修改方法部分
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龙澳
@@ -179,7 +179,7 @@ After the construction of the hyperbolic spatial hypergraph, the next step is to
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1) Spatial Intent Extraction and Hyperedge Retrieval: Given a user query $q$, we first employ the LLM to extract spatial intent, including target entities, spatial constraints (footprint, region), temporal constraints ($L_s$ range, Sol range), and resolution preferences. These are denoted as query elements $\mathcal{K}_q$.
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For each topic entity $e_s \in \mathcal{E}_q$ extracted from the query, we retrieve its incident spatial observation hyperedges $\mathcal{F}_{e_s} = \{f_{spa}^n \in \mathcal{F}_{spa} : e_s \in f_{spa}^n\}$ and derive pseudo-binary triples $(e_h, f_{spa}^n, e_t)$ for pairwise reasoning, following the approach of HyperRAG [18]:
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For each topic entity $e_s \in \mathcal{E}_q$ extracted from the query, we retrieve its incident spatial observation hyperedges $\mathcal{F}_{e_s} = \{f_{spa}^n \in \mathcal{F}_{spa} : e_s \in f_{spa}^n\}$ and derive pseudo-binary triples $(e_h, f_{spa}^n, e_t)$ for pairwise reasoning, following the approach of HyperRAG \cite{luo25hyperrag}:
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\begin{equation}
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\label{equ:Spatial Intent Extraction and Hyperedge Retrieval}
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@@ -187,12 +187,11 @@ For each topic entity $e_s \in \mathcal{E}_q$ extracted from the query, we retri
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\end{equation}
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2) Hyperbolic Spatial Encoding and Plausibility Scoring: For each candidate triple, we compute a spatiotemporal encoding that fuses semantic, structural, and physical-spatial signals:
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\begin{equation}
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\label{equ:spatiotemporal encoding}
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\mathbf{x} = \left[\varphi(q) \| \varphi(e_h) \| \varphi(f_{spa}^n) \| \varphi(e_t) \| \delta(e_h, f_{spa}^n, e_t) \| \psi_{geo}(e_h, e_t)\right],
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\end{equation}
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where $\varphi$ denotes a text embedding model, $\delta$ denotes a structural proximity encoding adapted from SubGraphRAG [19] to operate on hyperedges, and $\psi_{geo}$ is the hyperbolic spatial encoding defined as:
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where $\varphi$ denotes a text embedding model, $\delta$ denotes a structural proximity encoding adapted from SubGraphRAG \cite{Li25SubGraphRAG} to operate on hyperedges, and $\psi_{geo}$ is the hyperbolic spatial encoding defined as:
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\begin{equation}
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\label{equ:hyperbolic spatial encoding}
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\psi_{geo}(e_h, e_t) = \left[d_K\left(\Phi(e_h), \Phi(e_t)\right), \; \Delta r(e_h, e_t), \; \cos\theta_{bearing}\right],
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@@ -203,23 +202,25 @@ where $d_K$ is the geodesic distance in $\mathbb{H}_K^d$ capturing physical prox
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\text{score}(e_h, f_{spa}^n, e_t) = f_\theta(\mathbf{x}) \in [0, 1].
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\end{equation}
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Top-scored triples are retained and their tail entities form the frontier for next-hop expansion, following an adaptive search strategy with density-aware thresholding as in [18]. Specifically, we initialize with threshold $\tau_0 = 0.5$ and iteratively reduce by a decay factor $c = 0.1$ if the number of retrieved triples falls below a minimum acceptable count $M$, ensuring sufficient evidence coverage in sparse regions while preventing over-retrieval in dense regions.
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Top-scored triples are retained and their tail entities form the frontier for next-hop expansion, following an adaptive search strategy with density-aware thresholding as in \cite{luo25hyperrag}. Specifically, we initialize with threshold $\tau_0 = 0.5$ and iteratively reduce by a decay factor $c = 0.1$ if the number of retrieved triples falls below a minimum acceptable count $M$, ensuring sufficient evidence coverage in sparse regions while preventing over-retrieval in dense regions.
