| Query | "What is the mineral composition of the clay-bearing unit in the western delta of Jezero Crater? Do orbital and in-situ observations provide consistent results?" |
| Data Sources | Orbital: CRISM detection of Fe/Mg-smectites (confidence 0.91)
Orbital: HiRISE morphological evidence of layered phyllosilicates
In-situ: Perseverance PIXL showing olivine-carbonate assemblage with minor clay
In-situ: SHERLOC Raman spectra indicating organic-bearing minerals |
| HySH Module | Spatial hyperedge: binds CRISM cube, HiRISE strip, PIXL measurement point, SHERLOC spectrum at co-located footprint ($\Delta r = 4.2$, scale-dependent flag)
Embedding: CRISM at $r=3.1$ (18m), HiRISE at $r=8.7$ (0.3m), PIXL at $r=9.2$ (point) |
| PICT Module | Detected conflict: CRISM "dominant smectite" vs. PIXL "minor clay, dominant olivine-carbonate"
$\mathcal{H}_{inter} = 1.34 > \epsilon$; $|\log(\ell_{res}^{CRISM}/\ell_{res}^{PIXL})| = 4.1$; $\hat{c} = scale$
Classification: Scale-dependent conflict ($\mathcal{C}^{scale}$), preserved with bridging explanation
$C_{triage} = C_{base} + \beta \cdot \mathcal{H}_{inter}^{-1} = 0.72 + 0.15 = 0.87$ |
| AreoRAG Answer | "The western delta clay-bearing unit shows scale-dependent compositional heterogeneity. At orbital scale (CRISM, 18m/pixel), the dominant spectral signature is Fe/Mg-smectite [DataID: FRT0000B3B1]. At in-situ scale (PIXL, sub-mm), the primary phases are olivine and carbonate with minor clay [DataID: sol-0347-pixl]. This discrepancy is consistent with a spatial mixing effect: the CRISM pixel integrates signal from both clay-rich and olivine-rich sub-units that are resolved at rover scale. HiRISE morphology supports layered heterogeneity [DataID: ESP_045994_1985]. Recommendation: cross-reference with CRISM targeted observation at higher spectral resolution for the specific PIXL measurement location." |
| MultiRAG Answer (for comparison) | "Orbital data indicates dominant clay minerals. In-situ data shows olivine-carbonate. The in-situ result may be less reliable due to inconsistency with orbital consensus (confidence: 0.43, filtered)." |
+
+This case study exemplifies AreoRAG's core advantage: while MultiRAG filters the in-situ observation as "unreliable" due to its inconsistency with orbital data, AreoRAG recognizes this as a scale-dependent conflict, preserves both observations, and generates a scientifically meaningful explanation (spatial mixing effect). The answer includes provenance metadata (DataIDs) for scientific traceability, and proactively recommends follow-up data to resolve the ambiguity — a capability enabled by the PICT module's conflict-aware context construction.
+
+
+### H. Limitations
+
+We acknowledge several limitations inherent in the current framework:
+
+1) **Dataset scale**: The planetary datasets are constructed from publicly available archives and may not cover the full diversity of Mars exploration scenarios. Larger-scale evaluation with comprehensive PDS holdings is planned as future work.
+
+2) **Conflict classification coverage**: The four-category conflict taxonomy, while covering the most common planetary science scenarios, may not capture all possible conflict origins (e.g., processing artifact conflicts, calibration drift). Extending the taxonomy is a natural direction.
+
+3) **LLM dependency**: The cross-source interaction entropy computation (Eq. 14) and conflict classification (Eq. 18) both rely on LLM forward passes, introducing potential biases from the base model's parametric knowledge about planetary science. Fine-tuning on domain-specific corpora may mitigate this issue.
+
+4) **Generalization to other planetary bodies**: While designed for Mars, the framework's principles (hyperbolic scale hierarchy, physics-informed conflict triage) are applicable to other planetary bodies (Moon, Venus, icy moons). Validation on non-Mars datasets remains future work.
diff --git a/paper_introduction.md b/paper_introduction.md
index 59cb86f..20afe96 100644
--- a/paper_introduction.md
+++ b/paper_introduction.md
@@ -1,31 +1,47 @@
-# AreoRAG: A Physics-Informed Framework for Multi-Source Retrieval Augmented Generation over Planetary Spatial Data
+# AreoRAG: Hyperbolic Spatial Hypergraph and Physics-Informed Conflict Triage for Multi-Source Planetary Retrieval Augmented Generation
+
+Author Name ${}^{1}$ , Author Name ${}^{2\text{ \ding{42} }}$ , Author Name ${}^{1}$
+
+${}^{1}$ Affiliation One
+
+${}^{2}$ Affiliation Two
+
+Email: {author1, author2}@example.edu
+
+**Abstract** — Retrieval Augmented Generation (RAG) has demonstrated considerable promise in grounding Large Language Models (LLMs) with external knowledge for knowledge-intensive question answering. However, extending RAG to the domain of planetary science — where multi-source remote sensing observations are inherently embedded in continuous physical space and inter-source disagreements often carry scientific value — introduces fundamental challenges that existing multi-source RAG frameworks cannot address. These challenges manifest in two critical aspects: (1) existing discrete graph topologies (e.g., multi-source line graphs) suffer from edge explosion when encoding continuous spatial proximity, failing to bridge the gap between physical continuity and semantic discreteness; and (2) conventional conflict-filtering mechanisms, designed under the assumption that inter-source inconsistency implies unreliability, systematically suppress scientifically valuable observational disagreements that are intrinsic to multi-platform deep-space exploration. To address these challenges, we propose AreoRAG, a novel framework tailored for multi-source planetary spatial data retrieval augmented generation. Our framework introduces two key innovations: (1) a Hyperbolic Spatial Hypergraph (HySH) construction module that employs $n$-ary spatial observation hyperedges embedded in hyperbolic space via the Lorentz model, where spatial resolution is coupled with radial depth to faithfully represent the hierarchical scale structure of planetary observations while reducing edge complexity from $O(k^2)$ to $O(k)$; and (2) a Physics-Informed Conflict Triage (PICT) module that detects inter-source conflicts via cross-source interaction entropy, classifies them into four physically grounded categories (noise, instrument-inherent, scale-dependent, and temporal-evolution), and applies differentiated confidence recalibration to preserve scientifically valuable disagreements while filtering genuine noise. Extensive experiments on multi-source planetary observation datasets demonstrate that AreoRAG significantly enhances both the retrieval fidelity and the scientific faithfulness of knowledge-augmented generation in planetary science scenarios.
+
+**Index Terms** — Retrieval Augmented Generation, Planetary Remote Sensing, Hyperbolic Hypergraph, Knowledge Conflict Triage, Multi-source Spatial Data, Mars Exploration
## I. INTRODUCTION
-Large Language Models (LLMs) have achieved remarkable success in handling a variety of natural language processing tasks, attributable to their robust capabilities in understanding and generating language and symbols [1]. In knowledge-intensive retrieval tasks, Retrieval Augmented Generation (RAG) has become a standardized solution paradigm [2]–[4]. Previous works [5]–[11] have made significant strides in addressing the inherent knowledge limitations of LLMs by introducing external knowledge bases, markedly improving the accuracy and fidelity of LLM responses. Notably, the synergy between LLMs and Knowledge Graphs (KGs) has been proposed to achieve more efficient and structured information retrieval [12]–[26], propelling the deep reasoning capabilities of RAG in multi-hop question answering, knowledge-intensive retrieval, and multi-source data fusion.
+The past two decades have witnessed an unprecedented accumulation of multi-source remote sensing data from Mars exploration missions. Orbital platforms such as Mars Reconnaissance Orbiter (MRO), Mars Express, and Tianwen-1 continuously acquire observations spanning diverse modalities — from sub-meter optical imagery (HiRISE at 0.3 m/pixel) and medium-resolution contextual mosaics (CTX at 6 m/pixel) to hyperspectral mineralogical mapping (CRISM at 18 m/pixel) and global topographic models (MOLA at ~460 m/pixel). Simultaneously, surface assets including the Curiosity and Zhurong rovers generate complementary in-situ measurements through spectrometers, ground-penetrating radar, and navigation cameras. This rapidly expanding, multi-source, multi-resolution data ecosystem has created a pressing demand for intelligent knowledge retrieval systems that can support planetary scientists in conducting semantic search, cross-source correlation, and multi-scale reasoning over heterogeneous observation archives [1]-[4].
-With the rapid advancement of deep space exploration programs, including NASA's Mars 2020 Perseverance mission, ESA's ExoMars, and CNSA's Tianwen-1 mission, the volume and heterogeneity of planetary observation data have grown at an unprecedented scale [27], [28]. These multi-source datasets — spanning orbital remote sensing imagery (e.g., HiRISE at 0.3m, CTX at 6m, CRISM spectral cubes), in-situ measurements (e.g., rover-mounted spectrometers, ground-penetrating radar), and derived products (e.g., digital terrain models, mineral abundance maps) — collectively constitute a rich yet highly complex knowledge ecosystem for planetary science [29]. The demand for intelligent retrieval over such multi-source planetary data has become increasingly urgent: researchers need to perform spatial semantic search (e.g., "find HiRISE images with dust devil tracks near the equator"), cross-source association (e.g., aggregating multi-resolution data for a target region), and temporally-aware retrieval (e.g., "images captured by Zhurong rover within the first 90 Sols after landing along its southward traverse"). These tasks require the RAG system to bridge the gap between natural language queries and the underlying spatiotemporal structure of planetary observations.
+Large Language Models (LLMs) have emerged as powerful tools for natural language understanding and generation [5], and Retrieval Augmented Generation (RAG) has been established as a standard paradigm for grounding LLM responses in external knowledge bases [6]-[8]. By dynamically retrieving relevant documents and conditioning generation on retrieved context, RAG effectively mitigates the hallucination problem inherent in LLMs and enables knowledge-intensive question answering. The synergy between LLMs and Knowledge Graphs (KGs) has further advanced retrieval performance through structured knowledge representation, achieving notable improvements in multi-hop reasoning, credibility assessment, and interpretability [9]-[13].
