Chinese title: 结构场拟合函数优化与模型选择
English title: Fit-Function Optimization and Model Selection for Structural Fields
One-line positioning
Upgrade fit functions from “it fits” to “interpretable, comparable, reproducible, and transferable.”
Improve fitting stability (convergence, robustness, multi-start consistency)
Reduce parameter redundancy and non-identifiability (identifiability)
Establish unified model-selection standards (AIC/BIC/cross-validation/Bayesian evidence)
Function-family benchmarking: tanh / logistic / arctan / piecewise-smooth / physically constrained families
Regularization and constraints: monotonicity, boundary conditions, non-negativity of physical quantities, scale-invariance constraints
Error modeling: measurement error, systematic error, outlier handling (robust losses)
Reproducibility benchmark: same datasets, same initialization protocol, and standardized outputs (R²/RMSE/residual spectra)
Fit-function benchmark report (tables + figures)
Open-source scripts and a unified interface (CLI + config)
“Recommended function families” with applicability domains (which objects suit which functions)
On representative datasets, the selected best family outperforms the baseline in RMSE, residual structure, and parameter stability
Multi-start optimization converges to the same optimum with a materially higher rate (e.g., >90%)
Chinese title: 跨尺度物理系统拟合与两常数一致性检验
English title: Cross-Scale Fitting of Physical Systems and Two-Constant Consistency Tests
One-line positioning
Upgrade the “two constants” from “appearing in some objects” to a testable conclusion that remains valid across object classes, datasets, and methods.
Galaxy rotation curves; strong gravitational lensing systems; (as applicable) CMB cold-spot/void profiles
Future extensions: Solar System structure, cluster dynamics, and other systems
Unified data pipeline: sources, cleaning, units, uncertainty models, and versioning
Unified fitting standard: consistent optimizer, multi-start strategy, confidence intervals, and residual diagnostics
Constant validation:
Distribution stability (do different object classes share the same distribution?)
Significance and sensitivity of linear/power-law relations
Quantitative comparisons to control models (empirical profiles, commonly used ΛCDM-related profiles, etc.)
Two-Constants Validation Report v1
Summary tables: parameters, confidence intervals, goodness-of-fit, and model comparisons per object
Reproducibility package (data index + scripts + one-click figure/table generation)
Statistically supported consistency of the two constants across multiple object classes—together with explicit failure boundaries (where it does not hold and why)
Chinese title: 微观系统中两常数的可追踪性与对照检验
English title: Tracking the Two Constants in Microscopic Systems with Control Tests
One-line positioning
Extend the “two constants” from astrophysical systems into microscopic/high-energy domains—while prioritizing controls and falsifiable predictions, avoiding purely post hoc fitting.
First, define the dimensionless invariants corresponding to the two constants and specify the observable mappings
Then, test whether consistent scaling behavior emerges in public datasets