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3) Spatial Outward Einstein Midpoint Aggregation: After retrieval, the selected multi-source evidence typically spans multiple resolutions. To aggregate these into a unified representation without losing fine-scale information, we introduce the Spatial Outward Einstein Midpoint (Spatial OEM). The motivation stems from a known failure mode: naively averaging hyperbolic embeddings collapses representations toward the origin, destroying the hierarchical structure encoded in radial depth [20].
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3) Spatial Outward Einstein Midpoint Aggregation: After retrieval, the selected multi-source evidence typically spans multiple resolutions. To aggregate these into a unified representation without losing fine-scale information, we introduce the Spatial Outward Einstein Midpoint (Spatial OEM). The motivation stems from a known failure mode: naively averaging hyperbolic embeddings collapses representations toward the origin, destroying the hierarchical structure encoded in radial depth \cite{madhu26hyprag}.
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Given spatial observation hyperedge embeddings $\{\Phi(f_i)\}_{i=1}^n \subset \mathbb{H}_K^d$ with query-relevance weights $w_i$ and resolution-aware radial weighting $\phi_{res}(f_i) = r(\Phi(f_i))^p$:
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$$\mathbf{m}_{K,p}^{Spa\text{-}OEM} = \Pi_K\left(\frac{\sum_{i=1}^{n} w_i \cdot \phi_{res}(f_i) \cdot \lambda_i \cdot \Phi(f_i)}{\sum_{i=1}^{n} w_i \cdot \phi_{res}(f_i) \cdot \lambda_i}\right)$$
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\begin{equation}
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\label{equ:Spatial OEM}
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\mathbf{m}_{K,p}^{Spa\text{-}OEM} = \Pi_K\left(\frac{\sum_{i=1}^{n} w_i \cdot \phi_{res}(f_i) \cdot \lambda_i \cdot \Phi(f_i)}{\sum_{i=1}^{n} w_i \cdot \phi_{res}(f_i) \cdot \lambda_i}\right),
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\end{equation}
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where $\lambda_i = \Phi(f_i)_0$ is the Lorentz factor and $\Pi_K$ denotes reprojection onto $\mathbb{H}_K^d$, defined as $\Pi_K(\mathbf{v}) = \frac{\mathbf{v}}{\sqrt{K \langle \mathbf{v}, \mathbf{v} \rangle_L}}$ for $\mathbf{v}$ with $\langle \mathbf{v}, \mathbf{v} \rangle_L < 0$ and $v_0 > 0$.
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**Theorem 1** (Spatial OEM Outward Bias). *For $p \geq 1$, the Spatial OEM satisfies:*
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Theorem~1 (Spatial OEM Outward Bias). For $p \geq 1$, the Spatial OEM satisfies:
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\begin{equation}
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\label{equ:Spatial OEM Outward Bias}
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r(\mathbf{m}_{K,p}^{Spa\text{-}OEM}) \geq r(\mathbf{m}_K^{Ein}),
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\end{equation}
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where $\mathbf{m}_K^{Ein}$ is the standard Einstein midpoint ($p = 0$).
