameter.

High-γ Discriminator

• Accelerator physics
• Metrology

Current state

The special-case true force and standard laboratory total force scale differently, while the coordinate generalized force matches numerically. Published fast electro-optic sampling offers a case study; this site has no ASD fit.

Reviewable deliverable

Two predictions for the same measurand; raw data and response function; parameter sensitivity, residuals and noise budget; an explicit discrimination or degeneracy conclusion.

Experimental sequence: P3

Longitudinal–Transverse Coupling

• PDE

Current state

The manuscript supplies a rotational scalar cubic coupling, mutual response terms and a locally bounded quartic completion. These remain candidate constitutive choices.

Reviewable deliverable

A complete candidate action and equations; dimensional and conservation checks; boundedness and stability spectra; a quantitative solution connecting density and transverse structure.

Unified Longitudinal–Transverse Dynamics

• PDE

Current state

The local two-field parent action, both variations, reciprocal sources and energy-square completion are established. The manuscript also gives an independent frame-stretch extension for the gravitational far field, the coupled vacuum spectrum and an analytic radius for the scale model. The task is joint closure of these existing ingredients, not finding an entirely unwritten master equation.

Reviewable deliverable

Deliver the full variation, conserved quantities, vacuum spectrum and parameter domain of one explicit truncation; map it to the static far field, stable localization and accompanying-field envelope, recording incompatible conditions.

Equal Propagation Speed Condition

• PDE
• Numerical physics

Current state

The common vacuum speed is currently effective constitutive matching. Ordered-amplitude feedback in the dual-field candidate can shift the longitudinal low-k speed while leaving the transverse branch at the bare speed.

Reviewable deliverable

Necessary/sufficient conditions for $c_L=c_T=c$, a stable parameter domain and protection mechanism; otherwise a calculable deviation and its validity scale.

Stable Nonlinear Topology

• PDE
• Topology

Current state

Competition between positive second- and fourth-gradient energies and a nonnegative volume potential gives a unique positive stationary R_* with positive radial second derivative. The fourth-order mechanism resisting collapse is analytic. The scale parameters of Chapters 4 and 5 are reciprocal, so powers must be compared using their definitions.

Reviewable deliverable

First reproduce the analytic radius and A_0→0 limit, then deliver a field solution and nonradial spectrum with equation residuals and boundary/grid convergence; state exactly which perturbations beyond radial curvature were tested.

Continuum-to-Microscopic Correspondence

• Numerical physics
• PDE

Current state

The equal-connection FCC scalar model has a full-wave-number cosine dispersion, second moment and long-wave expansion. Continuous-time lattice propagation, the full multicomponent field and feedback-renormalized speeds are different checks. This review finds that Eq. (5.1.11), its following half-angle form and fourth-order expansion cannot all be identical with their printed coefficients; the FCC page records the specific difference.

Reviewable deliverable

Deliver a reproducible neighbour table, dynamical matrix, inter-equation coefficient check and reviewable correction options; only then provide coefficient-dependent dispersion plots, domains and directional experimental response.

Longitudinal-Wave Detection

• Metrology

Current state

A sourced longitudinal wave equation and flux are available, but no confirmed free longitudinal spatial-wave detection is included. Static gravity, comoving structure and neutrino candidates remain distinct.

Reviewable deliverable

An experimental proposal with a source–propagation–receiver transfer function, noise budget, reference-cancellation test and analysis rule stating what would distinguish or constrain the model.

Source Coupling

• PDE

Current state

With smooth all-space fields and zero far boundary, the local $sF$ candidate gives density supported with the core. Independent stretch admits a $1/r$ far field, but its source functional has not been derived from a stable matter core.

Reviewable deliverable

A complete solution chain from stable matter core to gravitational far field, computing energy, active/passive gravitational mass and inertia from the same solution with independently specified coefficients.

Accompanying-Field Source Equation

• PDE
• Quantum foundations

Current state

Mismatch sources, weighted projection, retarded solutions and two-dimensional responses are available; connect them to a finite core and actual source spectrum from one action.

Reviewable deliverable

A specified core and channel source, spectrum, boundary and initial data, convergence, residuals and energy flux with explicit parameter provenance.

Phase–Momentum Locking

• Quantum foundations
• PDE

Current state

The final manuscript adopts single-excitation cycle-action locking to connect the complete dressed state’s energy–momentum with accompanying-field phase. Given that matching and the gapped dispersion, group velocity, energy-centre motion and mechanical momentum have explicit relations. A source already absorbed into the dressed state and effective Hamiltonian must not be counted again as an independent drive.

Reviewable deliverable

Deliver independent integrals and phase mapping for a motion family, with source, surface terms, normalization and errors; test differentiation of the full dispersion for anisotropic or momentum-dependent propagation tensors.

Schrödinger Effective Limit

• PDE
• Numerical physics

Current state

Exact carrier substitution, its remainder and the leading slow envelope are available; study microscopic branch origins, coefficients and controlled initial–boundary errors.

Reviewable deliverable

A band-limited uniform-background comparison of second-order and envelope solutions, units, error norms, time domain and convergence, followed by one explicit variable-background problem.

Core–Field Coupling in Tunneling

• Quantum foundations
• Numerical physics

Current state

For a one-dimensional stationary rectangular barrier with identical propagation parameters on both sides, the exact envelope boundary solution is established: the hyperbolic transmission form equals its exponential rational form, and reflection plus transmission equals one. A variable-coefficient barrier has a divergence-form equation, amplitude transport and first-order WKB expression. These solve specified effective-envelope propagation problems.

Reviewable deliverable

Deliver a joint initial-boundary evolution for a specified barrier, including conservation residuals, grid/boundary convergence, the model basis of core trajectories and statistical initial conditions. Reproduce the exact rectangular result and threshold limit before reporting departures from the effective description.

Experimental Discriminator

• Quantum foundations
• Metrology
• Statistical inference

Current state

The seven entries are mainly recovery requirements; no unique apparatus-level difference has been calculated.

Reviewable deliverable

A complete Prediction → Observable → Instrument → Required Precision → Current Data → Falsification Criterion chain; report no discriminatory power when no reliable signal remains.