Anchor Collapse Model (ACM)

The Rigid Holographic Trunk for Galactic Dynamics

One rigid baseline. No galaxy-by-galaxy rescue. The evidence comes first.

一条刚性基线，不做逐星系营救，先把证据摆出来。

Paper | 论文: Preprint available on Zenodo (10.5281/zenodo.19163963)

A clean public release of the retained ACM galaxy trunk.
一个面向公开发布的 ACM 星系主干版本。

Primary Evidence | 首要证据

This figure is the first thing a reader should see, because it is the core vidence of Paper I. Under one rigid ACM baseline, the retained trunk outperforms fixed-$a_0$ MOND on both the matched SPARC comparison set and the deterministic holdout subset. This is the claim in its cleanest form: the same function remains effective without galaxy-by-galaxy rescue knobs, hidden interpolation switches, or post hoc local fixes.

这张图就是 Paper I 最核心的证据：在同一个刚性 ACM 基准下，保留下来的主干 同时在匹配 SPARC 样本和确定性 holdout 子样本上优于固定 $a_0$ 的 MOND。这 也是 Paper I 最核心的主张：真正有效的不是“多几个自由度”，而是同一个函数 在不依赖逐星系营救、不引入隐藏插值开关、也不诉诸事后局部修补的前提下依然 成立。

Quick Links | 快速导航

Philosophy · Performance · Quick Start · Manuscript · Origin · Follow

At a Glance | 一眼看懂

Item	English	中文
Scope	Public release of the retained ACM galaxy trunk	保留下来的 ACM 星系主干公开版本
Claim	A rigid holographic alternative to threshold-style galaxy dynamics	一个刚性的、全息背景响应驱动的星系动力学框架
Evidence	23.76 vs 39.88, holdout 9 : 3, slope ≈ -0.035	23.76 vs 39.88，留存测试 9 : 3，斜率 ≈ -0.035
Output	Code, figures, manuscript, and minimal SPARC inputs	代码、图表、论文与最小 SPARC 数据

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Philosophy | Core Philosophy | 核心哲学

Traditional galaxy-dynamics frameworks often preserve flexibility by repairing individual systems: local mass-to-light adjustments, halo-profile freedom, or threshold-style interpolation between regimes. The retained ACM trunk rejects that strategy. It asks a different question: if a cosmologically anchored background floor is real, how much of it remains visible inside a given baryonic environment?

传统的星系动力学框架，往往依赖对单个星系做局部修补来保住拟合能力，例如恒星 质光比调整、暗晕轮廓自由度，或在不同区间之间切换经验插值函数。ACM 主干拒 绝这种思路。它追问的是另一件事：如果一个被宇宙学锚定的背景底座确实存在， 那么在不同的重子环境中，它究竟还能显现出多少？

In this release, the ACM trunk keeps a fixed global constant family and derives galactic dynamics from a baryonic transmission chain. The model does not rewrite the Newtonian baryonic term. Instead, it treats the observed departure from that term as the visible share of a screened holographic background response.

在这个发布版本中，ACM 主干保留一组固定的全局常数，并通过重子传输链来推导 星系动力学。模型并不改写牛顿重子项，而是把观测到的偏离解释为：一个被局部 结构部分屏蔽的全息背景响应，重新进入可见动力学之后所留下的可见份额。

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Pure Release | 为什么这个版本保持纯净

• Locked baryons: stellar population inputs remain tied to the SPARC-recommended values rather than being retuned galaxy by galaxy.

• Linear superposition: ACM uses an additive background compensatory term instead of a hand-switched interpolation function.

• Geometric discipline: residual control enters through structural and confidence filtering, not through object-specific repair knobs.

• 锁定重子输入：恒星群体输入遵循 SPARC 推荐标定，不对每颗星系重新调整 质光比。

• 线性叠加结构：ACM 使用背景代偿项的加法结构，而不是手动切换经验插值 函数。

• 几何纪律：残差控制来自结构与几何置信度过滤，而不是按对象修补的拟合 旋钮。

This repository is intentionally narrow. It exposes the retained trunk only, not the full research archive.

这也是为什么本仓库刻意保持精简：它只公开保留下来的主干，不公开完整研究过 程档案。

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Performance & Evidence | 结果与证据

Headline Results | 核心战果

• Global advantage: median per-point residual improves from 39.88 (fixed-a0 MOND) to 23.76 (ACM) on the matched SPARC sample.

• Predictive power: on the deterministic 12-galaxy holdout set, ACM wins by 9 : 3.

• Density neutrality: the residual trend with effective surface brightness is nearly flat, with ACM slope ≈ -0.035.

• 全局优势：在匹配 SPARC 样本上，ACM 的每点残差中位值从固定 a0 的 MOND 的 39.88 降至 23.76。

• 预测能力：在 12 颗未参与锚定的确定性 holdout 样本中，ACM 以 9 : 3 胜出。

• 密度中性：残差相对于有效面亮度的趋势几乎为零，ACM 的斜率约为 -0.035。

Evidence Map | 证据地图

• Figure 1: headline statistical dominance across matched sample and holdout

• Figure 3: density neutrality and environmental decoding

• Figure 2: RAR consistency under the retained ACM trunk

• 图 1：匹配样本与留存测试上的统计主背书

• 图 3：密度中性与环境感知能力

• 图 2：保留主干下的 RAR 一致性

Figure 1 | 图 1

Matched sample and holdout comparison

匹配样本与留存测试对比

This figure provides the statistical backbone of the current paper: the retained ACM trunk outperforms fixed-a0 MOND both on the matched SPARC comparison sample and on the deterministic holdout subset.