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$$r(\mathbf{m}_{K,p}^{Spa\text{-}OEM}) \geq r(\mathbf{m}_K^{Ein})$$
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*where $\mathbf{m}_K^{Ein}$ is the standard Einstein midpoint ($p = 0$).*
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*Proof.* The OEM weights $\tilde{w}_i \propto w_i \cdot r(\Phi(f_i))^{p+1}$ concentrate more mass on high-radius points than the Einstein weights $w_i \cdot r(\Phi(f_i))$. By the Chebyshev sum inequality applied to the co-monotonic sequences $a_i = r(\Phi(f_i))^{p+1}$ and $b_i = r(\Phi(f_i))$, the pre-projection time component satisfies $\tilde{v}_0 \geq \bar{r}_w$ (weighted mean radius). Since reprojection $\Pi_K$ preserves the ordering of time components, the result follows. $\square$
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Proof. The OEM weights $\tilde{w}_i \propto w_i \cdot r(\Phi(f_i))^{p+1}$ concentrate more mass on high-radius points than the Einstein weights $w_i \cdot r(\Phi(f_i))$. By the Chebyshev sum inequality applied to the co-monotonic sequences $a_i = r(\Phi(f_i))^{p+1}$ and $b_i = r(\Phi(f_i))$, the pre-projection time component satisfies $\tilde{v}_0 \geq \bar{r}_w$ (weighted mean radius). Since reprojection $\Pi_K$ preserves the ordering of time components, the result follows. $\square$
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The outward bias guarantees that high-resolution observations dominate the aggregated representation. This is essential for planetary science retrieval: when a user queries a specific geological feature, the aggregated evidence should preserve the fine-scale observational details rather than being smoothed into a coarse-resolution summary.
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@@ -227,28 +228,33 @@ The outward bias guarantees that high-resolution observations dominate the aggre
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We define the multi-source spatial evidence retrieved in a single query as observation-grounded homologous data (Definition 4). Although targeting the same query object, these data often provide inconsistent factual statements due to differences in instrument principles, observation geometry, and acquisition epochs. Unlike MultiRAG's Multi-level Confidence Computing (MCC), which assumes that inconsistency indicates unreliability and employs mutual information entropy to filter conflicting nodes, we adopt a fundamentally different paradigm: Physics-Informed Conflict Triage (PICT), which classifies conflicts by their physical origin and applies differentiated processing strategies.
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1) Cross-Source Interaction Entropy: The first stage detects conflicts by measuring the information-theoretic interaction effect when two sources are jointly presented to the LLM. Existing entropy-based conflict detection methods, such as TruthfulRAG [17], compare retrieval-augmented entropy against parametric-only entropy ($\Delta H_p = H(P_{aug}) - H(P_{param})$). However, this formulation is inapplicable to our setting where all knowledge is external observational data rather than LLM parametric knowledge. We instead propose cross-source interaction entropy that measures the mutual interference between two observation sources:
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$$\mathcal{H}_{inter}(p_i, p_j \mid q) = H\left(P(\text{ans} \mid q, p_i \oplus p_j)\right) - \frac{1}{2}\left[H\left(P(\text{ans} \mid q, p_i)\right) + H\left(P(\text{ans} \mid q, p_j)\right)\right],$$
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1) Cross-Source Interaction Entropy: The first stage detects conflicts by measuring the information-theoretic interaction effect when two sources are jointly presented to the LLM. Existing entropy-based conflict detection methods, such as TruthfulRAG \cite{liu26truthfulrag}, compare retrieval-augmented entropy against parametric-only entropy ($\Delta H_p = H(P_{aug}) - H(P_{param})$). However, this formulation is inapplicable to our setting where all knowledge is external observational data rather than LLM parametric knowledge. We instead propose cross-source interaction entropy that measures the mutual interference between two observation sources:
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\begin{equation}
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\label{equ:interaction entropy}
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\mathcal{H}_{inter}(p_i, p_j \mid q) = H\left(P(\text{ans} \mid q, p_i \oplus p_j)\right) - \frac{1}{2}\left[H\left(P(\text{ans} \mid q, p_i)\right) + H\left(P(\text{ans} \mid q, p_j)\right)\right],
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\end{equation}
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where $H(\cdot)$ is the token-averaged entropy over top-$k$ candidate tokens:
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$$H\left(P(\text{ans} \mid \text{context})\right) = -\frac{1}{|l|}\sum_{t=1}^{|l|}\sum_{i=1}^{k} pr_i^{(t)} \log_2 pr_i^{(t)}$$
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\begin{equation}
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\label{equ:token-averaged entropy}
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H\left(P(\text{ans} \mid \text{context})\right) = -\frac{1}{|l|}\sum_{t=1}^{|l|}\sum_{i=1}^{k} pr_i^{(t)} \log_2 pr_i^{(t)},
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\end{equation}
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and $p_i \oplus p_j$ denotes the concatenation of both reasoning paths derived from sources $\mathcal{K}_i$ and $\mathcal{K}_j$ respectively. The interaction entropy admits a clear physical interpretation: positive values ($\mathcal{H}_{inter} > 0$, super-additive uncertainty) indicate that the two sources contradict each other, jointly creating more confusion than either alone; near-zero values indicate independence or consistency; negative values (sub-additive) indicate mutual complementarity where the sources reinforce each other.
