CEDex: Multi-Domain Scientific Perspectives

• In robotics, CEDex employs human hand-inspired conditional variational autoencoders and SDF-based optimization to generate diverse, robust grasp configurations across varied robotic end-effectors.
• In computational economics, CEDex defines a formal language for specifying combinatorial exchange protocols, enabling precise bidding representations and automated market mechanism verification.
• In astrophysics, CEDEX models central engine driven supernovae with trans-relativistic, baryon-loaded blastwave dynamics that accurately reproduce radio afterglow observations such as those seen in SN 2009bb.

CEDex refers to three distinct and technically unrelated concepts within the contemporary scientific literature: (1) the “Cross-Embodiment Dexterous Grasp Generation” method in robotics and manipulation, (2) the “Combinatorial Exchange Description Language” in auction theory and computational economics, and (3) the “Central Engine Driven EXplosion” model in supernova astrophysics. Each usage is domain-specific and technically independent. For arXiv readers, the distinctness of these usages is critical; what follows are comprehensive accounts of each.

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1. CEDex for Cross-Embodiment Dexterous Grasp Generation in Robotics

1.1 Problem Setting: Cross-Embodiment Grasp Synthesis

Cross-embodiment dexterous grasp synthesis targets the reliable generation and optimization of grasp configurations for arbitrary robotic hands—three/four/five-fingered, anthropomorphic or non-anthropomorphic—conditioned solely on an object's geometric input (e.g., point cloud). The principal challenge is generalizing across robotic end-effectors of divergent kinematic structure, where direct mapping of human-gathered or synthetic demonstrations to the robot’s native DoF is inapplicable. Conventional approaches either rely on per-gripper data collection (highly restrictive) or analytical physics-based optimization lacking human-derived contact priors, yielding suboptimal robustness and diversity (Wu et al., 29 Sep 2025).

1.2 Human-like Contact Representation via Conditional Variational Autoencoder

The CEDex method leverages human hand–object contact distributions as a universal prior. Using the MANO hand model (16 semantic parts), a conditional variational autoencoder (CVAE) is trained to model the conditional distribution $p(\mathbf{C}^h, \mathbf{P}^h \mid \mathbf{O})$, where $\mathbf{O}$ is an object point cloud, $\mathbf{C}^h$ a probabilistic human contact map, and $\mathbf{P}^h$ encodes which hand part contacts each object point. The model’s architecture includes:

• Encoder: $$q_\phi(\mathbf{z}_c, \mathbf{z}_p \mid \mathbf{C}^h, \mathbf{P}^h, \mathbf{O}) \sim \mathcal{N}(0, \mathbf{I})$$.
• Decoder: Branches predict contact probabilities and hand part assignments conditioned on object features and latent codes.
• Training loss: $$\mathcal{L} = \|\mathbf{C}^h - \hat{\mathbf{C}}^h\|_1 + \lambda_p \mathcal{L}_{\rm CE}(\mathbf{P}^h, \hat{\mathbf{P}}^h) + \lambda_{\rm KL} D_{\rm KL}(q_\phi\,||\,\mathcal{N}(0, I))$$.

Sampling this model with a novel object rapidly yields diverse, human-like contact patterns, efficiently seeding large-scale synthetic demonstration without new human data (Wu et al., 29 Sep 2025).

1.3 Topological/Kinematic Alignment and SDF-Based Optimization

Direct transfer from MANO hand semantics to arbitrary robot hands is non-trivial due to mismatched topologies. CEDex implements a hand-specific mapping by manually defining part correspondences (e.g., merging multiple human digits to a robotic Barrett finger) and performing geometric remapping (merging distributions of contact points via centroid-based vector field projection). The resulting robot-specific contact maps $(\mathbf{C}^r, \mathbf{P}^r)$ guide the alignment, where SDF-based optimization is employed:

$$\mathcal{L}_c = \sum_{k=1}^N c^r_k \sum_{b=1}^{B'} p^r_{k, b} |\mathrm{SDF}_b(o_k)|$$