Must include standard-model / mainstream-theory control fits and information-criterion comparisons
Public high-energy scattering cross sections, spectra, and structure-function datasets (e.g., CMS, HERA, LEP/OPAL public tables)
Optional extensions: cosmic-ray spectra, astroparticle statistics, etc., depending on the mapping you establish
Micro-domain Tracking Note v1 (methods and negative results published as first-class outputs)
A unified control framework: same metrics, same model-selection workflow, and consistent uncertainty propagation
In at least one microscopic domain, the constant mapping yields ex ante predictions (holdout or future data) that pass testing; or, alternatively, a clearly documented “non-validity boundary”
Chinese title: 对偶张量不变性原理：公理化、推导与可检验推论
English title: Dual Tensor Invariance Principle: Axiomatization, Derivation, and Testable Implications
One-line positioning
Upgrade the core theory from explanatory narrative to a reviewable mathematical structure with falsifiable implications.
Axiomatic formulation: define objects, transformation groups, conserved quantities/invariants, domains of validity, and boundary conditions
Derivation chain: from invariance → observable relations → necessary/sufficient conditions under which the two constants emerge (prefer explicit propositions)
Connection to established theory: symmetry–conservation links (Noether-style structure as a reference point, while keeping your framework primary)
Testable implications: list at least 3–5 observable predictions spanning astrophysical and microscopic directions
Principle Paper v1 (a submission-ready theoretical-paper framework)
Formal notation glossary; theorem/proposition list; proof sketches; and a versioned review log
Prediction Table: each implication mapped to data sources and test protocols
A peer-reviewable formal text (definitions → propositions → proofs/derivations → implications)
Implications can be independently tested and replicated using public data
外太阳系速度曲线平坦性检验与对照研究（MEST-TPC）
Outer Solar System Velocity-Profile Flattening: Tests & Controls (MEST-TPC)
中文：用统一口径的观测约束轨道数据，检验外太阳系是否存在超出标准引力模型的系统性“平坦化残差”，并用对照模型区分物理效应与数据/选择偏差。
English: Using uniformly defined, observation-constrained orbital data, we test whether the outer Solar System exhibits systematic “flattening residuals” beyond standard gravitational models, and use controls to separate physics from selection and data-definition artifacts.
公众可理解：速度曲线“变平”是直观信号，容易解释给非专业受众。
科学可检验：可直接给出“成立/不成立/证据不足”的结论与失败边界。
与总假设对接：在“质能—时空系统”框架下，若存在一致残差，可作为“时空结构/暗部门效应”的候选证据链之一；若不存在，也能形成强有力的约束（同样有价值）。
我们不以“证明暗物质存在”为预设结论；我们以“可证伪检验 + 显式对照 + 可复现流程”为核心产出。
Unified Orbit-Velocity Dataset v1：统一历元、统一口径（a/q/Q/瞬时 r）、含误差与来源索引
Flattening Test Report v1：三种平坦性定义的统计检验 + 控制组结论
Controls & Disconfirmation Table v1：哪些结果意味着“只是选择效应/口径混用”，哪些结果才支持“额外项”
Join as Collaborator：共同定义指标、检验设计、统计方法与失败边界
Data Contributor：提供公开数据链接、误差说明、或独立对照计算
Reviewer：审阅对照设计与复现包，确保结论可被独立复核
同上：/research/themes/orbits/outer-solar-system-flattening
外太阳系速度曲线平坦性检验与对照研究（MEST-TPC）
Outer Solar System Velocity-Profile Flattening: Tests & Controls (MEST-TPC)
中文
在统一口径下（同一历元、同一“半径/速度”定义），外太阳系天体的速度—半径关系可能呈现某种“平坦化特征”。该特征若存在，必须满足：
在显式对照模型（开普勒两体/多体标准模型 + 观测选择效应）下仍不能被解释；
可被表述为稳定的统计残差结构（例如 Δv(r)\Delta v(r)Δv(r) 的近常数项或特定尺度拐点）；