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Reasoning path pairs exhibiting interaction entropy exceeding a predefined threshold $\epsilon$ are classified as detected conflicts:
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$$\mathcal{C}^{detected} = \{(\psi_i, \psi_j) \mid \mathcal{H}_{inter}(p_i, p_j \mid q) > \epsilon\}$$
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\begin{equation}
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\label{equ:conflict detection}
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\mathcal{C}^{detected} = \{(\psi_i, \psi_j) \mid \mathcal{H}_{inter}(p_i, p_j \mid q) > \epsilon\}.
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\end{equation}
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2) Physics-Informed Conflict Classification: The second stage classifies each detected conflict by its physical origin. We introduce the central distinction of PICT:
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**Definition 7. Explainable conflict and opaque conflict.** A pairwise conflict $(\psi_i, \psi_j) \in \mathcal{C}_{i,j}$ is *explainable* if there exists a physical bridging function $\mathcal{B}$ such that:
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Definition~7 (Explainable conflict and opaque conflict). A pairwise conflict $(\psi_i, \psi_j) \in \mathcal{C}_{i,j}$ is explainable if there exists a physical bridging function $\mathcal{B}$ such that:
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\begin{equation}
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\label{equ:explainable conflict}
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\mathcal{B}(\Omega_i, \Omega_j, \mathcal{M}_i, \mathcal{M}_j) \models \neg(\psi_i \bot \psi_j).
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\end{equation}
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$$\mathcal{B}(\Omega_i, \Omega_j, \mathcal{M}_i, \mathcal{M}_j) \models \neg(\psi_i \bot \psi_j).$$
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i.e., the apparent inconsistency is resolvable by accounting for observation constraint differences ($\Omega_i$, $\Omega_j$) and measurement model differences ($\mathcal{M}_i$, $\mathcal{M}_j$). Otherwise, the conflict is *opaque*.
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Based on this distinction, we define four conflict categories, each with a differentiated processing strategy:
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i.e., the apparent inconsistency is resolvable by accounting for observation constraint differences ($\Omega_i$, $\Omega_j$) and measurement model differences ($\mathcal{M}_i$, $\mathcal{M}_j$). Otherwise, the conflict is opaque.