Optimization is augmented by three physics-derived losses: surface proximity (SPF), external collision (ERF), and self-collision (SRF) to ensure stability and physical feasibility. The overall energy for gradient-based optimization is

$$E(\theta) = \lambda_c \mathcal{L}_c + \lambda_{\rm SPF} \mathcal{L}_{\rm SPF} + \lambda_{\rm ERF} \mathcal{L}_{\rm ERF} + \lambda_{\rm SRF} \mathcal{L}_{\rm SRF}$$

where $\theta$ comprises wrist and joint parameters.

1.4 Scale and Results: The CEDex Grasp Dataset

CEDex was used to generate the largest cross-embodiment grasp dataset to date: 500,000 object models (synthetic and real), four hand embodiments (Barrett, Robotiq-3F, Allegro, Shadow), producing more than 20 million unique robot-object grasp pairs. Batch sampling of contact priors and Monte Carlo optimization yielded for each instance a filtered pool of stable, diverse grasps (e.g., for 10 unseen objects and three hands, achieving 88.7% mean six-direction force success and substantial 6-DoF/joint diversity: 0.512 rad across successful grasps) (Wu et al., 29 Sep 2025).

1.5 Baseline Comparison and Ablation

Relative to state-of-the-art methods such as DRO-Grasp, CEDex exhibits higher average grasp success and diversity when tested on previously unseen robotic hands and objects. Ablation studies confirm the necessity of the kinematic alignment step—without it, performance deteriorates sharply (success: 27.7% versus 89.3% for full pipeline). Additionally, each physics-aware loss incrementally enhances grasp feasibility (Wu et al., 29 Sep 2025).

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2. CEDex as Combinatorial Exchange Description Language in Market Design

2.1 Language Structure and Syntax

Here, “CEDex” denotes the Combinatorial Exchange Description Language, a formal logical language for specifying, analyzing, and reasoning about exchange protocols involving combinatorial (bundle) trades of multiple goods. CEDex separates bidding language expressiveness (specifying agent preferences) from protocol (market rule) semantics (Mittelmann et al., 2021). Its core syntactic constructs are:

a) Tree-Based Bidding Language (TBBL): $$\beta ::= \langle q, j, v \rangle \quad|\quad IC^x_y (\beta_1,\ldots,\beta_k, v)$$ where leaves $\langle q, j, v \rangle$ represent single good bundles, and inner nodes represent interval-choose (allows bid logic: XOR, AND, OR as special cases).

b) Exchange Protocol Layer: A temporal logic, inspired by General Game Description Language (GDL), defines the state space, legal moves, allocations, payments, and critical numerical relations. Atomic propositions, action quantifiers (does, legal), and update rules specify protocol transitions.

2.2 Semantics: Allocation, Payments, and Validity

A CEDex instance defines for $n$ agents and $m$ goods the feasible set of “trades” (allocations), subject to:

• Bidding trees $T_i$ per agent,
• Initial allocation vectors,
• Market clearing ($\sum_{i} \lambda_{i, j} = 0$ per good),
• Node-level bid satisfaction constraints (min/max number of satisfied sub-bids, for each node).

The “winner-determination” task is formulated as a mixed-integer program with objective maximizing total declared value.

2.3 Expressivity and Protocol Properties

A CEDex specification can encode diverse protocol features:

• Budget-balance: $\sum_i \text{payment}_i = 0$,
• No-deficit/No-excess: $\sum_i \text{payment}_i \geq 0$,
• Individual rationality: utility for every agent is at least as high as if unilaterally opting out.

Formal properties are expressed as logical formulas over CEDex variables, enabling automated verification (in PTIME if the winner-determination is itself PTIME, otherwise intractable due to NP-completeness of the combinatorial allocation).