与行星星历/动力学约束在量级上相容。
English
Under a unified definition (same epoch and consistent radius/velocity conventions), outer Solar System objects may exhibit an apparent “flattening” in velocity–radius behavior. If real, it must: (1) persist after explicit controls (Keplerian/N-body baselines plus selection effects), (2) appear as a stable statistical residual structure (e.g., near-constant Δv(r)\Delta v(r)Δv(r) or a turning-point signature), and (3) remain compatible in magnitude with planetary ephemeris and dynamical constraints.
我们同时检验三种“平坦性定义”，避免概念混淆：
定义：圆轨道等效速度 vc(r)v_c(r)vc(r) 在某区间是否趋于常数
数据口径：用统一的 rrr 定义（瞬时距离或半长轴 a）与统一历元
定义：不同天体的近日点速度 v(q)v(q)v(q) 是否在某范围异常聚集
注意：该现象可能由 qqq 分布聚集与发现偏置造成，必须做控制组
定义：Δv(r)=vobs−vbaseline\Delta v(r)=v_{\text{obs}}-v_{\text{baseline}}Δv(r)=vobs−vbaseline 是否存在系统性近常数项或拐点结构
优势：直接检验“标准模型缺失项”，最容易形成可发表的“约束/否证结论”
至少三层对照并行运行：
Baseline dynamics
两体开普勒基线（太阳主导）
多体/N-body 基线（太阳 + 主要行星扰动；或用公开星历/简化扰动模型）
Definition controls（口径对照）
半径采用 aaa、瞬时 rrr、近日点 qqq、远日点 QQQ 的对照比较
速度采用圆轨道等效、瞬时速度模、近日点/远日点速度的对照比较
目的：验证“平坦性是否由口径混用造成”
Selection-bias controls（选择效应对照）
以“可探测性/发现概率”构造加权或截断样本
置换检验/随机化检验（null models）
目的：排除“近日点更易被发现”的偏差导致的假聚集
D1 — Unified Orbit-Velocity Dataset v1
统一历元（epoch）、统一坐标系说明
每个对象：状态矢量（位置/速度）、轨道要素（a,e,i,Ω,ω,M）、误差/来源索引
数据字典 + 下载/生成脚本 + 版本号
D2 — Flattening Test Report v1
三种平坦性定义的结果（A/B/C）
每种定义给出：统计显著性、敏感性（对口径/样本/误差假设）、控制组结论
输出：图（log-log 关系、残差曲线、相图）+ 表（参数约束）
D3 — Controls & Disconfirmation Table v1
明确写出：
哪些结果意味着“仅是口径混用/选择效应”
哪些结果才支持“标准模型之外的缺失项”
对缺失项的量级上限与不确定性
本项目将把以下情况视为对“真实平坦化效应”的否证或大幅降级：
口径敏感：平坦性只在混用 a/q/Qa/q/Qa/q/Q 时出现，统一口径后消失
选择效应可解释：引入发现偏置控制后，所谓平坦/聚集不再显著
残差不稳定：Δv(r)\Delta v(r)Δv(r) 对样本划分、误差模型、时间窗高度不稳定
量级冲突：若拟合的额外项所需质量/势场量级与已知动力学约束明显冲突（即使统计上“拟合变好”也不接受）
Q1（定义与数据管线）
明确三种平坦性定义与统计指标
建立数据抓取/生成管线（统一 epoch、格式与字典）
生成 Dataset v1-alpha（小样本）
Q2（首次检验与口径对照）
完成 A/B/C 三类检验的 v1 结果
完成口径对照（a/q/Q 与速度口径切换）并报告差异
Q3（选择效应与稳健性）
引入发现偏置控制、置换检验、敏感性分析
输出残差平坦性（C）的稳健约束（或否证结论）
Q4（年度报告与复现包）
发布 Flattening Test Report v1 + Controls & Disconfirmation Table v1
打包复现包（版本化脚本、一键出图、数据索引）
中文
“时空是暗物质/暗部门有效表征”在本项目中仅作为候选解释之一。我们首先完成对照与否证框架：若平坦化效应不可复现或可被对照解释，则形成对该假说的约束；若出现稳健残差结构，则进入下一阶段：量级约束、跨数据源复核与与透镜/行星轨道项目的一致性检验。
English
The working hypothesis “spacetime structure as a dominant manifestation of the dark sector” is treated as a candidate interpretation only. We first establish falsification and control frameworks: if flattening is not reproducible or is explained by controls, we derive constraints; if a robust residual structure emerges, we proceed to magnitude bounds, cross-dataset replication, and consistency checks with lensing and planetary-orbit projects.
Sponsorship Proposal (Short Form)
1. Project Title and Positioning
Project Title: Structural-Field Fitting and Two-Constant Validation: Reproducible Methods and Falsifiable Conclusions (2026 Research Themes)
Applicant: AEEA Research Team (Avoid Earth Extinction Association)
Core Engine: MEST-AI and MEST-TPC (Mass–Energy–Spacetime Turning-Point Tensor Computation)
Mission Statement: To raise structural-field fitting from “it fits” to “interpretable, comparable, reproducible, and transferable,” and to test the “two constants” as a cross-object, cross-dataset, cross-method hypothesis—explicitly documenting both validation evidence and failure boundaries.