这张图是当前论文的统计主背书：保留的 ACM 主干不仅在匹配 SPARC 样本上优于 固定 a0 的 MOND，在确定性的留存子样本上也保持了优势。

Figure 3 | 图 3

Residual neutrality against effective surface brightness

残差对有效面亮度的中性

This figure is the environmental test. ACM residuals remain close to neutral across effective surface brightness, while fixed-a0 MOND retains a stronger systematic density-linked offset.

这张图是环境感知测试。ACM 的残差在有效面亮度方向上保持近乎中性，而固定 a0 的 MOND 仍保留更明显的密度相关系统偏移。

Figure 2 | 图 2

RAR consistency under the retained ACM trunk

保留主干下的 RAR 一致性

The RAR figure shows that ACM preserves the main observed phenomenology without falling back on a hand-switched low-acceleration law. The low-acceleration band emerges through continuous transmission and additive background response.

RAR 图展示的是：ACM 在不诉诸手工切换的低加速度经验律的前提下，仍然保住了 主现象学结构。低加速度区间的行为来自连续的传输链与背景响应加法结构。

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Repo Layout | 仓库结构

anchor-collapse-model/
  analyze_acm_vs_mond.py
  analyze_lh_hacc_blind_holdout.py
  config.py
  requirements.txt
  data/
    sparc/
  src/
  figures/
  main.tex
  references.bib
  build.bat
  make_figures.py

• analyze_acm_vs_mond.py: matched SPARC comparison against fixed-a0 MOND

• analyze_lh_hacc_blind_holdout.py: deterministic holdout comparison

• src/: retained ACM trunk modules needed for the current paper

• data/sparc/: minimal SPARC files required for reproduction

• main.tex, references.bib, build.bat, make_figures.py: manuscript and reproduction entrypoints

• figures/: cited manuscript figures

• analyze_acm_vs_mond.py：与固定 a0 的 MOND 进行匹配 SPARC 样本对比

• analyze_lh_hacc_blind_holdout.py：确定性 holdout 对比脚本

• src/：当前论文所需的 ACM 主干代码模块

• data/sparc/：复现实验所需的最小 SPARC 数据

• main.tex、references.bib、build.bat、make_figures.py：论文与复现 入口文件

• figures/：论文正式引用图表

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Quick Start | 快速开始

Install the dependencies:

安装依赖：

pip install -r requirements.txt

Run the full comparison chain:

运行完整对比链：

python analyze_acm_vs_mond.py
python analyze_lh_hacc_blind_holdout.py
python make_figures.py

Run the matched-sample comparison:

运行匹配样本对比：

python analyze_acm_vs_mond.py

Run the deterministic holdout test:

运行确定性 holdout 测试：

python analyze_lh_hacc_blind_holdout.py

Generate the three manuscript figures:

生成当前论文的三张主图：

python make_figures.py

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Reproducing the Manuscript | 复现当前论文

The current manuscript is included directly in this repository:

本仓库直接包含当前论文的源文件：

• main.tex
• references.bib
• main.pdf

On Windows, the manuscript can be rebuilt with:

在 Windows 环境中，可以通过以下方式重新编译论文：

build.bat

The figure-generation script will automatically regenerate the required matched sample and holdout summaries if the corresponding CSV outputs are missing.

如果配套的 CSV 输出缺失，出图脚本会自动先补跑匹配样本与 holdout 的分析结 果，再生成论文主图。

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Origin | Origin of the Idea | 思路缘起

This framework did not begin as another local repair to existing galaxy-dynamics models. It began from a different question: can one build a rigid structure that avoids galaxy-by-galaxy tuning and remains conceptually consistent across scales? The idea grew out of long reflection on interference, black holes, galactic structure, and the role of the speed of light, combined with an engineering and information-theoretic perspective shaped by large-scale systems and AI. The present ACM release is the retained trunk that emerged from that process.

这个框架的出发点，并不是在已有星系动力学模型上继续做局部修补，而是反过来 追问：是否存在一种既不依赖逐星系调参、又能在不同尺度上保持概念一致性的刚 性结构？这一思路来自长期对干涉、黑洞、星系结构、光速角色等现象的跨尺度思 考，也受到工程系统、信息论与 AI 方法论的启发。当前这个 ACM 发布版本，就是 这种长期推敲之后保留下来的主干。

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Scope | 当前范围

This repository is deliberately limited to the retained galaxy trunk presented in the current paper. It does not attempt to publish the full research archive, the cluster-scale branch, lensing-side extensions, or the cosmology-side closure program.

本仓库刻意只覆盖当前论文中保留下来的星系主干。它不试图同时公开完整研 究档案、星系团分支、透镜扩展或宇宙学闭环程序。

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Data Source | 数据来源

The galaxy data used here are based on the publicly available SPARC database. This release includes the minimum SPARC files required to reproduce the current results in this repository layout.

本仓库使用的星系数据基于公开可得的 SPARC 数据库。当前发布版仅包含复现 当前论文所需的最小 SPARC 文件集合。

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Citation | 引用方式

If you use this repository, please cite the accompanying manuscript and acknowledge the SPARC data source.

如果你使用本仓库，请引用配套论文，并注明 SPARC 数据来源。

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Follow | 关注与联系

For updates on ACM, manuscript releases, and related notes:

• Bluesky: @zero-compensation.bsky.social

获取 ACM 更新、论文发布与相关说明：

• Bluesky：@zero-compensation.bsky.social