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\begin{table}
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\renewcommand{\arraystretch}{1.3}
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@@ -256,7 +262,7 @@ Based on this distinction, we define four conflict categories, each with a diffe
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\label{table_conflict_triage}
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\vspace{-0.13in}
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\centering
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\begin{tabular}{|m{3cm}|m{3cm}|m{3cm}|}
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\begin{tabular}{|m{2.1cm}|m{2.8cm}|m{2.8cm}|}
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\hline
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\makecell[c]{\textbf{Category}} & \makecell[c]{\textbf{Condition}} & \makecell[c]{\textbf{Strategy}} \\
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\hline
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@@ -272,29 +278,40 @@ Based on this distinction, we define four conflict categories, each with a diffe
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\end{tabular}
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\end{table}
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For each detected conflict, we construct a feature vector that fuses information-theoretic, physical, and neural signals:
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$$\mathbf{z}_{conf} = \left[\mathcal{H}_{inter}, \; \|\Omega_i - \Omega_j\|, \; |\log(\ell_{res}^i / \ell_{res}^j)|, \; \Delta\mathcal{T}, \; \rho_{auth}(i,j), \; \mathbf{h}^{(l^*)}_{conf}\right]$$
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Based on this distinction, we define four conflict categories, each with a differentiated processing strategy, as shown in Table~\ref{table_conflict_triage}. For each detected conflict, we construct a feature vector that fuses information-theoretic, physical, and neural signals:
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\begin{equation}
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\label{equ:conflict classification feature vector}
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\mathbf{z}_{conf} = \left[\mathcal{H}_{inter}, \; \|\Omega_i - \Omega_j\|, \; |\log(\ell_{res}^i / \ell_{res}^j)|, \; \Delta\mathcal{T}, \; \rho_{auth}(i,j), \; \mathbf{h}^{(l^*)}_{conf}\right],
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\end{equation}
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where $\|\Omega_i - \Omega_j\|$ is the observation geometry disparity, $|\log(\ell_{res}^i / \ell_{res}^j)|$ is the resolution ratio in log-scale, $\Delta\mathcal{T}$ is the temporal separation, $\rho_{auth}(i,j)$ is the authority disparity between sources, and $\mathbf{h}^{(l^*)}_{conf}$ is the LLM hidden state at the conflict encoding layer. The inclusion of $\mathbf{h}^{(l^*)}_{conf}$ is motivated by the finding that knowledge conflict signals concentrate in mid-to-late layers of LLMs and are linearly separable with > 93% AUC [21].
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A lightweight classifier maps the feature vector to conflict type:
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$$\hat{c} = \arg\max_{c \in \{noise, inst, scale, temp\}} P_\theta(c \mid \mathbf{z}_{conf})$$
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\begin{equation}
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\label{equ:conflict classification}
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\hat{c} = \arg\max_{c \in \{noise, inst, scale, temp\}} P_\theta(c \mid \mathbf{z}_{conf}).
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\end{equation}
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Lemma~1 (Conflict Type Separability). The four conflict types are distinguished by orthogonal physical dimensions: $\|\Omega_i - \Omega_j\|$ separates instrument conflicts; $|\log(\ell_{res}^i / \ell_{res}^j)|$ separates scale conflicts; $\Delta\mathcal{T}$ separates temporal conflicts; $\rho_{auth}$ separates noise conflicts. Since these physical features are independent of and complementary to the hidden state features $\mathbf{h}^{(l^*)}_{conf}$ (which encode semantic inconsistency), the four conflict types are linearly separable in the augmented feature space $\mathbf{z}_{conf}$.
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3) Conflict-Aware Confidence Recalibration: Based on the classification result, we recalibrate the node confidence. This is the key departure from MultiRAG's MCC, which uniformly penalizes inconsistency:
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$$C_{triage}(v) = \begin{cases} C_{base}(v) & \text{if } v \notin \mathcal{C}^{detected} \\ \alpha \cdot C_{base}(v) + (1-\alpha) \cdot \eta & \text{if } \hat{c} = noise \\ C_{base}(v) + \beta \cdot \mathcal{H}_{inter}^{-1} & \text{if } \hat{c} \in \{inst, scale\} \\ C_{base}(v) \cdot \gamma(|\Delta\mathcal{T}|) & \text{if } \hat{c} = temp \end{cases}$$
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\begin{equation}
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\label{equ:conflict classification}
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C_{triage}\left( v \right) =\begin{cases}
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C_{base}\left( v \right)& \text{if\,\,}v\ni \mathcal{C}^{detected}\\
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\alpha \cdot C_{base}\left( v \right) +\left( 1-\alpha \right) \cdot \eta& \text{if\,\,}\hat{c}=noise\\
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C_{base}\left( v \right) +\beta \cdot \mathcal{H}_{inter}^{-1}& \text{if\,\,}\hat{c}\in \{inst,scale\}\\
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C_{base}\left( v \right) \cdot \gamma \left( |\Delta \mathcal{T}| \right)& \text{if\,\,}\hat{c}=temp,\\
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\end{cases}
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\end{equation}
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where $C_{base}(v)$ is the baseline confidence computed via semantic similarity (analogous to the node consistency score in [14]), $\eta < 0$ is a penalty term for noise conflicts, $\beta > 0$ is a boost coefficient for scientifically explainable conflicts, and $\gamma(|\Delta\mathcal{T}|)$ is a time-decay weighting function that prioritizes recent observations while preserving temporal evolution signals. Specifically, $\gamma(|\Delta\mathcal{T}|) = 1 + \beta_{temp} \cdot \exp(-|\Delta\mathcal{T}| / \tau_{decay})$, where $\beta_{temp} > 0$ ensures $\gamma > 1$ for temporal contrasts with scientific significance.
