Pith Number

pith:Z72TIE6M

pith:2026:Z72TIE6MHEOL2LUJCREIQ57OVN

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Ergodic Trajectory Design by Learned Pushforward Maps: Provable Coverage via Conditional Flow Matching

Ahmad Ghasemi, Ehsan Aghazadeh, Hossein Pishro-Nik, Masoud Malekzadeh

A learned pushforward map turns an analytic uniform ergodic path into trajectories whose time-averaged occupancy matches any target density with error controlled by training loss.

arxiv:2605.13063 v1 · 2026-05-13 · cs.LG

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Claims

C1strongest claim

The composed trajectory is asymptotically ergodic with respect to the learned pushforward distribution, with deviation from the target controlled by the flow-matching training loss; the three bounds combine into an end-to-end coverage bound estimable from CFM training diagnostics (certified given an architectural Lipschitz bound on v_θ).

C2weakest assumption

That a single offline-trained conditional flow matching map can transport the exact uniform ergodic occupancy of the analytic latent trajectory onto an arbitrary target density while respecting all operational constraints, with the approximation error bounded solely by the training loss and a Lipschitz constant on the learned velocity field.

C3one line summary

An analytic uniform ergodic latent trajectory is pushed forward by a conditional flow matching map to produce asymptotically ergodic trajectories matching any target density with provable coverage bounds.

References

58 extracted · 58 resolved · 0 Pith anchors

[1] Abraham, I. and Murphey, T. D. Decentralized ergodic control: distribution-driven sensing and exploration for multiagent systems.IEEE Robotics and Automation Letters, 3(4):2987–2994, 2018. 9 2018

[2] Caffarelli, L. A. The regularity of mappings with a convex potential.Journal of the American Mathematical Society, 5(1):99–104, 1992 1992

[3] and ´Swie ¸ch, A 1998

[4] Moving aerial base station networks: A stochastic geometry analysis and design perspective.IEEE Trans 2019

[5] Galceran, E. and Carreras, M. A survey on coverage path planning for robotics.Robotics and Autonomous Systems, 61(12):1258–1276, 2013 2013

Formal links

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Receipt and verification

First computed	2026-05-18T03:08:59.039144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cff53413cc391cbd2e8914488877eeab711756544351396a482b03de40127188

Aliases

arxiv: 2605.13063 · arxiv_version: 2605.13063v1 · doi: 10.48550/arxiv.2605.13063 · pith_short_12: Z72TIE6MHEOL · pith_short_16: Z72TIE6MHEOL2LUJ · pith_short_8: Z72TIE6M

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Z72TIE6MHEOL2LUJCREIQ57OVN \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: cff53413cc391cbd2e8914488877eeab711756544351396a482b03de40127188

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "140fdf4a0d0fc34f1d63f78e2254f3b5ed82df3732fb519f77882420aafcb0c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T06:34:08Z",
    "title_canon_sha256": "3fe0a4f0daee464b4049d970f977a226b85e334e3ca85535bd5516d6a32514b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13063",
    "kind": "arxiv",
    "version": 1
  }
}