Mechanism–Direction Decomposition in CMB Acoustic Phase Deformation — W_CMB v10.0 Package

This deposit advances the WCMB (Wγ) acoustic phase diagnostic series from v6.0 to v10.0. The v6.0 breakthrough — raw deformation-weighted σraw achieving four-family separation with S(M↔E) = 8.41 — established that unnormalized spread recovers information lost by CDF compression. The present v10.0 asks the complementary question: what role does the sign of phase deformation play? Background: the compression problem The v4.0–v6.0 series showed that Wγ possesses an internal geometry whose family boundaries encode perturbation mechanism (E: expansion/free-streaming via Neff and ωcdm; A: acoustic/baryon loading via ωb; P: primordial/spectral tilt via ns; M: neutrino mass via Σmν). However, the v8.0-lite analysis identified a limitation: coordinate compression via absolute-value accumulation destroys differences visible to Fisher information. This raised the question of whether retaining the sign of ΔW(ℓ) would restore the lost discrimination. Discovery narrative v9.0: Signed cumulative does not improve inter-family discrimination. Sixteen perturbations across four parameters (Nur ±0.2/±0.5, ωcdm ±0.005/±0.010, ωb ±0.0005/±0.0010, ns ±0.01/±0.02) were computed using CLASS with Planck 2018 fiducial cosmology. The unsigned kernel ℓ50 separates E/A/P families with S ≈ 99; IQR achieves S ≈ 16; Bowley skewness achieves S ≈ 64. In contrast, the best signed indicator (number of sign changes) achieves only S ≈ 2.3. All other signed indicators — positive fraction, signed centroid, signed balance, net signed integral, spectral slope — fall below S = 1. v9.1: The sign encodes a different quantity. The signed information is not noise — it encodes perturbation direction (+δ vs −δ), not perturbation mechanism. Within single-parameter families, the positive fraction clearly separates +δ from −δ: Family A shows 0.414 (increase) vs 0.581 (decrease); Family P shows 0.592 vs 0.408. Family E shows no separation (0.500 vs 0.501) due to internal heterogeneity between Nur-type and ωcdm-type perturbations. v10.0: Mechanism–direction decomposition ★ The WCMB response decomposes into two approximately orthogonal coordinates: Mechanism axis (unsigned kernel shape): identifies which physical process deformed the phase. Separation ratio S ≈ 99 on ℓ50. Direction axis (signed structure): encodes whether the cosmological parameter increased or decreased. Pearson correlation with mechanism axis: r = −0.008 (p = 0.975). Absolute-value compression |ΔW| preserves the mechanism axis while erasing the direction axis. This is not information destruction — it is dimensional reduction along a physically interpretable coordinate. Spine (v3.0 → v10.0) v3.0: W_CMB is established v4.0: Internal geometry is family-structured (E/A/P; within-family RMS ≤ 0.018, between-family RMS 0.054–0.091) v5.0: That geometry is discriminative (ARI = 1.000, 3 families) v5.0 v6.0/v6.1: Σmν is E-adjacent in normalized kernel v5.0 v8.0-lite: E-adjacency is compression, not information absence v9.0: Signed