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**Theorem 2** (Anti-Over-Smoothing Guarantee). *Let $V_{sci} \subset V$ denote the set of nodes involved in explainable scientific conflicts ($\mathcal{C}^{inst} \cup \mathcal{C}^{scale} \cup \mathcal{C}^{temp}$). Under PICT with $\beta > 0$:*
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Theorem~2 (Anti-Over-Smoothing Guarantee). Let $V_{sci} \subset V$ denote the set of nodes involved in explainable scientific conflicts ($\mathcal{C}^{inst} \cup \mathcal{C}^{scale} \cup \mathcal{C}^{temp}$). Under PICT with $\beta > 0$:
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\begin{equation}
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\label{equ:Anti-Over-Smoothing Guarantee}
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C_{triage}(v) > C_{base}(v) \quad \forall v \in V_{sci}.
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\end{equation}
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$$C_{triage}(v) > C_{base}(v) \quad \forall v \in V_{sci}$$
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*Proof.* For $v \in \mathcal{C}^{inst} \cup \mathcal{C}^{scale}$: $C_{triage}(v) = C_{base}(v) + \beta \cdot \mathcal{H}_{inter}^{-1}$. Since $\beta > 0$ and $\mathcal{H}_{inter} > \epsilon > 0$ (by the detection threshold in Eq. 16), $\beta \cdot \mathcal{H}_{inter}^{-1} > 0$, thus $C_{triage}(v) > C_{base}(v)$. For $v \in \mathcal{C}^{temp}$: $\gamma(|\Delta\mathcal{T}|) > 1$ by construction (since $\beta_{temp} > 0$ and $\exp(\cdot) > 0$), thus $C_{triage}(v) = C_{base}(v) \cdot \gamma(|\Delta\mathcal{T}|) > C_{base}(v)$. $\square$
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Proof. For $v \in \mathcal{C}^{inst} \cup \mathcal{C}^{scale}$: $C_{triage}(v) = C_{base}(v) + \beta \cdot \mathcal{H}_{inter}^{-1}$. Since $\beta > 0$ and $\mathcal{H}_{inter} > \epsilon > 0$ (by the detection threshold in Eq. 16), $\beta \cdot \mathcal{H}_{inter}^{-1} > 0$, thus $C_{triage}(v) > C_{base}(v)$. For $v \in \mathcal{C}^{temp}$: $\gamma(|\Delta\mathcal{T}|) > 1$ by construction (since $\beta_{temp} > 0$ and $\exp(\cdot) > 0$), thus $C_{triage}(v) = C_{base}(v) \cdot \gamma(|\Delta\mathcal{T}|) > C_{base}(v)$. $\square$
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This theorem provides a formal guarantee that scientifically valuable conflict nodes can never be suppressed below their baseline confidence by the triage mechanism, directly addressing the over-smoothing problem.
