Pith Number

pith:CTLQIUCC

pith:2026:CTLQIUCCJVYJEYLBQGDZ7MUC6C

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Asymptotic Plateaus for Generalized Abel Equations with Financial Applications

Dragos-Patru Covei

Generalized Abel differential equations with any polynomial degree n greater than or equal to 1 possess regular solutions that exhibit sharp growth rates and exact asymptotic plateaus on bounded and unbounded domains.

arxiv:2605.02831 v2 · 2026-05-04 · math.NA · cs.NA · math.AP

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\pithnumber{CTLQIUCCJVYJEYLBQGDZ7MUC6C}

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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

We present a comprehensive investigation into a generalized class of Abel ordinary differential equations (ODEs), extending the classical cubic form to arbitrary polynomial nonlinearities of degree n ≥ 1. [...] establishing the first systematic treatment of such generalizations in the literature.

C2weakest assumption

Utilizing a unified barrier-based approach, we derive sharp growth rates and prove the existence of exact asymptotic plateaus, assuming this barrier method applies uniformly across all polynomial degrees n and both bounded and unbounded domains without additional restrictions.

C3one line summary

Generalized Abel ODEs of arbitrary polynomial degree have existence, uniqueness, and sharp asymptotics proven via barriers, validated by Radau IIA numerics, and applied to financial modeling.

Formal links

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Receipt and verification

First computed	2026-05-20T00:04:33.781009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14d70450424d7092616181879fb282f0a8ff2261aba6388ad068609646b8cd58

Aliases

arxiv: 2605.02831 · arxiv_version: 2605.02831v2 · doi: 10.48550/arxiv.2605.02831 · pith_short_12: CTLQIUCCJVYJ · pith_short_16: CTLQIUCCJVYJEYLB · pith_short_8: CTLQIUCC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CTLQIUCCJVYJEYLBQGDZ7MUC6C \
  | 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: 14d70450424d7092616181879fb282f0a8ff2261aba6388ad068609646b8cd58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9eda40382fb61959ad925d88ba89ae8a9358dc74e051bf876d273e16e95d1174",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-04T17:07:25Z",
    "title_canon_sha256": "ffcffab8ef20bf71169cf7c05ab94ca5bf34129f99c475827f8f6918877e0f09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02831",
    "kind": "arxiv",
    "version": 2
  }
}