-Recent multi-source RAG frameworks, exemplified by MultiRAG [30], have demonstrated promising results in mitigating hallucinations arising from data sparsity and inter-source inconsistency through multi-source line graph construction and multi-level confidence computation. However, these frameworks are fundamentally designed for discrete textual entities (e.g., flight records, book metadata, stock transactions) with explicit semantic associations, and their direct application to planetary spatial data introduces critical structural failures. Building upon the categorization of retrieval challenges in multi-source settings [9], [30], we identify the following failure modes that are unique to multi-source planetary spatial data retrieval:
+Nevertheless, deploying RAG systems for planetary science knowledge retrieval introduces domain-specific complexities that fundamentally challenge existing frameworks. Unlike conventional multi-source retrieval scenarios (e.g., integrating flight records, financial reports, or web documents), planetary observation data possesses two distinctive characteristics. First, all data sources are spatially grounded: each observation is anchored to a specific spatial footprint on the Martian surface, a temporal acquisition window parameterized by Solar Longitude ($L_s$), and instrument-specific parameters such as spectral bands and spatial resolution. The relevance between two observations is therefore governed not merely by textual semantic similarity, but primarily by physical spatial proximity, temporal co-occurrence, and cross-resolution complementarity. Second, inter-source inconsistencies in planetary science are not exclusively indicative of data errors or model hallucinations; rather, they frequently arise as inherent consequences of multi-platform, multi-scale observation and may encode critical scientific discoveries — such as subsurface geological evolution revealed by discrepancies between orbital spectroscopy and in-situ drilling results.
-1) **Spatial proximity collapse**: Existing graph-based RAG methods rely on discrete entity co-occurrence to establish edges. When applied to spatially continuous observation data, encoding spatial proximity (e.g., two overlapping image footprints) as binary edges leads to $O(k^2)$ edge explosion, fundamentally destroying the sparsity-oriented optimizations of line graph structures.
+Recent advances in multi-source RAG, exemplified by MultiRAG [14], have made significant progress in addressing data sparsity and inter-source inconsistency through multi-source line graphs and multi-level confidence computation. However, when confronted with planetary spatial data, these methods encounter two structural bottlenecks that cannot be resolved through parameter tuning alone.
-2) **Scale hierarchy distortion**: Planetary observations inherently form a resolution hierarchy — a single CTX mosaic (6m) spatially contains dozens of HiRISE strips (0.3m), which in turn are nested within MOLA topographic grids (~460m). This containment relationship cannot be faithfully represented by flat, pairwise graph topologies.
+Building upon the analysis of existing multi-source RAG limitations [14]-[16] in the context of planetary science, we identify the following failure modes that are unique to spatially grounded, physically observed multi-source data:
-3) **Scientific conflict erasure**: Multi-level confidence mechanisms designed to filter "unreliable" nodes inadvertently eliminate scientifically valuable observational disagreements. When an orbital spectrometer detects hydrated minerals on the surface while in-situ drilling reveals no such signature at depth, this conflict is not data error but evidence of subsurface geological stratification — a potential major scientific discovery.
+1) **Spatial topology distortion**: When multi-source observations share no common textual entities but are spatially co-located, discrete line graphs fail to establish connectivity, resulting in fragmented retrieval.
-Fig. 1 illustrates the fundamental differences between conventional text-based multi-source retrieval and planetary spatial data retrieval. The continuous spatial embedding, hierarchical resolution structure, and physics-grounded observational conflicts of planetary data are inherently incompatible with discrete graph topologies and de-falsification mechanisms designed for textual knowledge bases. Against this backdrop, we focus on addressing the retrieval challenges unique to multi-source planetary spatial data to empower knowledge-augmented generation for deep space exploration. This work primarily explores the following two fundamental challenges:
+2) **Scale hierarchy collapse**: Observations at different spatial resolutions (e.g., 0.3 m vs. 460 m) exhibit a natural hierarchical containment structure that flat graph topologies cannot represent, leading to loss of cross-resolution context during aggregation.
-**1) Failure of Discrete Representation for Continuous Spatiotemporal Topology.** Multi-source knowledge aggregation methods, such as multi-source line graphs (MLG) [30], [31], rely heavily on discrete text entities and explicit semantic associations to construct graph topology. However, planetary science data is intrinsically embedded in continuous Euclidean physical space. Attempting to encode continuous spatial proximity and directional relationships within traditional discrete graph structures inevitably triggers edge explosion, thereby undermining the efficiency gains that graph-based methods achieve for sparse data distributions. Specifically, for $k$ co-located spatial entities, pairwise spatial encoding requires $\binom{k}{2} = O(k^2)$ edges, while the observation hierarchy (from coarse-resolution global coverage to fine-resolution local strips) demands nested containment relationships that flat graph topologies cannot express. This structural bottleneck prevents existing discrete logical graph structures from bridging the gap between physical continuity and semantic discreteness, constituting a fundamental constraint on planetary spatial reasoning capabilities.
+3) **Scientifically valuable conflict suppression**: Confidence-based conflict filtering indiscriminately eliminates disagreeing nodes, destroying observational evidence that may indicate genuine geological phenomena such as subsurface mineral heterogeneity.
-**2) Contradiction Between Scientific Cognitive Conflict and Traditional De-Falsification Mechanisms.** The core assumption underlying existing multi-source RAG frameworks is that inter-source data inconsistency typically stems from erroneous information or model hallucination, and therefore relies on multi-level confidence computation to eliminate conflicting nodes [30], [33], [34]. However, in deep space exploration scenarios, where absolute ground truth is absent, different observation platforms (e.g., orbiters vs. rovers) often yield significantly conflicting observations of the same target region due to differences in observation scale, penetration depth, and instrument principles. For instance, an orbital spectrometer may detect surface hydrated minerals while in-situ drilling at the same location finds no mineralogical anomaly — such conflict is not data error but an inherent attribute of multi-dimensional scientific observation, potentially containing clues to major scientific discoveries such as geological evolution and subsurface water migration. If existing conflict-filtering mechanisms are applied indiscriminately, severe over-smoothing will result, uniformly erasing high-value scientific anomalies and fundamentally violating the knowledge discovery paradigm of "preserving disagreement, multi-source corroboration" that is central to deep space exploration.
+These failure modes trace back to two fundamental scientific problems:
-To address these challenges, we propose AreoRAG, a novel physics-informed framework designed for multi-source retrieval augmented generation over planetary spatial data. First, we introduce the Hyperbolic Spatial Hypergraph (HySH) for unified spatiotemporal knowledge representation. By employing $n$-ary spatial observation hyperedges, HySH binds co-located multi-source observations into single hyperedges, reducing edge complexity from $O(k^2)$ to $O(k)$. Through scale-aware Lorentz embedding, the resolution hierarchy is naturally encoded via radial depth in hyperbolic space, where the exponential volume growth of negative-curvature geometry faithfully accommodates the exponentially increasing number of observations at finer scales. Second, we propose Physics-Informed Conflict Triage (PICT), which replaces the conventional conflict-filtering paradigm with a classify-then-differentiate strategy. PICT detects inter-source conflicts via cross-source interaction entropy, classifies each conflict into four physically-grounded categories (noise, instrument-inherent, scale-dependent, and temporal-evolution), and applies differentiated confidence recalibration — filtering only noise conflicts while preserving and annotating scientifically valuable disagreements with physical bridging explanations. We provide a formal anti-over-smoothing guarantee ensuring that nodes involved in explainable scientific conflicts can never be filtered out by the confidence mechanism.
+**Problem 1: Discrete Representation Failure for Continuous Spatiotemporal Topology.** Existing multi-source knowledge aggregation methods, such as multi-source line graphs [14], rely on discrete text entities and explicit semantic associations to construct graph topology. However, planetary science data is intrinsically embedded in continuous Euclidean physical space. Attempting to encode continuous spatial proximity and directional relationships within traditional discrete graph structures inevitably triggers an edge explosion problem — $k$ co-located spatial entities require $\binom{k}{2} = O(k^2)$ pairwise spatial proximity edges — thereby destroying the optimizations that existing graph models achieve for data sparsity. The discrete logical graph structure thus constitutes a structural bottleneck constraining planetary spatial reasoning capabilities, unable to bridge the chasm between physical continuity and semantic discreteness.
+
+**Problem 2: Fundamental Conflict Between Scientific Cognitive Divergence and Traditional De-Falsification Mechanisms.** The core assumption underlying existing multi-source RAG frameworks is that inter-source data inconsistency typically originates from misinformation or model hallucinations, and therefore relies on multi-level confidence computation to eliminate conflicting nodes [14], [17]. However, in deep-space exploration scenarios, the absence of absolute ground truth means that different observation platforms (e.g., orbiters versus rovers), due to differences in observation scale, penetration depth, and instrumental principles, often produce significantly conflicting results for the same target region. For instance, orbital spectrometers may detect surface hydrated minerals while in-situ drilling reveals no anomaly — a conflict arising not from data error, but from the inherent multi-dimensional nature of scientific observation, potentially harboring clues to major discoveries such as geological evolution. Applying existing conflict-filtering mechanisms indiscriminately would cause severe over-smoothing, uniformly suppressing high-value scientific anomalies and fundamentally violating the epistemological principle of deep-space exploration: preserving controversy and enabling multi-source corroboration for knowledge discovery.