cumulative ≡ magnitude after normalization v9.1: Sign encodes direction, not mechanism v10.0: Mechanism–direction decomposition — unsigned = mechanism (S ≈ 99), signed = direction (r ≈ −0.008) ★ Physical interpretation The decomposition principle has a natural physical reading. The shape of acoustic phase deformation — where in ℓ-space the deformation concentrates — is determined by the physical mechanism (free-streaming damps small scales; baryon loading shifts acoustic peaks; spectral tilt redistributes primordial power). This shape is invariant to perturbation sign. The polarity — whether the deformation is positive or negative at a given ℓ — depends on whether the parameter was increased or decreased. These two aspects of deformation are logically independent, and the data confirm they are statistically independent (r ≈ 0). Next steps The weak direction separation in Family E likely reflects internal heterogeneity between Nur-type and ωcdm-type perturbations, whose signed deformations partially cancel in aggregate statistics. A natural next step is to split Family E into parameter-coherent subfamilies and re-evaluate the direction axis. Contents Research note (v10.0 manuscript, Markdown) Two computation scripts (Python): v9.0 signed-phase test, v10.0 decomposition analysis Numerical results (JSON) and diagnostic figures (PNG) for each step本数据集将WCMB（Wγ）声学相位诊断工具包从v6.0升级至v10.0。v6.0版本的突破性成果——原始形变加权σ_raw（σ_raw）实现四族分离，S(M↔E)=8.41——证实未归一化展宽能够恢复CDF压缩所丢失的信息。本v10.0版本则提出互补性问题：相位形变的符号发挥着何种作用？ 背景：压缩问题 v4.0至v6.0系列研究表明，Wγ具备内在几何结构，其族边界编码了微扰机制（E类：通过Neff与ωcdm实现的膨胀/自由流；A类：通过ωb实现的声学/重子加载；P类：通过ns实现的原初/谱倾斜；M类：通过Σmν实现的中微子质量）。但v8.0-lite分析发现一处局限：通过绝对值累加实现的坐标压缩会破坏费舍尔信息（Fisher information）可观测的差异，由此提出问题：保留ΔW(ℓ)的符号是否能够恢复丢失的区分能力？ 发现历程 v9.0：带符号累积无法提升族间区分能力。基于普朗克2018标准宇宙学（Planck 2018 fiducial cosmology），使用CLASS软件计算了4个参数下的16组微扰（Nur：±0.2/±0.5，ωcdm：±0.005/±0.010，ωb：±0.0005/±0.0010，ns：±0.01/±0.02）。无符号核ℓ50可区分E/A/P族，区分度S≈99；四分位距（IQR）的S≈16；鲍利偏度（Bowley skewness）的S≈64。与之相比，最优带符号指标（符号变化次数）的S仅约2.3，其余所有带符号指标——正样本占比、带符号质心、带符号平衡度、净带符号积分、谱斜率——的S值均低于1。 v9.1：符号编码的是另一类物理量。带符号信息并非噪声，它编码的是微扰方向（+δ与−δ），而非微扰机制。在单参数族内，正样本占比可清晰区分+δ与−δ：A族的正样本占比为0.414（参数上调）与0.581（参数下调）；P族为0.592与0.408。E族则无区分效果（0.500与0.501），这源于Nur型与ωcdm型微扰间的内在异质性。 v10.0：机制-方向分解 ★ WCMB的响应可分解为两个近似正交的坐标： - 机制轴（无符号核形状）：用于识别使相位发生形变的物理过程。在ℓ50下的区分度S≈99。 - 方向轴（带符号结构）：用于编码宇宙学参数是上调还是下调。与机制轴的皮尔逊相关系数（Pearson correlation）r=−0.008，p=0.975。 绝对值压缩|ΔW|会保留机制轴，但抹去方向轴。这并非信息丢失，而是沿物理可解释坐标进行的维度约简。 发展脉络（v3.0 → v10.0） v3.0：确立W_CMB v4.0：内在几何呈现族结构（E/A/P；族内均方根≤0.018，族间均方根0.054~0.091） v5.0：该几何结构具备区分能力（调整兰德指数（ARI）=1.000，3个族） v5.0与v6.0/v6.1：在归一化核中，Σmν与E族相邻 v5.0与v8.0-lite：E族相邻性是压缩导致的，而非信息缺失 v9.0：带符号累积等价于归一化后的幅值 v9.1：符号编码的是方向，而非机制 v10.0：机制-方向分解——无符号项对应机制（S≈99），带符号项对应方向（r≈−0.008）★ 物理解释 该分解原则具备自然的物理解读。声学相位形变的形状——即形变在ℓ空间中的集中位置——由物理机制决定（自由流会阻尼小尺度；重子加载会平移声学峰；谱倾斜会重新分布原初功率谱）。该形状与微扰符号无关。而极性——即给定ℓ处形变的正负——则取决于参数是上调还是下调。形变的这两个属性在逻辑上相互独立，数据也证实二者在统计上相互独立（r≈0）。 后续研究方向 E族中较弱的方向区分能力，大概率源于Nur型与ωcdm型微扰间的内在异质性，二者的带符号形变在总体统计中发生了部分抵消。自然的后续研究方向是将E族拆分为参数相干的子族，并重估方向轴的区分能力。 数据集内容 1. 研究笔记（v10.0手稿，Markdown格式） 2. 两份Python计算脚本：v9.0带符号相位测试脚本、v10.0分解分析脚本 3. 各步骤的数值结果（JSON格式）与诊断图（PNG格式）