2. Why This Is Worth Supporting
Cross-scale modeling efforts often face recurring bottlenecks:
• Fit functions may match data yet remain non-interpretable and non-comparable across studies.
• Non-identifiability and parameter redundancy can create “apparent laws” that are difficult to falsify.
• Differences in datasets, uncertainty treatment, optimizers, and initialization strategies undermine reproducibility and lead to non-aligned conclusions.
This project addresses these gaps by delivering:
1. Standardized benchmarks (same data, same protocols, same metrics)
2. Formal model selection (AIC/BIC/cross-validation/Bayesian evidence)
3. Falsifiability-first outputs (negative results and failure boundaries are first-class deliverables)
4. Reproducibility packages (data indices, versioning, scripts, and one-click figure/table generation)

3. Research Themes and Deliverables
Theme 1: Fit-Function Optimization and Model Selection for Structural Fields
Goal: Improve fitting stability and interpretability, reduce redundancy and non-identifiability, and establish unified model-selection standards.
Primary deliverables:
• Fit-function benchmark report (tables + figures)
• Open-source scripts and a unified interface (CLI + config)
• “Recommended function families” and applicability guidance (object-to-function mapping)

Theme 2: Cross-Scale Fitting of Physical Systems and Two-Constant Consistency Tests
Goal: Upgrade the “two constants” from “appearing in some objects” to a testable conclusion that remains valid across object classes, datasets, and methods—or yields explicit failure boundaries.
Primary deliverables:
• Two-Constants Validation Report v1
• Summary tables: parameters, confidence intervals, goodness-of-fit, and control-model comparisons per object
• Reproducibility package (data index + scripts + one-click figure/table generation)

Theme 3: Tracking the Two Constants in Microscopic Systems with Control Tests
Goal: Extend the two-constant hypothesis into microscopic/high-energy public datasets with controls and ex ante predictions as the core—avoiding purely post hoc fitting.
Primary deliverables:
• Micro-domain Tracking Note v1 (methods and negative results published as first-class outputs)
• Unified control framework: consistent metrics, identical model-selection workflow, and uncertainty propagation

Theme 4: Dual Tensor Invariance Principle—Axiomatization, Derivation, and Testable Implications
Goal: Elevate the core theory from explanatory narrative to a reviewable mathematical structure with falsifiable implications.
Primary deliverables:
• Principle Paper v1 (a submission-ready theoretical-paper framework)
• Formal notation glossary; theorem/proposition list; proof sketches; and a versioned review log
• Prediction Table: each implication mapped to data sources and test protocols

4. 2026 Work Plan (Proposed Milestones)
Q1 — Standards and pipelines
• Finalize dataset and uncertainty conventions; define fitting protocols (optimizer, multi-start, output metrics)
• Theme 1: initial function-family comparisons; reproducibility interface (CLI) prototype
Q2 — Benchmarking and controls
• Theme 1: publish Benchmark v1 (stability, residual structure, parameter stability)
• Theme 2: begin systematic multi-class validation and compile midterm summary tables
Q3 — Cross-domain extension and ex ante testing
• Theme 2: complete cross-object consistency tests and sensitivity analyses
• Theme 3: complete at least one micro-domain mapping + control comparisons + holdout testing
Q4 — Annual deliverables and publication-grade outputs
• Two-Constants Validation Report v1 + reproducibility package
• Principle Paper v1 (formal text + implication table)
• Annual Methods & Integrity Report (including negative results and failure boundaries)

5. Budget Usage (High-Level)
Sponsorship support will primarily fund four categories:
1. Data curation and versioning: source indexing, unit/uncertainty standardization, archival publishing
2. Compute and engineering: multi-start optimization, cross-validation, model selection, batch pipelines
3. Review and integrity process: third-party review, reproducibility verification, and versioned documentation
4. Publication and dissemination: reproducibility package releases, figures/reports, public briefs/workshops
(If requested, we can provide a tiered budget with quarterly acceptance criteria and line items for compute, labor, and data-publication costs.)