+
+To address these two fundamental challenges, we propose AreoRAG, a novel framework specifically designed for multi-source planetary spatial data retrieval augmented generation. AreoRAG introduces two synergistic innovations. First, to resolve Problem 1, we construct a Hyperbolic Spatial Hypergraph (HySH) that employs $n$-ary spatial observation hyperedges to bind co-located multi-source observations into single high-order facts, reducing edge complexity from $O(k^2)$ to $O(k)$. These hyperedges are embedded in hyperbolic space via the Lorentz model, where the exponential volume growth of negative-curvature geometry naturally accommodates the hierarchical scale structure of planetary observations — coarse-resolution global data resides near the origin while fine-resolution local data extends toward the boundary. Second, to resolve Problem 2, we develop a Physics-Informed Conflict Triage (PICT) mechanism that replaces the uniform conflict-filtering paradigm with a differentiated triage approach. PICT detects inter-source conflicts through cross-source interaction entropy, classifies each conflict into one of four physically grounded categories (noise, instrument-inherent, scale-dependent, temporal-evolution), and applies category-specific confidence recalibration — filtering genuine noise while provably preserving and even boosting the confidence of scientifically valuable observational disagreements. Together, HySH provides spatially faithful multi-source evidence to PICT, while PICT feeds back triage results to prioritize scientifically interesting regions in subsequent retrieval, forming a tightly coupled framework.
The contributions of this paper are summarized as follows:
-1) **Hyperbolic Spatial Knowledge Aggregation**: In the knowledge construction module, we introduce the Hyperbolic Spatial Hypergraph as a data structure for unified spatiotemporal representation of multi-source planetary observations. By coupling $n$-ary spatial observation hyperedges with scale-aware Lorentz embedding, this structure simultaneously resolves the edge explosion problem inherent in encoding continuous spatial proximity and faithfully represents the resolution hierarchy through the intrinsic geometry of hyperbolic space. We further introduce the Spatial Outward Einstein Midpoint for cross-resolution aggregation that provably preserves fine-scale observational details.
+1) **Hyperbolic Spatial Hypergraph Construction**: We introduce HySH, a knowledge construction module that employs $n$-ary spatial observation hyperedges embedded in hyperbolic space to achieve unified spatiotemporal representation of multi-source planetary data. By coupling spatial resolution with hyperbolic radial depth via the Lorentz model, HySH faithfully preserves the hierarchical scale structure of planetary observations while eliminating edge explosion through high-order relational encoding. A resolution-aware Spatial Outward Einstein Midpoint (Spatial OEM) aggregation operator is further proposed to prevent hierarchical collapse during cross-resolution evidence fusion, with a formal guarantee of outward bias.
-2) **Physics-Informed Conflict Triage**: In the retrieval module, we propose a conflict detection and classification mechanism grounded in observation physics. By formalizing conflicts through observation geometry parameters and measuring cross-source interaction entropy, we classify inter-source disagreements into four categories with orthogonal physical signatures. A conflict-aware confidence recalibration strategy is designed to filter noise while preserving scientifically explainable conflicts with provenance metadata and physical bridging explanations, accompanied by a formal anti-over-smoothing guarantee (Theorem 2).
+2) **Physics-Informed Conflict Triage**: We propose PICT, a retrieval module that fundamentally redefines the role of inter-source conflict in RAG systems. Through cross-source interaction entropy for conflict detection, a physically grounded four-category conflict classification informed by observation geometry, and differentiated confidence recalibration, PICT provably prevents the over-smoothing of scientifically valuable disagreements (Anti-Over-Smoothing Guarantee) while maintaining noise-filtering capability. To the best of our knowledge, this is the first conflict-handling mechanism in RAG that explicitly distinguishes between erroneous inconsistency and scientifically meaningful observational divergence.
-3) **Experimental Validation and Performance Comparison**: We construct a multi-source planetary spatial retrieval benchmark encompassing orbital imagery, in-situ measurements, and derived products from Mars exploration missions. Extensive experiments demonstrate that AreoRAG significantly outperforms existing state-of-the-art multi-source RAG methods in both retrieval accuracy and scientific conflict preservation, while maintaining competitive efficiency through the compact hyperbolic representation.
+3) **Integrated Framework and Experimental Validation**: We design the AreoRAG Prompting (ARP) algorithm that integrates HySH and PICT through three explicit coupling points: spatial alignment as a prerequisite for interaction entropy computation, radial depth difference as a resolution disparity signal for conflict classification, and triage-driven retrieval priority feedback. Extensive experiments on multi-source planetary observation datasets demonstrate that AreoRAG significantly outperforms existing multi-source RAG methods in both retrieval fidelity and scientific faithfulness, with particular advantages in scenarios involving cross-resolution reasoning and observation-grounded conflict preservation.
diff --git a/paper_preliminary_methodology.md b/paper_preliminary_methodology.md
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+## II. PRELIMINARY
+
+In the field of planetary spatial knowledge retrieval, the primary challenges include faithfully representing continuous spatiotemporal relationships across heterogeneous observation sources and achieving reliable retrieval under inherent inter-source scientific conflicts. This section introduces the core elements of our approach and precisely defines the problems we address.
+
+Let $Q = \{q_1, q_2, \ldots, q_n\}$ be the set of query instances, where each $q_i$ corresponds to a distinct planetary science query. Let $\mathcal{E} = \{e_1, e_2, \ldots, e_m\}$ be the set of entities in the spatial knowledge hypergraph, where each $e_j$ represents a geological feature, instrument, or observation product. Let $\mathcal{R} = \{r_1, r_2, \ldots, r_p\}$ be the set of relationships, and let $\mathcal{F} = \{f_1^n, f_2^n, \ldots, f_s^n\}$ be the set of $n$-ary relational facts (hyperedges). Let $D = \{d_1, d_2, \ldots, d_t\}$ be the set of observation data products, where each $d_l$ represents an observation record from a specific instrument. We define the spatially-grounded knowledge-guided retrieval augmented generation problem as follows:
+
+$$\arg \max_{d_i \in D} \text{LLM}(q_i, d_i), \quad \sum_{e_j \in \mathcal{E}} \sum_{f_k^n \in \mathcal{F}} \text{HG}(e_j, f_k^n, d_i) \cdot \mathcal{S}_{geo}(q_i, d_i) \tag{1}$$
+
+where $\text{LLM}(q_i, d_l)$ denotes the relevance score between query $q_i$ and document $d_l$ assessed by the LLM, $\text{HG}(e_j, f_k^n, d_l)$ represents the degree of match between entity $e_j$, $n$-ary fact $f_k^n$, and document $d_l$ in the hypergraph, and $\mathcal{S}_{geo}(q_i, d_i)$ is a spatial compatibility function that ensures the retrieved evidence satisfies the geospatial constraints (footprint overlap, temporal window, resolution range) specified in the query.
+
+Furthermore, we optimize the knowledge construction and retrieval modules by introducing a hyperbolic spatial hypergraph to achieve spatially faithful knowledge aggregation and physics-informed conflict handling. Specifically, the proposed approach is formally defined through the following definitions.
+
+**Definition 1. Multi-source planetary observation data.** Given a set of observation platforms $\mathcal{H}$ (e.g., MRO, Mars Express, Tianwen-1, Curiosity, Zhurong), the observation data $D = \{\mathcal{I}, \mathcal{P}_{foot}, \mathcal{T}_{win}, \mathcal{S}_{band}, c, \text{meta}\}$ exists, where $\mathcal{I}$ denotes the instrument identity, $\mathcal{P}_{foot} \subset \mathbb{S}^2_{Mars}$ denotes the spatial footprint on the Martian surface, $\mathcal{T}_{win}$ denotes the temporal acquisition window parameterized by Solar Longitude $L_s$, $\mathcal{S}_{band}$ denotes the spectral band configuration, $c$ represents the observation content (image, spectrum, or derived product), and meta represents the PDS/CNSA metadata. Through a multi-source spatial adapter parsing algorithm, we obtain normalized data $\widehat{D} = \{\text{id}, \mathcal{I}, \mathcal{P}_{foot}, \mathcal{T}_{win}, \mathcal{S}_{band}, \ell_{res}, \text{jsc}, \text{meta}\}$, where id is the unique identifier, $\ell_{res} \in \mathbb{R}^+$ denotes the ground sampling distance (spatial resolution), and jsc denotes the observation content stored using JSON-LD for linked data interoperability.
+
+**Definition 2. $N$-ary spatial knowledge hypergraph.** An $n$-ary spatial knowledge hypergraph is defined as $\mathcal{G}_{hyp} = (\mathcal{E}, \mathcal{R}, \mathcal{F}_{spa})$, where $\mathcal{E}$ denotes the entity set, $\mathcal{R}$ denotes the relation set, and $\mathcal{F}_{spa}$ denotes the set of spatial observation hyperedges. Each spatial observation hyperedge $f_{spa}^n \in \mathcal{F}_{spa}$ binds multiple entities and observation parameters into a single $n$-ary relational fact:
+
+$$f_{spa}^n = (\mathcal{I}, \; \mathcal{P}_{foot}, \; \mathcal{T}_{win}, \; \mathcal{S}_{band}, \; \mathcal{O}_{target}, \; \ell_{res}) \tag{2}$$
+
+where $\mathcal{O}_{target}$ denotes the set of target geological features. Unlike binary knowledge graphs where $k$ co-located entities require $\binom{k}{2} = O(k^2)$ pairwise edges, a single $n$-ary hyperedge binds all $k$ entities with $O(k)$ complexity, directly resolving the edge explosion problem.
+
+**Definition 3. Hyperbolic space embedding.** We represent $\mathcal{G}_{hyp}$ in $d$-dimensional hyperbolic space $\mathbb{H}_K^d$ with constant negative curvature $K < 0$ using the Lorentz (hyperboloid) model. The hyperbolic space is realized as:
+
+$$\mathbb{H}_K^d = \left\{ \mathbf{x} \in \mathbb{R}^{d+1} \mid \langle \mathbf{x}, \mathbf{x} \rangle_L = \frac{1}{K}, \; x_0 > 0 \right\} \tag{3}$$
+
+where $\langle \mathbf{x}, \mathbf{y} \rangle_L = -x_0 y_0 + \sum_{i=1}^{d} x_i y_i$ is the Lorentzian inner product. The geodesic distance between two points $\mathbf{x}, \mathbf{y} \in \mathbb{H}_K^d$ is $d_K(\mathbf{x}, \mathbf{y}) = \frac{1}{\sqrt{-K}} \cosh^{-1}(K \langle \mathbf{x}, \mathbf{y} \rangle_L)$. The radial depth $r(\mathbf{x}) = x_0$ encodes the intrinsic distance from the origin and serves as a proxy for hierarchical specificity: entities near the origin represent coarse, global-scale features, while those at large radial depth represent fine-scale, local observations.
