Pith Number

pith:U6ZI5NWR

pith:2026:U6ZI5NWRLFIM2EU2WKRABIEVJV

not attested not anchored not stored refs pending

Global Convergence of the Return Dynamics in the Class $\mathcal{O}_C$

Mohamed El Morsalani, Mohammed Barkatou

The return dynamics in class O_C domains converge globally to the critical points of the thickness function.

arxiv:2603.28453 v3 · 2026-03-30 · math.DS

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\pithnumber{U6ZI5NWRLFIM2EU2WKRABIEVJV}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The fixed points of this dynamics coincide with the critical points of the thickness function. The motion behaves, to a first-order approximation, like an adaptive gradient descent for the domain's thickness.

C2weakest assumption

The domains belong to the class O_C with a fixed convex core and admit a radial structure defined by a thickness function linking the boundaries.

C3one line summary

Return dynamics in the class O_C converge globally to critical points of the thickness function by approximating adaptive gradient descent.

Cited by

1 paper in Pith

Inverse Problems for the Return Map in the Class ( $\mathcal{O}_C$ ): Reconstruction and Identifiability

Receipt and verification

First computed	2026-07-15T01:21:52.390726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7b28eb6d15950cd129ab2a200a0954d79d795296fd5e118e3bd463572592fa6

Aliases

arxiv: 2603.28453 · arxiv_version: 2603.28453v3 · doi: 10.48550/arxiv.2603.28453 · pith_short_12: U6ZI5NWRLFIM · pith_short_16: U6ZI5NWRLFIM2EU2 · pith_short_8: U6ZI5NWR

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/U6ZI5NWRLFIM2EU2WKRABIEVJV \
  | 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: a7b28eb6d15950cd129ab2a200a0954d79d795296fd5e118e3bd463572592fa6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f15749869138aac3531ec7dc54d6abfae1290f00ae846ec02efc55f33384d57d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-03-30T13:56:24Z",
    "title_canon_sha256": "e655bbfc0c42ff2063a9cce0596045bf706bef0e080bbdc0fe34578d44a48f83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.28453",
    "kind": "arxiv",
    "version": 3
  }
}