6. Integrity, Compliance, and Research Standards
• Mandatory control models: all key claims must be benchmarked against controls that do not rely on our framework (empirical models, widely used profiles, etc.).
• Falsifiability-first: we will explicitly state what observations would refute each hypothesis or implication.
• Reproducible by design: reports will ship with data indices, version numbers, scripts, and full configuration settings.
• No over-claims: improved fits are not treated as proof of physical truth; decisions rely on information criteria, robustness, and controls.

7. Sponsor Value (Non-Equity, Research-Oriented Returns)
• Early access: quarterly progress briefs, annual reports, and reproducibility-package updates
• Transparent reviewability: access to protocols, control designs, version logs, and negative results
• Acknowledgment: sponsor recognition in public reports and publications (aligned with sponsor preference)
• Engagement option: sponsors may nominate a representative as a reviewer/observer for milestone reviews (without influencing conclusions)

8. Sponsorship Request
We invite sponsors to support the 2026 research themes and their public, reproducible deliverables through:
• Annual sponsorship: full coverage of Themes 1–4 and annual deliverables
• Directed sponsorship: focus on one theme (e.g., Theme 2 validation or Theme 4 formalization)
• In-kind support: compute credits, data services, or reproducibility-review support
Upon request, we can provide:
• A one-page sponsor brief (ultra-condensed)
• A tiered budget with quarterly deliverables and acceptance criteria
• Sample table of contents for public vs technical report editions
赞助申请报告（简要版）
1. 项目名称与定位
项目名称（中文）：结构场拟合与两常数验证：从可复现方法到可证伪结论（2026 研究主题集）
Project Title (EN): Structural-Field Fitting and Two-Constant Validation: Reproducible Methods and Falsifiable Conclusions (2026 Research Themes)
申请单位：AEEA Research Team（Avoid Earth Extinction Association）
研究引擎：MEST-AI 与 MEST-TPC（Mass–Energy–Spacetime Turning-Point Tensor Computation） 统一方法平台
核心价值：以“可复现、可对照、可证伪”为硬标准，将结构场拟合从“能拟合”升级为“可解释、可比较、可推广”，并对“两常数”给出跨对象、跨数据源、跨方法的一致性检验与失败边界。

2. 资助方为什么值得支持
当前跨尺度建模研究面临普遍问题：
• 拟合函数可拟合但不可解释，结果难以比较与复核；
• 参数不可辨识（identifiability）与过拟合造成“看似规律、难以证伪”；
• 不同研究在数据、误差、优化器与初始化策略上差异巨大，导致结论不可对齐。
本项目以方法学为主轴，明确提供：
1. 统一基准（Benchmark）：同数据、同协议、同指标；
2. 模型选择（Model Selection）：AIC/BIC/交叉验证/贝叶斯证据等标准化流程；
3. 可证伪输出：不仅给“成功案例”，也发布负结果与失败边界；
4. 可复现包：数据索引、版本号、脚本与一键出图，便于第三方复核。