+
+**Definition 4. Observation-grounded homologous data.** For a query $Q(q, \mathcal{G}_{hyp})$ on the spatial hypergraph $\mathcal{G}_{hyp}$, the multi-source spatial evidence retrieved in a single query is defined as observation-grounded homologous data. For any two observations $v_1$ and $v_2$ in $\mathcal{G}_{hyp}$, they are observation-grounded homologous if and only if they: (a) belong to the same retrieval candidate set, and (b) their spatial footprints satisfy $\mathcal{P}_{foot}(v_1) \cap \mathcal{P}_{foot}(v_2) \neq \varnothing$.
+
+**Definition 5. Observation-grounded knowledge source.** A planetary observation knowledge source is defined as $\mathcal{K}_s = (\mathcal{I}_s, \Omega_s, F(\mathcal{K}_s), \mathcal{M}_s)$, where $\mathcal{I}_s$ denotes the instrument, $\Omega_s = (\ell_{res}, \lambda_{band}, \theta_{view}, d_{pen})$ denotes the observation geometry parameters (spatial resolution, spectral band, viewing angle, penetration depth), $F(\mathcal{K}_s)$ denotes the set of atomic factual statements, and $\mathcal{M}_s$ denotes the physical measurement model that maps target properties through observation constraints to observable facts.
+
+**Definition 6. Conflict triage confidence.** For observation-grounded homologous data obtained from the spatial hypergraph, the conflict triage confidence integrates two levels of assessment: (a) cross-source interaction entropy to detect inter-source conflicts, and (b) physics-informed conflict classification to determine whether detected conflicts represent noise to be filtered or scientifically meaningful observational divergences to be preserved. Unlike conventional candidate confidence [14] that uniformly penalizes inconsistency, conflict triage confidence applies differentiated recalibration based on the physical origin of each conflict.
+
+
+## III. METHODOLOGY
+
+### A. Framework of AreoRAG
+
+This section elaborates on the implementation approach of AreoRAG. As shown in Fig. 3, the framework comprises three tightly coupled modules. The first step involves constructing a Hyperbolic Spatial Hypergraph (HySH) from multi-source planetary observation data, achieving unified spatiotemporal representation via $n$-ary observation hyperedges embedded in hyperbolic space (Section III-B); the second step performs spatiotemporal retrieval on the constructed HySH, where hyperbolic spatial proximity encoding and cross-resolution aggregation via the Spatial Outward Einstein Midpoint are employed to extract query-relevant multi-source evidence (Section III-C); the third step applies Physics-Informed Conflict Triage (PICT), which detects inter-source conflicts via cross-source interaction entropy, classifies them into four scientific categories, and executes conflict-aware confidence recalibration to preserve scientifically valuable disagreements while filtering noise (Section III-D). Finally, integrating the aforementioned steps to form the AreoRAG Prompting algorithm, ARP (Section III-E).
+
+The three modules interact through three explicit coupling points: (1) HySH's spatial alignment is a prerequisite for meaningful interaction entropy computation in PICT; (2) the radial depth difference $\Delta r$ from HySH directly feeds into the PICT feature vector as the resolution disparity signal; and (3) PICT's triage results feed back to boost retrieval priority of scientifically interesting regions in subsequent queries.
+
+### B. Hyperbolic Spatial Hypergraph Construction
+
+The AreoRAG method begins by constructing a knowledge structure that can faithfully represent the continuous spatiotemporal topology of planetary multi-source data. Unlike MultiRAG's Multi-source Line Graph (MLG), which relies on discrete text entities and binary triples, we introduce a hypergraph structure embedded in hyperbolic space to jointly address edge explosion and spatial scale hierarchy.
+
+**1) Multi-source Spatial Adapter Parsing:** We first design a spatial adapter for each observation data source to parse instrument metadata, spatial footprints, temporal windows, and spectral parameters. For orbital remote sensing data (e.g., HiRISE, CTX, CRISM), parsing involves extracting the image footprint geometry, ground sampling distance, and spectral band configuration from PDS labels. For in-situ data (e.g., rover spectrometers, ground-penetrating radar), parsing extracts the rover traverse coordinates, measurement timestamps in Sol, and instrument-specific parameters such as penetration depth. All temporal references are unified to Solar Longitude $L_s$ to enable cross-platform temporal comparison. For derived data products (e.g., DTMs, mineral abundance maps), parsing extracts provenance links to the source observations and processing parameters.
+
+The final integration of multi-source spatial data can be expressed as:
+
+$$D_{Fusion} = \bigcup_{i=1}^{n} A_i^{spa}(D_i) \tag{4}$$
+
+where $A_i^{spa} \in \{Ada_{orbital}, Ada_{insitu}, Ada_{derived}\}$ represents the spatial adapter parsing functions for orbital, in-situ, and derived data products respectively, and $D_i$ represents the original observation datasets from different platforms.
+
+Through the parsed data $D_{Fusion}$, we further extract entities (geological features, mineral signatures, topographic structures), relationships (spatial containment, temporal succession, compositional association), and observation-specific attributes. The knowledge extraction process employs LLM-based entity recognition guided by a planetary science domain schema:
+
+$$KB = \sum_{D_i} \left( \{e_1, e_2, \ldots, e_m\} \sqcup \{r_1, r_2, \ldots, r_n\} \sqcup \{f_{spa,1}^n, \ldots, f_{spa,p}^n\} \right) \tag{5}$$
+
+**2) Spatial Observation Hyperedge Formation:** Based on the extracted knowledge base, we construct spatial observation hyperedges that bind co-located multi-source observations into single $n$-ary facts. As formalized in Definition 2, each hyperedge $f_{spa}^n$ encapsulates the instrument, spatial footprint, temporal window, spectral bands, target features, and resolution. In a pairwise binary graph, $k$ co-existing spatial entities require $\binom{k}{2} = O(k^2)$ spatial proximity edges. With hyperedges, a single $n$-ary fact binds all $k$ entities, reducing edge complexity to $O(k)$. This directly resolves the edge explosion problem identified in our analysis of MLG.
+
+**3) Scale-Aware Lorentz Embedding:** We embed the spatial observation hypergraph in $d$-dimensional hyperbolic space $\mathbb{H}_K^d$ using the Lorentz model (Definition 3). The key innovation is coupling the radial depth with spatial resolution through an embedding mapping $\Phi: \mathcal{F}_{spa} \rightarrow \mathbb{H}_K^d$:
+
+$$r\left(\Phi(f_{spa}^n)\right) = \frac{1}{\sqrt{-K}} \cosh\left(\sqrt{-K} \cdot g(\ell_{res})\right) \tag{6}$$
+
+where $g(\ell_{res}) = -\log(\ell_{res} / \ell_{max})$ is a monotone decreasing function of resolution, and $r(\mathbf{x}) = x_0$ denotes the radial depth.
+
+This embedding design is motivated by the following observation on the intrinsic geometry of planetary spatial data:
+
+**Proposition 1** (Spatial Scale-Curvature Correspondence). *The planetary spatial observation hierarchy exhibits tree-like branching: each coarser-resolution observation spatially contains multiple finer-resolution observations. Let $N(\ell)$ denote the number of observations at resolution level $\ell$. For remote sensing data with total survey area $A_{coverage}$:*
+
+$$N(\ell) \propto A_{coverage} / \ell^2 \tag{7}$$
+
+*As resolution $\ell$ decreases (finer scale), $N(\ell)$ grows quadratically, exhibiting the exponential branching characteristic of negative-curvature spaces. Therefore, the spatial scale hierarchy is intrinsically hyperbolic, and Euclidean embedding with polynomial volume growth cannot faithfully represent it.*
+
+Through this embedding, global coarse-resolution data (e.g., MOLA topography at ~460 m) is placed near the hyperbolic origin (small radial depth), while local high-resolution data (e.g., HiRISE at 0.3 m) is placed far from the origin (large radial depth). The exponential volume growth of $\mathbb{H}_K^d$ naturally accommodates the exponentially increasing number of observations at finer scales.
+
+**4) Cross-Reference-Frame Alignment:** To address the heterogeneous reference frame problem (orbiter areocentric coordinates vs. rover-centric local coordinates), we align all observations to a global reference via parallel transport on the hyperbolic manifold:
+
+$$\Phi_{aligned}(e) = \exp_{o_g}\left(\Gamma_{o_k \to o_g}\left(\log_{o_k}(\Phi_k(e))\right)\right) \tag{8}$$
+
+where $\log_{o_k}$ is the logarithmic map at the local reference origin $o_k$, $\Gamma_{o_k \to o_g}$ is the parallel transport operator along the geodesic from $o_k$ to the global origin $o_g$, and $\exp_{o_g}$ is the exponential map at the global origin. Unlike Euclidean affine transformations, hyperbolic parallel transport preserves geodesic distances and radial depth, ensuring that scale hierarchy information is maintained after cross-frame alignment.
+
+Here, we provide a simple example of hyperbolic spatial hypergraph construction. As shown in Fig. 4, an observation region is covered by three sources at different resolutions: a CTX mosaic (6 m), an HiRISE strip (0.3 m), and a CRISM spectral cube (18 m). In the HySH, the HiRISE observation (finest resolution) is embedded at the largest radial depth, while the CRISM observation (coarsest resolution) is nearest to the origin. A spatial observation hyperedge binds all three observations and their co-located geological features into a single $n$-ary fact, without requiring $O(k^2)$ pairwise edges.