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@@ -324,13 +341,13 @@ We propose the AreoRAG Prompting (ARP) algorithm for multi-source planetary spat
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\end{algorithmic}
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\end{algorithm}
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Given a user query $q$, the LLM is first employed to extract entities, spatial constraints ($\mathcal{P}_{foot}$, region), and temporal constraints ($\mathcal{T}_{win}$, $L_s$ range), generating corresponding logical and spatial relationships. The observation data then undergoes multi-source spatial adapter parsing to derive normalized datasets (Eq. 4), followed by constructing a Hyperbolic Spatial Hypergraph via scale-aware Lorentz embedding and cross-reference-frame alignment (Eq. 6-8).
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Given a user query $q$, the LLM is first employed to extract entities, spatial constraints ($\mathcal{P}_{foot}$, region), and temporal constraints ($\mathcal{T}_{win}$, $L_s$ range), generating corresponding logical and spatial relationships. The observation data then undergoes multi-source spatial adapter parsing to derive normalized datasets (line 4), followed by constructing a Hyperbolic Spatial Hypergraph via scale-aware Lorentz embedding and cross-reference-frame alignment (lines 6-8).
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Subsequently, spatiotemporal retrieval is performed using hyperbolic spatial encoding and MLP-based plausibility scoring (Eq. 10-12), with Spatial OEM aggregation (Eq. 13) to produce a unified cross-resolution representation. The cross-source interaction entropy mechanism (Eq. 14-16) then detects inter-source conflicts, after which each detected conflict is classified via the physics-informed feature vector (Eq. 18-19) and the node confidence is recalibrated accordingly (Eq. 20).
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Subsequently, spatiotemporal retrieval is performed using hyperbolic spatial encoding and MLP-based plausibility scoring (lines 10-12), with Spatial OEM aggregation (line 13) to produce a unified cross-resolution representation. The cross-source interaction entropy mechanism (lines 14-16) then detects inter-source conflicts, after which each detected conflict is classified via the physics-informed feature vector (lines 18-19) and the node confidence is recalibrated accordingly (line 20).
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The final step constructs a differential context based on the triage result. For noise conflicts, the low-authority source is filtered, compatible with conventional conflict elimination. For instrument-inherent and scale-dependent conflicts, both sources are preserved with a physical bridging explanation $\mathcal{B}(\Omega_i, \Omega_j)$ appended to the context, enabling the LLM to reason about the physical origin of the disagreement. For temporal-evolution conflicts, a temporal ordering is constructed, allowing the LLM to trace the evolution of observations over time. All preserved evidence carries provenance metadata (DataID, source institution, instrument identity, observation timestamp in $L_s$) to ensure scientific traceability, analogous to the citation anchors in Perplexity-style retrieval systems.
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It should be noted that the ARP algorithm constructs the HySH offline as a preprocessing step, while the PICT module operates online during each query. The HySH construction time is dominated by the LLM-based entity extraction (comparable to MultiRAG's MLG construction), while the online PICT overhead consists primarily of $|\mathcal{C}^{detected}|$ forward passes through the lightweight conflict classifier (Eq. 19), which is negligible compared to the LLM generation cost.
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It should be noted that the ARP algorithm constructs the HySH offline as a preprocessing step, while the PICT module operates online during each query. The HySH construction time is dominated by the LLM-based entity extraction (comparable to MultiRAG's MLG construction), while the online PICT overhead consists primarily of $|\mathcal{C}^{detected}|$ forward passes through the lightweight conflict classifier (line 19), which is negligible compared to the LLM generation cost.
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\section{Experiments}
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This section conducts experiments and performance analysis on the Hyperbolic Spatial Hypergraph (HySH) construction and the Physics-Informed Conflict Triage (PICT) modules. Baseline methods are compared with SOTA multi-source retrieval, graph-based RAG, and conflict-resolution methods. Extensive experiments are conducted to assess the robustness and efficiency of AreoRAG, which aims to answer the following questions.
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