3. 研究主题与产出（四大 Theme）
Theme 1：结构场拟合函数优化与模型选择
目标：提升拟合稳定性与可解释性，降低参数冗余与不可辨识性，建立统一模型选择标准。
主要产出：
• Fit-function benchmark 报告（表格 + 图）
• 开源脚本与统一接口（CLI + config）
• “推荐函数族”与适用域指南（对象—函数映射）
Theme 2：跨尺度物理系统拟合与两常数一致性检验
目标：将“两常数”从“部分对象出现”升级为**跨对象、跨数据源、跨方法仍成立（或明确不成立边界）**的可检验结论。
主要产出：
• Two-Constants Validation Report v1
• 汇总表：参数、置信区间、拟合优度、对照模型比较
• 可复现包（数据索引 + 脚本 + 一键生成图表）
Theme 3：微观系统对两常数的追踪研究（含对照检验）
目标：把两常数映射到微观/高能公开数据域，强调对照组与事前预测，避免纯后验拟合。
主要产出：
• Micro-domain Tracking Note v1（方法与负结果同样发布）
• 统一对照框架：同指标、同模型选择流程、同不确定性传播
Theme 4：对偶张量不变性原理的论证（公理化、推导、推论）
目标：把核心理论升级为可审阅的数学结构，产出可证伪推论与数据检验路线。
主要产出：
• Principle Paper v1（可投稿的理论论文框架）
• 符号表、命题/定理列表、证明草案与审阅记录
• Prediction Table（每条推论对接数据源与检验方法）

4. 2026 年工作计划（建议里程碑）
Q1：基准与管线成型
• 数据与误差口径统一；拟合协议（优化器、多起点、输出指标）定版
• Theme 1 函数族对比与约束机制初版；复现接口（CLI）雏形
Q2：系统化 benchmark 与对照框架
• Theme 1 发布第一版 benchmark（含稳定性、残差结构、参数稳定性）
• Theme 2 开始多类别对象批量验证，形成中期汇总表
Q3：跨域扩展与事前预测
• Theme 2 完成跨对象一致性检验与敏感性分析
• Theme 3 完成至少一个微观数据域的“映射定义 + 对照比较 + holdout 检验”
Q4：年度交付与可发布版本
• Two-Constants Validation Report v1 + 复现包
• Principle Paper v1（理论文本 + 推论表）
• 年度 Methods & Integrity Report（包括负结果与失败边界）

5. 预算使用方向（简要说明）
赞助资金将主要用于四类成本：
1. 数据整理与版本化：数据源索引、单位与误差模型规范、存档与可追溯发布
2. 算力与工程化：多起点拟合、交叉验证、模型选择与批处理管线
3. 研究与审阅机制：第三方审阅、复现验证、方法文档与审阅记录维护
4. 成果发布与传播：可复现包发布、图表与报告制作、公开简报/研讨会
（如赞助方需要，我们可提供分档预算与资源明细：算力、人员工时、数据发布成本等。）

6. 合规与学术诚信声明（重点）
• 对照模型强制：所有核心结论必须与不依赖本框架的对照模型比较（经验模型、主流剖面等）。
• 可证伪优先：报告中将明确列出“哪些观测会否定我们的假说/推论”。
• 可复现交付：数据索引、版本号、脚本与参数设置随报告发布；负结果与失败边界同等披露。
• 不做夸大承诺：不将“拟合更好”直接等同于“物理真实”，以信息准则、稳健性与对照为裁决标准。

7. 赞助方获得的回报（非股权、学术型回报）
• 优先获取：季度进展简报、年度报告、复现包更新
• 透明可审阅：方法定义、对照设计、版本记录与负结果同步披露
• 署名与致谢：公开报告与论文中的赞助致谢（按赞助等级与意愿）
• 参与机制：赞助方可指定代表作为 Reviewer/Observer 参与阶段评审（不干预结论）

8. 赞助请求（可填金额档位）
我们诚挚邀请赞助方支持 2026 年度研究主题集的推进。
可选支持方式：
• 年度赞助：覆盖全主题（Theme 1–4）与年度交付物
• 定向赞助：指定某一主题（如 Theme 2 两常数验证 或 Theme 4 原理公理化）
• 资源赞助：算力/数据服务/复现审阅支持
如需，我们可以提供：
• 1 页 Sponsor Deck（更短版）
• 分档预算与具体交付清单（按季度验收）
• 公开版与技术版报告样例目录