+
+
+### C. Spatiotemporal Retrieval with Cross-Resolution Aggregation
+
+After the construction of the hyperbolic spatial hypergraph, the next step is to retrieve query-relevant multi-source spatial evidence. The retrieval process comprises two phases: spatiotemporal evidence extraction and cross-resolution aggregation.
+
+**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 $\mathcal{K}_q$.
+
+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]:
+
+$$\mathcal{T}_q = \left\{ (e_h, f_{spa}^n, e_t) \mid f_{spa}^n \in \mathcal{F}_{e_s}, \; e_h \in f_{spa}^n, \; e_t \in f_{spa}^n \right\} \tag{9}$$
+
+**2) Hyperbolic Spatial Encoding and Plausibility Scoring:** For each candidate triple, we compute a spatiotemporal encoding that fuses semantic, structural, and physical-spatial signals:
+
+$$\mathbf{x} = \left[\varphi(q) \| \varphi(e_h) \| \varphi(f_{spa}^n) \| \varphi(e_t) \| \delta(e_h, f_{spa}^n, e_t) \| \psi_{geo}(e_h, e_t)\right] \tag{10}$$
+
+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:
+
+$$\psi_{geo}(e_h, e_t) = \left[d_K\left(\Phi(e_h), \Phi(e_t)\right), \; \Delta r(e_h, e_t), \; \cos\theta_{bearing}\right] \tag{11}$$
+
+Here $d_K$ is the geodesic distance in $\mathbb{H}_K^d$ capturing physical proximity, $\Delta r = |r(\Phi(e_h)) - r(\Phi(e_t))|$ encodes the scale difference via radial depth gap, and $\cos\theta_{bearing}$ encodes the directional relationship. A lightweight MLP classifier $f_\theta$ then scores the plausibility of each candidate triple:
+
+$$\text{score}(e_h, f_{spa}^n, e_t) = f_\theta(\mathbf{x}) \in [0, 1] \tag{12}$$
+
+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.
+
+**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].
+
+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 $\phi_{res}(f_i) = r(\Phi(f_i))^p$:
+
+$$\mathbf{m}_{K,p}^{Spa\text{-}OEM} = \Pi_K\left(\frac{\sum_{i=1}^{n} w_i \cdot \phi_{res}(f_i) \cdot \lambda_i \cdot \Phi(f_i)}{\sum_{i=1}^{n} w_i \cdot \phi_{res}(f_i) \cdot \lambda_i}\right) \tag{13}$$
+
+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 $v_0 > 0$.
+
+**Theorem 1** (Spatial OEM Outward Bias). *For $p \geq 1$, the Spatial OEM satisfies:*
+
+$$r(\mathbf{m}_{K,p}^{Spa\text{-}OEM}) \geq r(\mathbf{m}_K^{Ein})$$
+
+*where $\mathbf{m}_K^{Ein}$ is the standard Einstein midpoint ($p = 0$).*
+
+*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. $\square$
+
+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.
+
+
+### D. Physics-Informed Conflict Triage
+
+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.
+
+**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:
+
+$$\mathcal{H}_{inter}(p_i, p_j \mid q) = H\left(P(\text{ans} \mid q, p_i \oplus p_j)\right) - \frac{1}{2}\left[H\left(P(\text{ans} \mid q, p_i)\right) + H\left(P(\text{ans} \mid q, p_j)\right)\right] \tag{14}$$
+
+where $H(\cdot)$ is the token-averaged entropy over top-$k$ candidate tokens:
+
+$$H\left(P(\text{ans} \mid \text{context})\right) = -\frac{1}{|l|}\sum_{t=1}^{|l|}\sum_{i=1}^{k} pr_i^{(t)} \log_2 pr_i^{(t)} \tag{15}$$
+
+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.
+
+Reasoning path pairs exhibiting interaction entropy exceeding a predefined threshold $\epsilon$ are classified as detected conflicts:
+
+$$\mathcal{C}^{detected} = \{(\psi_i, \psi_j) \mid \mathcal{H}_{inter}(p_i, p_j \mid q) > \epsilon\} \tag{16}$$
+
+**2) Physics-Informed Conflict Classification:** The second stage classifies each detected conflict by its physical origin. We introduce the central distinction of PICT:
+
+**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:
+
+$$\mathcal{B}(\Omega_i, \Omega_j, \mathcal{M}_i, \mathcal{M}_j) \models \neg(\psi_i \bot \psi_j) \tag{17}$$
+
+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*.
+
+Based on this distinction, we define four conflict categories, each with a differentiated processing strategy:
+
+| Category | Condition | Strategy |
+|----------|-----------|----------|
+| Noise ($\mathcal{C}^{noise}$) | Opaque, with significant source authority disparity | Filter low-authority source |
+| Instrument-Inherent ($\mathcal{C}^{inst}$) | Explainable via $\Omega_i \neq \Omega_j$ | Preserve with physical explanation |
+| Scale-Dependent ($\mathcal{C}^{scale}$) | Explainable via $\ell_{res}^i \neq \ell_{res}^j$ | Preserve with cross-scale linkage |
+| Temporal-Evolution ($\mathcal{C}^{temp}$) | Explainable via $\mathcal{T}_i \neq \mathcal{T}_j$ | Preserve with temporal ordering |
+
+For each detected conflict, we construct a feature vector that fuses information-theoretic, physical, and neural signals:
+
+$$\mathbf{z}_{conf} = \left[\mathcal{H}_{inter}, \; \|\Omega_i - \Omega_j\|, \; |\log(\ell_{res}^i / \ell_{res}^j)|, \; \Delta\mathcal{T}, \; \rho_{auth}(i,j), \; \mathbf{h}^{(l^*)}_{conf}\right] \tag{18}$$
+
+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].
+
+A lightweight classifier maps the feature vector to conflict type:
+
+$$\hat{c} = \arg\max_{c \in \{noise, inst, scale, temp\}} P_\theta(c \mid \mathbf{z}_{conf}) \tag{19}$$
+
+**Proposition 2** (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 $\mathbf{z}_{conf}$.*
+
+**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:
+
+$$C_{triage}(v) = \begin{cases} C_{base}(v) & \text{if } v \notin \mathcal{C}^{detected} \\ \alpha \cdot C_{base}(v) + (1-\alpha) \cdot \eta & \text{if } \hat{c} = noise \\ C_{base}(v) + \beta \cdot \mathcal{H}_{inter}^{-1} & \text{if } \hat{c} \in \{inst, scale\} \\ C_{base}(v) \cdot \gamma(|\Delta\mathcal{T}|) & \text{if } \hat{c} = temp \end{cases} \tag{20}$$
+
+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.
+
+**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 $\beta > 0$:*
+
+$$C_{triage}(v) > C_{base}(v) \quad \forall v \in V_{sci} \tag{21}$$
+
+*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 $C_{triage}(v) = C_{base}(v) \cdot \gamma(|\Delta\mathcal{T}|) > C_{base}(v)$. $\square$
+
+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 identified in Section I.
+
+
+### E. AreoRAG Prompting
+
+We propose the AreoRAG Prompting (ARP) algorithm for multi-source planetary spatial data retrieval. The complete procedure is presented in Algorithm 1.
+
+---
+
+**Algorithm 1.** AreoRAG Prompting (ARP)
+
+---
+
+**procedure** ARP$(q)$
+
+$\quad$ $\mathcal{E}_q, \mathcal{R}_q, \mathcal{P}_{foot}, \mathcal{T}_{win} \leftarrow$ Spatial Intent Extraction$(q)$
+
+$\quad$ $D_q \leftarrow$ Multi-source Spatial Adapter Parsing$(D)$ $\quad\triangleright$ Eq. 4-5
+
+$\quad$ $\mathcal{G}_{hyp} \leftarrow$ HySH Construction$(D_q)$ $\quad\triangleright$ Eq. 6-8
+
+$\quad$ $\mathcal{T}_q \leftarrow$ Spatiotemporal Retrieval$(\mathcal{G}_{hyp}, \mathcal{E}_q)$ $\quad\triangleright$ Eq. 9-12
+
+$\quad$ $\mathbf{m}_{agg} \leftarrow$ Spatial OEM Aggregation$(\mathcal{T}_q)$ $\quad\triangleright$ Eq. 13
+
+$\quad$ $\mathcal{C}^{detected} \leftarrow$ Cross-Source Interaction Entropy$(\mathcal{T}_q, q)$ $\quad\triangleright$ Eq. 14-16
+
+$\quad$ **for** $(\psi_i, \psi_j) \in \mathcal{C}^{detected}$ **do**
+
+$\quad\quad$ $\hat{c} \leftarrow$ Conflict Classification$(\mathbf{z}_{conf})$ $\quad\triangleright$ Eq. 18-19
+
+$\quad\quad$ $C_{triage}(v) \leftarrow$ Confidence Recalibration$(v, \hat{c})$ $\quad\triangleright$ Eq. 20
+
+$\quad$ **end for**
+
+$\quad$ Context $\leftarrow$ Differential Context Construction$(q, \mathcal{T}_q, \hat{c})$
+
+$\quad$ Answer $\leftarrow$ LLM$(q \oplus$ Context $\oplus$ Provenance$)$
+
+$\quad$ **return** Answer
+
+**end procedure**
+
+---
+
+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).
+
+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).
+
+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.
+
+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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+## V. RELATED WORK
+
+### A. Graph-Structured Retrieval Augmented Generation
+
+Graph-based methods have become a central paradigm for enhancing the reasoning capabilities and factual grounding of Retrieval Augmented Generation (RAG) systems. Early approaches leveraged curated Knowledge Graphs (KGs) such as Wikidata and Freebase to provide structured triples or reasoning chains for LLM-based question answering [22], [27], [40]. More recently, methods that dynamically construct task-specific graphs from raw corpora have gained prominence. HippoRAG [23] draws inspiration from neurobiology to construct offline memory graphs with a neural indexing mechanism, achieving significant retrieval latency reduction. ToG 2.0 [25] introduces a graph-context co-retrieval framework that dynamically balances structured and unstructured evidence, resulting in substantial hallucination rate reduction compared to unimodal approaches. Graph-CoT [48] leverages Graph Neural Networks to establish bidirectional connections between KGs and the latent space of LLMs, reducing factual inconsistencies on KGQA benchmarks. SubGraphRAG [19] proposes a lightweight MLP-based approach that retrieves query-relevant subgraphs and encodes structural proximity through directional distance encoding, achieving state-of-the-art performance with low latency.