2.4 Technological Context and Limitations

CEDex subsumes prior Auction Description Language (ADL), enabling richer double-sided logic for modern combinatorial/heterogeneous exchanges (e.g., combinatorial double auctions). The language does not model epistemic or behavioral strategy; it is strictly a mechanism-specification and logical verification tool (Mittelmann et al., 2021).

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3. CEDEX: Central Engine Driven EXplosion Model in Supernovae

3.1 Origin and Physical Definition

CEDEX, in astrophysics, denotes the Central Engine Driven EXplosion scenario for certain core-collapse supernovae. Unlike canonical models where blastwave evolution is dictated by negligible ejecta mass (Blandford–McKee) or completely non-relativistic ejecta (Sedov–Taylor), CEDEX models consider a baryon-loaded, mildly relativistic shell launched by a central engine with energy $E_0$ and ejecta mass $M_0$ (Chakraborti et al., 2011, Chakraborti et al., 2010).

3.2 Dynamical Evolution

The CEDEX solution provides the exact blastwave dynamics for a shell of initial Lorentz factor $\Gamma_0$ in a stellar wind ($\rho(r) = A/(4\pi r^2)$): $$\Gamma(R) = \frac{\Gamma_0 M_0 + A R}{\sqrt{M_0^2 + 2A\Gamma_0 M_0 R + (AR)^2}}$$

$$E_{\rm th}(R) = c^2\left[-M_0 - AR + \sqrt{M_0^2 + 2A\Gamma_0 M_0 R + (AR)^2}\right]$$

The shell exhibits an extended free-expansion phase before transiting to the decelerating regime as swept-up mass becomes significant. The observer-frame time–radius relation and asymptotic behaviors bridge the gap between the BM and ST dynamics.

3.3 Synchrotron Emission and Radio Afterglow

Adopting standard shock microphysics, a fraction ($\epsilon_e$) of post-shock energy populates a power-law electron distribution, and ($\epsilon_B$) amplifies magnetic field:

$$\gamma_m = \frac{p-2}{p-1} \frac{m_p}{m_e} (\Gamma - 1)\epsilon_e$$

$B \propto \frac{1}{R}$

Key observables (break frequencies, flux normalization) evolve predictably in time, e.g., $\nu_p(t)\propto t^{-1}$, $F_{\nu_p}\approx$ const (free expansion phase), permitting direct diagnostic of engine, mass-loss, and microphysics in radio data.

3.4 Application to SN 2009bb

The CEDEX formalism explains SN 2009bb, the prototypical relativistic SN without a GRB association: with $\Gamma_0 \simeq 1.8-2.3$, $M_0 \gtrsim 10^{-2.5} M_\odot$, $E_0 \sim 10^{49}$ erg, and wind parameter $A \sim 10^{13}~{\rm g\,cm^{-1}}$, the observed radio afterglow and expansion is reproduced. The observed flat radio lightcurve and slowly evolving spectral peak directly reflect the model's predictions for a massive, baryon-loaded, engine-driven blastwave (Chakraborti et al., 2011, Chakraborti et al., 2010).

3.5 Astrophysical Implications

The CEDEX paradigm classifies a new category of trans-relativistic, engine-driven supernovae, distinct from classic GRBs, providing a unified self-similar solution across all $(M_0,\Gamma_0)$. The model is central for interpreting high-cadence radio surveys of nearby Type Ibc SNe and constraining central engine physics independent of γ-ray (GRB) detection.

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Table: Overview of CEDex Across Domains

CEDex Usage	Domain	Core Concept / Purpose
Cross-Embodiment Dexterous Grasp Generation	Robotics, AI	Human-to-robot grasp transfer and dataset scaling
Combinatorial Exchange Description Language	Computational Economics	Logical protocol specification for exchanges
Central Engine Driven EXplosion	Astrophysics	Relativistic SN blastwave analytic solution

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Each meaning of “CEDex” is defined by domain-specific literature, with no overlap of technical detail, notation, or application. For rigorous use, context and precise citation are essential (Wu et al., 29 Sep 2025, Mittelmann et al., 2021, Chakraborti et al., 2011).