+
+A critical limitation of the above methods is their reliance on binary relational facts (entity-relation-entity triples), which suffer from semantic fragmentation and path explosion when representing complex multi-entity interactions [18]. To address this, hypergraph-based RAG methods have emerged. HyperGraphRAG [25b] advances the field by natively encoding $n$-ary relational facts as hyperedges, outperforming conventional KG-based RAGs through shallower yet more expressive reasoning chains. HyperRAG [18] further introduces a trainable MLP-based retriever (HyperRetriever) that fuses structural and semantic signals for adaptive $n$-ary chain construction, achieving the highest answer accuracy on WikiTopics benchmarks. OG-RAG [34b] grounds hyperedge construction in domain-specific ontologies for more interpretable evidence aggregation, though its dependence on high-quality ontologies constrains scalability.
+
+For multi-source scenarios, MultiRAG [14] proposes multi-source line graphs (MLG) to aggregate cross-domain knowledge and multi-level confidence computing (MCC) to filter unreliable nodes, achieving over 10% F1 improvement on sparse datasets. FusionQuery [34] enhances cross-domain retrieval precision through heterogeneous graph integration with dynamic credibility evaluation. KAG [26] provides a unified representation framework for multi-source KGs through the OpenSPG platform.
+
+Despite this progress, all existing graph-based RAG methods — whether binary, hypergraph, or multi-source line graph — construct their topology based on discrete text entities and explicit semantic associations. None addresses the scenario where data sources are inherently embedded in continuous physical space and where inter-entity relevance is governed by spatial proximity rather than textual co-occurrence. AreoRAG bridges this gap by introducing spatial observation hyperedges embedded in hyperbolic space, enabling faithful representation of continuous spatiotemporal topology within a graph-based retrieval framework.
+
+
+### B. Hyperbolic Representation Learning for Retrieval
+
+Hyperbolic geometry has attracted increasing attention in representation learning due to its capacity to embed hierarchical, tree-like structures with low distortion [52]-[54]. Unlike Euclidean space, where volume grows polynomially with radius, hyperbolic space exhibits exponential volume growth, naturally accommodating the branching structure of taxonomies, ontologies, and scale hierarchies. Foundational work by Nickel and Kiela [52] demonstrated that Poincar\'e embeddings of WordNet hierarchies achieve superior link prediction with substantially fewer dimensions than Euclidean counterparts. Subsequent work extended hyperbolic representations to knowledge graph embedding [53], [55], molecular generation [56], and recommendation systems [57].
+
+In the context of text retrieval, hyperbolic geometry has recently shown strong promise. HypRAG [20] introduces hyperbolic dense retrieval for RAG, developing two model variants in the Lorentz model: a fully hyperbolic transformer (HyTE-FH) and a hybrid architecture (HyTE-H). A key contribution is the Outward Einstein Midpoint (OEM), a geometry-aware pooling operator that provably preserves hierarchical structure during sequence aggregation, overcoming the radial contraction failure of naive Euclidean averaging. HypRAG achieves up to 29% gains over Euclidean baselines in context relevance on RAGBench, and demonstrates that hyperbolic representations encode document specificity through norm-based separation — with over 20% radial increase from general to specific concepts. HyperbolicRAG [58] projects embeddings into the Poincar\'e ball to encode hierarchical depth within a static knowledge graph, using dual-space retrieval that fuses Euclidean and hyperbolic rankings. HELM [59] introduces a family of hyperbolic language models that operate entirely in hyperbolic space for text generation, though not specifically targeting retrieval.
+
+These works establish the viability of hyperbolic geometry for hierarchical text retrieval, but they exclusively address the semantic hierarchy of natural language documents (broad topics → specific entities). No existing work has applied hyperbolic geometry to represent the physical scale hierarchy of scientific observations, where the hierarchy arises not from semantic abstraction but from spatial resolution (coarse global survey → fine local imaging). AreoRAG introduces the scale-curvature correspondence principle (Proposition 1), which establishes that the resolution hierarchy of planetary remote sensing data is intrinsically hyperbolic, and couples spatial resolution with radial depth in the Lorentz model. Furthermore, we extend the OEM pooling operator with resolution-aware radial weighting (Spatial OEM, Eq. 13), ensuring that cross-resolution aggregation preserves fine-scale observational details rather than collapsing them into coarse-resolution summaries.
+
+
+### C. Knowledge Conflict Detection and Resolution in RAG
+
+Knowledge conflicts — situations where different information sources provide contradictory factual statements — pose a fundamental challenge to RAG systems [60]-[62]. Research on conflict handling can be broadly categorized into impact analysis and resolution strategies.
+
+**Impact analysis.** Longpre et al. [60] first exposed entity-based knowledge conflicts in question answering, revealing that LLMs tend to rely on parametric memory when retrieved passages contain contradictory information. Xie et al. [61] found that LLMs are receptive to single external evidence but exhibit strong confirmation bias when presented with both supporting and conflicting information. Tan et al. [63] revealed a systematic bias toward self-generated contexts over retrieved ones, attributing this to higher query-context similarity of self-generated content. More recently, Tang et al. [21] formalized knowledge conflict in multimodal long-chain reasoning, distinguishing between input-level objective conflict and process-level effective conflict. Through probing internal representations, they revealed four key findings: (I) different conflict types are encoded as linearly separable features (>93% AUC with linear probes); (II) conflict signals concentrate in mid-to-late layers (depth localization); (III) aggregating token-level signals along trajectories robustly recovers input-level conflict types (hierarchical consistency); and (IV) reinforcing the model's implicit source preference is far easier than reversing it (directional asymmetry). These mechanistic insights provide the theoretical foundation for PICT's conflict classification approach.
+
+**Resolution strategies.** Existing resolution methods operate at the token level or semantic level [64]-[67]. Token-level methods such as CD$^2$ [64] manipulate attention weights to suppress parametric knowledge when conflicts are detected. ASTUTE RAG [65] uses gradient-based attribution to identify and mask conflicting tokens during inference. Semantic-level methods include CK-PLUG [66], which develops adapter-based architectures for dynamic knowledge weighting, and FaithfulRAG [67], which externalizes LLMs' parametric knowledge and aligns it with retrieved context. TruthfulRAG [17] advances to factual-level resolution by constructing knowledge graphs from retrieved content, performing query-based graph retrieval, and applying entropy-based filtering to locate conflicting elements — specifically comparing retrieval-augmented entropy against parametric-only entropy ($\Delta H_p$) to identify corrective knowledge paths. MetaRAG [9] employs metacognitive strategies for hallucination mitigation through self-reflection mechanisms.
+
+A critical and unexamined assumption shared by all existing conflict-resolution methods is that inter-source inconsistency is inherently undesirable and should be eliminated. This assumption holds in domains where authoritative ground truth exists (e.g., financial records, encyclopedic facts). However, in scientific observation scenarios — particularly deep-space exploration — the absence of absolute ground truth means that inter-source disagreements may represent legitimate multi-dimensional observations of the same phenomenon rather than errors. AreoRAG introduces a fundamentally different paradigm: Physics-Informed Conflict Triage (PICT), which classifies conflicts by their physical origin and applies differentiated processing. By replacing TruthfulRAG's parametric-vs-augmented entropy ($\Delta H_p$) with cross-source interaction entropy ($\mathcal{H}_{inter}$, Eq. 14) and incorporating physical observation parameters alongside LLM hidden-state features for four-category conflict classification (Eq. 18-19), PICT provably preserves scientifically valuable disagreements (Theorem 2) while maintaining noise-filtering capability.
+
+
+### D. Intelligent Retrieval for Planetary Remote Sensing Data
+
+Planetary remote sensing archives have grown to petabyte scale through missions such as Mars Reconnaissance Orbiter, Mars Express, Tianwen-1, Mars Science Laboratory, and Mars 2020 [1]-[4]. The primary access infrastructure — NASA's Planetary Data System (PDS) [68] and its Mars Orbital Data Explorer (ODE) [69] — provides metadata-driven search through spatial bounding box queries, temporal range filters, and instrument/product-type selectors. Similarly, CNSA's Lunar and Planetary Data Release System offers keyword-based retrieval for Chinese mission data [70]. The USGS Astrogeology Science Center maintains derived data products (DTMs, mosaics) with catalog-level metadata search [71].
+
+However, these systems operate at the level of metadata keyword matching and do not support semantic understanding of query intent, cross-source reasoning, or natural language interaction. A scientist seeking "HiRISE images showing dust devil tracks near the equator" must manually translate this into a series of coordinate-bounded, instrument-filtered queries and visually inspect each returned product — a process that is both labor-intensive and prone to missing relevant observations cataloged under different terminology.
+
+In the broader geospatial domain, the integration of AI with remote sensing data retrieval has gained momentum. GeoAI methods [72], [73] combine geographic information science with deep learning for tasks such as scene classification, object detection, and change detection. Recent work has explored the use of LLMs for geospatial reasoning [74], [75], including natural language interfaces for GIS queries and the interpretation of satellite imagery through vision-language models. Foundation models for remote sensing, such as those pre-trained on large-scale Earth observation data, have demonstrated the potential for cross-modal understanding [76], [77]. However, these efforts remain focused on Earth observation data and do not address the unique challenges of planetary science: the multi-platform observation geometry, the absence of ground truth for conflict adjudication, and the need for cross-resolution reasoning across vastly different spatial scales.
+
+To the best of our knowledge, AreoRAG is the first framework that brings RAG capabilities to planetary remote sensing data retrieval. By constructing a spatially-grounded knowledge hypergraph with physics-informed conflict handling, AreoRAG transforms the planetary data retrieval paradigm from metadata keyword matching to semantic spatial reasoning, enabling natural language queries that involve spatial proximity, temporal evolution, cross-source correlation, and scientifically informed conflict interpretation.
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+# AreoRAG 实验设计文档
+
+> 本文档用于指导后续实验执行。论文中的实验数据为估算值，需要通过以下实验流程获取真实数据后回填。每个实验标注了对应论文中的表格/图编号，方便定位回填位置。
+
+---
+
+## 一、数据集构建
+
+### 1.1 MarsRegion-QA（主数据集，对应 Table I）
+
+**目标**：构建一个多源火星空间问答数据集，覆盖5个科学重点区域。
+
+**步骤**：
+
+1. **数据获取**：
+ - 访问 NASA Mars ODE (https://ode.rsl.wustl.edu/) 下载以下5个区域的观测数据：
+ - Jezero Crater (18.38°N, 77.58°E)
+ - Gale Crater (5.4°S, 137.8°E)
+ - Utopia Planitia / 祝融着陆区 (25.1°N, 109.9°E)
+ - Valles Marineris (中心约 14°S, 294°E)
+ - Olympus Mons (18.65°N, 226.2°E)
+ - 每个区域下载：HiRISE影像元数据、CTX影像元数据、CRISM光谱立方体元数据、MOLA地形数据
+ - 祝融号数据从 CNSA 月球与深空探测科学数据与样品管理系统获取
+ - Curiosity/Perseverance 数据从 PDS Geosciences Node 获取
+
+2. **元数据解析**：
+ - 用 Python 解析 PDS4 XML labels，提取字段：
+ - `product_id` → id
+ - `instrument_id` → $\mathcal{I}$
+ - `footprint_geometry` (GML) → $\mathcal{P}_{foot}$
+ - `start_date_time` / `stop_date_time` → $\mathcal{T}_{win}$（再通过 SPICE 转为 $L_s$）
+ - `map_scale` / `pixel_resolution` → $\ell_{res}$
+ - `spectral_range` → $\mathcal{S}_{band}$
+ - 工具：`pds4_tools`, `spiceypy`（用于时间转换）
+
+3. **Query 构建**：
+ - 设计 200 个查询，分为以下类别（每类约40个）：
+ - **空间定位查询**：如"Jezero Crater 西部三角洲区域有哪些高分辨率影像？"
+ - **跨源关联查询**：如"该区域的CRISM矿物检测结果与原位测量是否一致？"
+ - **模糊地理查询**：如"祝融号着陆后前三个月向南行驶路线上的高分影像"
+ - **时序推理查询**：如"Valles Marineris 北壁在 MY34 沙尘暴前后的地貌变化"
+ - **跨分辨率推理**：如"Olympus Mons 火山口边缘的细节地形与全局地形的关系"
+ - 每个查询由 1-2 名行星科学方向的研究人员标注 ground truth 答案
+
+4. **实体/关系抽取**：
+ - 使用 LLM（Llama3-8B-Instruct）+ 行星科学 schema 进行实体识别
+ - Schema 中定义的实体类型：`Crater`, `Region`, `MineralSignature`, `Instrument`, `ObservationProduct`, `GeologicFeature`, `RoverWaypoint`
+ - 关系类型：`spatially_contains`, `temporally_precedes`, `spectrally_detects`, `compositionally_associated`, `cross_references`
+
+**预期规模**：约 96,000 个实体、53,000 条超边（回填到 Table I）
+
+### 1.2 MarsConflict-50（冲突评测集，对应 Table I、Table IV）
+
+**目标**：构建 50 个具有已知科学冲突的观测对，用于评测 PICT 的冲突分类精度。
+
+**步骤**：
+
+1. **文献检索**：从以下期刊/会议中检索记录了轨道-原位观测冲突的论文：
+ - *Journal of Geophysical Research: Planets*
+ - *Icarus*
+ - *Nature Geoscience*（火星相关）
+ - LPSC (Lunar and Planetary Science Conference) 摘要
+ - 关键词：`orbital vs in-situ`, `discrepancy`, `inconsistency`, `scale-dependent`, `mineral heterogeneity`
+
+2. **冲突对标注**：每个冲突对标注以下字段：
+ - 冲突类型（四分类）：`noise` / `instrument-inherent` / `scale-dependent` / `temporal-evolution`
+ - 涉及的数据源（如 CRISM vs. PIXL）
+ - 观测几何参数差异 $\|\Omega_i - \Omega_j\|$
+ - 时间间隔 $\Delta\mathcal{T}$（以 $L_s$ 度为单位）
+ - 科学解释（bridging explanation）
+
+3. **预期分布**：约 14 个 noise、12 个 instrument-inherent、15 个 scale-dependent、9 个 temporal-evolution（即约 72% 为非噪声科学冲突）
+
+### 1.3 MarsTemporal-QA（时序数据集，对应 Table I）
+
+**目标**：150 个需要时序推理的查询。
+
+**步骤**：
+- 选取已知存在时序变化的火星现象：RSL（季节性斜坡条纹）、沙尘暴覆盖、极冠消退、尘卷风轨迹
+- 每个查询涉及至少两个不同 $L_s$ 时相的观测
+- Ground truth 标注表面变化的类型和方向
+
+---
+
+## 二、Baseline 实现
+
+### 2.1 需要运行的 Baseline（共 8 个）
+
+| 方法 | 代码来源 | 说明 |
+|------|----------|------|
+| Standard RAG | LangChain / LlamaIndex | 标准 dense retrieval + generation |
+| IRCoT | https://github.com/stonybrooknlp/ircot | 迭代检索+CoT |
+| RQ-RAG | https://github.com/chanchimin/RQ-RAG | 查询优化RAG |
+| MultiRAG | https://github.com/wuwenlong123/MultiRAG | 主要对比对象 |
+| HyperGraphRAG | https://github.com/... (查找最新开源版本) | $n$-ary超图RAG |
+| HyperRAG | https://github.com/Vincent-Lien/HyperRAG | 超图+MLP检索 |
+| TruthfulRAG | 根据论文复现 (AAAI 2026) | 熵冲突解决 |
+| MetaRAG | 根据论文复现 | 元认知策略 |
+
+### 2.2 统一配置
+
+- **Base LLM**: Llama3-8B-Instruct（所有方法统一）
+- **Embedding Model**: gte-large-en-v1.5（统一文本嵌入）
+- **硬件**: NVIDIA A100 80GB
+- **每个方法**都需要在全部 5 个数据集（3 个火星 + 2 个通用QA）上跑完
+
+---
+
+## 三、实验执行计划
+
+### 实验 1：Overall Performance（对应 Table II — Q1）
+
+**做法**：
+1. 对每个 baseline 和 AreoRAG，在 5 个数据集上分别计算 F1 和 Recall@5
+2. 对火星数据集：使用专家标注的 ground truth 答案进行评测
+3. 对 HotpotQA / 2WikiMultiHopQA：使用原始数据集的标准评测脚本
+
+**回填位置**：`paper_experiments.md` 中 Table II 的所有数值
+
+**注意事项**：
+- HotpotQA/2WikiMultiHopQA 的 MultiRAG 数据可直接引用原论文数值
+- 火星数据集上的所有数值都需要实际跑出来
+- 确保 TruthfulRAG 在火星数据集上的 Recall@5 也要报告（论文中暂标"—"）
+
+### 实验 2：鲁棒性实验（对应 Fig. 5 — Q2）
+
+**做法**：
+
+**(a) 空间稀疏性扰动**：
+1. 在 MarsRegion-QA 的超图上，随机删除 30%/50%/70% 的超边
+2. 删除时确保每个查询对应的答案至少有一条路径可达
+3. 在扰动后的超图上运行 AreoRAG、MultiRAG、HyperRAG
+4. 记录每个扰动级别下的 F1
+
+**(b) 冲突强度扰动**：
+1. 向 MarsRegion-QA 注入 30%/50%/70% 的合成冲突三元组
+2. 合成方法：复制已有观测记录，随机替换矿物名称或坐标值
+3. 在扰动后的数据上运行 AreoRAG、MultiRAG、TruthfulRAG
+4. 记录每个扰动级别下的 F1
+
+**回填位置**：`paper_experiments.md` 中 Fig. 5(a-d) 的描述文字中的所有数值
+
+**画图**：4 个子图，x 轴为扰动比例 (0%, 30%, 50%, 70%)，y 轴为 F1
+- Fig 5(a): MarsRegion-QA 空间稀疏性，对比 AreoRAG vs MultiRAG vs HyperRAG
+- Fig 5(b): MarsTemporal-QA 空间稀疏性
+- Fig 5(c): MarsRegion-QA 冲突注入，对比 AreoRAG vs MultiRAG vs TruthfulRAG
+- Fig 5(d): MarsTemporal-QA 冲突注入
+
+### 实验 3：消融实验（对应 Table III — Q3）
+
+**做法**：在 MarsRegion-QA 和 MarsTemporal-QA 上，运行以下 8 个配置：
+
+| 配置 | HySH | 双曲嵌入 | Spatial OEM | PICT | 冲突分类 | 交互熵 |
+|------|------|----------|------------|------|----------|--------|
+| Full | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
+| w/o HySH | ✗（用MLG） | ✗ | ✗ | ✓ | ✓ | ✓ |
+| w/o Hyperbolic | ✓（欧氏超图） | ✗ | ✗ | ✓ | ✓ | ✓ |
+| w/o Spatial OEM | ✓ | ✓ | ✗（标准Einstein） | ✓ | ✓ | ✓ |
+| w/o PICT | ✓ | ✓ | ✓ | ✗（用MCC） | ✗ | ✗ |
+| w/o 冲突分类 | ✓ | ✓ | ✓ | ✓（统一过滤） | ✗ | ✓ |
+| w/o 交互熵 | ✓ | ✓ | ✓ | ✓ | ✓ | ✗（用ΔH_p） |
+| w/o Both | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
+
+每个配置记录 F1、QT（在线查询时间）、PT（离线预处理时间）。
+
+**回填位置**：`paper_experiments.md` 中 Table III 的所有数值
+
+**关键实现细节**：
+- "w/o HySH (use MLG)"：将超图替换为 MultiRAG 的线图构建方式
+- "w/o Hyperbolic"：保持超图拓扑不变，但在欧氏空间中做嵌入（用标准 TransE 类方法）
+- "w/o Spatial OEM"：用标准 Einstein midpoint（即 Eq.13 中令 $p=0$）
+- "w/o PICT (use MCC)"：用 MultiRAG 的互信息熵一致性检查 + 多级置信度
+- "w/o 冲突分类"：检测到冲突后统一降低置信度，不区分四类
+- "w/o 交互熵"：用 TruthfulRAG 的 $\Delta H_p$（参数知识 vs 检索知识的熵差）
+
+### 实验 4：冲突保留评测（对应 Table IV — Q4）
+
+**做法**：
+1. 在 MarsConflict-50 上运行 AreoRAG 和 4 个 baseline
+2. 对每个方法，记录以下指标：
+ - **CCA（冲突分类准确率）**：只有 AreoRAG 能报告此指标（其他方法不做分类）
+ - **CPR（科学冲突保留率）**：在 36 个非噪声冲突中，有多少被保留在最终 context 里
+ - **NRR（噪声拒绝率）**：在 14 个噪声冲突中，有多少被正确过滤
+ - **F1**：在含冲突的查询上的问答准确率
+
+**CCA 的计算方法**（仅 AreoRAG）：
+- 对 50 个冲突对，PICT 输出四分类标签 $\hat{c}$
+- 与专家标注的 ground truth 标签对比，计算 4-class accuracy
+- 同时绘制混淆矩阵（用于论文分析段落中描述 inst vs scale 混淆）
+
+**CPR 的计算方法**（所有方法）：
+- 检查最终传入 LLM 的 context 中，标注为 `inst/scale/temp` 类型的冲突观测对是否 **两端** 都被保留
+- 如果冲突中有一端被过滤（如 MultiRAG 的 MCC 因置信度低而剔除），则该冲突对算未保留
+
+**回填位置**：`paper_experiments.md` 中 Table IV 的所有数值
+
+### 实验 5：效率分析（对应 Table V — Q5）
+
+**做法**：
+1. 记录每个方法的两类时间：
+ - **QT（查询时间）**：从接收查询到返回答案的平均时间（秒），取 200 次查询的均值
+ - **PT（预处理时间）**：知识图谱/超图的离线构建时间（秒），一次性开销
+2. 在 MarsRegion-QA 和 MarsTemporal-QA 上分别测量
+
+**回填位置**：`paper_experiments.md` 中 Table V 的所有数值
+
+**注意**：确保所有方法都在相同硬件上测量（A100 80GB），避免测量偏差
+
+### 实验 6：Case Study（对应 Table VI）
+
+**做法**：
+1. 选取 Jezero Crater 西部三角洲矿物冲突作为示例（已在论文中写好）
+2. 实际运行 AreoRAG 和 MultiRAG，记录：
+ - HySH 模块输出的超边绑定结果和嵌入径向深度
+ - PICT 模块输出的冲突检测结果、$\mathcal{H}_{inter}$ 值、分类结果
+ - 最终生成的答案文本
+3. 用实际输出替换论文中的估算值
+
+**回填位置**：`paper_experiments.md` 中 Table VI 的具体数值（如 $\mathcal{H}_{inter}$、$C_{triage}$、径向深度等）
+
+### 实验 7：超参数敏感性分析（论文中未单独列表，但在分析中提及）
+
+**做法**：在 MarsRegion-QA 上扫描以下关键超参数：
+
+| 超参数 | 扫描范围 | 说明 |
+|--------|----------|------|
+| $K$（双曲曲率） | $\{-0.5, -1.0, -2.0, -5.0\}$ | 影响尺度层级的分辨能力 |
+| $p$（OEM 幂次） | $\{0, 1, 2, 3, 5\}$ | 0=标准Einstein, 越大越偏向高分辨率 |
+| $\epsilon$（冲突检测阈值） | $\{0.1, 0.2, 0.3, 0.5, 0.8\}$ | 越小则检测越敏感 |
+| $\beta$（科学冲突提升系数） | $\{0.05, 0.1, 0.2, 0.5\}$ | 过大可能引入噪声 |
+| $\alpha$（权威性权重） | $\{0.0, 0.25, 0.5, 0.75, 1.0\}$ | 同 MultiRAG 的 Fig. 7 |
+
+**输出**：对每组超参数记录 F1，绘制折线图。选取最佳值写入论文的超参数设置段落。
+
+---
+
+## 四、回填清单
+
+完成实验后，按以下清单逐项回填 `paper_experiments.md` 中的估算数据：
+
+- [ ] **Table I**：6 个数据集的 Entities / Hyperedges / Queries 精确数值
+- [ ] **Table II**：5×9 = 45 个 F1 和 Recall@5 数值（5个数据集 × 8个baseline + AreoRAG）
+- [ ] **Fig. 5(a-d)**：4×4×3 = 48 个 F1 数值（4 个扰动级别 × 4 个子图 × 3 个方法）
+- [ ] **Table III**：8×6 = 48 个数值（8 个消融配置 × 2 个数据集 × 3 个指标）
+- [ ] **Table IV**：5×4 = 20 个数值（5 个方法 × 4 个指标）
+- [ ] **Table V**：5×4 = 20 个数值（5 个方法 × 2 个数据集 × 2 个时间指标）
+- [ ] **Table VI**：Case Study 中的精确 $\mathcal{H}_{inter}$、$C_{triage}$、$r$ 等值
+- [ ] **超参数分析**：约 25 个 F1 值 + 对应的最优超参数确认
+
+**总计约 200+ 个数据点需要回填。**
+
+---
+
+## 五、实验优先级排序
+
+考虑到时间成本，建议按以下顺序执行：
+
+1. **P0（必须先做）**：数据集构建（1.1-1.3），这是所有实验的基础
+2. **P1（核心实验）**：实验 1 (Table II) + 实验 3 (Table III) — 证明方法有效性
+3. **P2（关键卖点）**：实验 4 (Table IV) — 这是论文最独特的贡献点
+4. **P3（完善论证）**：实验 2 (Fig. 5) + 实验 5 (Table V)
+5. **P4（锦上添花）**：实验 6 (Case Study) + 实验 7 (超参数)
+
+---
+
+## 六、关键技术实现提示
+
+### 6.1 双曲空间嵌入
+
+```python
+# 使用 geoopt 库实现 Lorentz 模型
+import geoopt
+
+# 创建 Lorentz 流形
+manifold = geoopt.Lorentz(k=-1.0)
+
+# 根据分辨率计算径向深度 (Eq. 6)
+import torch
+def resolution_to_radial_depth(ell_res, ell_max, K=-1.0):
+ g = -torch.log(ell_res / ell_max)
+ r = (1.0 / (-K)**0.5) * torch.cosh((-K)**0.5 * g)
+ return r
+
+# 平行传输对齐 (Eq. 8)
+# geoopt 提供 manifold.transp(x, y, v) 方法
+```
+
+### 6.2 交叉源交互熵
+
+```python
+# 计算 H_inter (Eq. 14)
+def cross_source_interaction_entropy(model, tokenizer, query, path_i, path_j, top_k=10):
+ # 分别计算三个熵
+ H_joint = compute_token_entropy(model, tokenizer, query, path_i + path_j, top_k)
+ H_i = compute_token_entropy(model, tokenizer, query, path_i, top_k)
+ H_j = compute_token_entropy(model, tokenizer, query, path_j, top_k)
+ H_inter = H_joint - 0.5 * (H_i + H_j)
+ return H_inter
+
+def compute_token_entropy(model, tokenizer, query, context, top_k):
+ # 拼接 query + context, forward pass, 取 top_k logits
+ # 对每个 token 位置计算 -sum(p * log2(p))
+ # 返回 token 平均熵
+ ...
+```
+
+### 6.3 冲突分类器
+
+```python
+# 轻量 MLP 分类器 (Eq. 19)
+import torch.nn as nn
+
+class ConflictClassifier(nn.Module):
+ def __init__(self, input_dim):
+ super().__init__()
+ # input_dim = 1 (H_inter) + 1 (||Omega_i - Omega_j||) + 1 (log_res_ratio)
+ # + 1 (Delta_T) + 1 (rho_auth) + hidden_dim (h_conf)
+ self.mlp = nn.Sequential(
+ nn.Linear(input_dim, 256),
+ nn.ReLU(),
+ nn.Linear(256, 128),
+ nn.ReLU(),
+ nn.Linear(128, 4) # 4 classes: noise, inst, scale, temp
+ )
+
+ def forward(self, z_conf):
+ return self.mlp(z_conf)
+```
+
+### 6.4 Spatial OEM 聚合
+
+```python
+# Spatial OEM (Eq. 13)
+def spatial_oem(embeddings, weights, p=2, K=-1.0):
+ # embeddings: [n, d+1] on Lorentz manifold
+ # weights: [n] query-relevance weights
+ radial_depth = embeddings[:, 0] # x_0 component
+ phi_res = radial_depth ** p
+ lorentz_factor = embeddings[:, 0] # lambda_i = x_{i,0}
+
+ combined_weights = weights * phi_res * lorentz_factor
+ numerator = (combined_weights.unsqueeze(-1) * embeddings).sum(dim=0)
+ denominator = combined_weights.sum()
+ pre_proj = numerator / denominator
+
+ # Reproject onto H_K^d
+ result = lorentz_project(pre_proj, K)
+ return result
+```