Pith Number

pith:B7KDYGNO

pith:2026:B7KDYGNOVIJ5H2VRDEJLAGVOEO

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Bifurcations and Structural Stability of Generic PC-HC Families

Alexey Dorovskiy

Generic families of PC-HC vector fields on the sphere are structurally stable near their large bifurcation supports under moderate equivalence.

arxiv:2605.12636 v1 · 2026-05-12 · math.DS

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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

In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere S² is proved.

C2weakest assumption

The families are generic within the PC-HC class and the classification and stability hold in neighborhoods of their large bifurcation supports under moderate equivalence.

C3one line summary

Structural stability of generic PC-HC vector field families on S² is proved, with classification via configuration and characteristic set invariants, a realization lemma, and constructed bifurcation diagrams.

References

9 extracted · 9 resolved · 1 Pith anchors

[1] Arnold, V. I.; Afrajmovich, V. S.; Ilyashenko, Yu. S.; Shilnikov, L. P. Bifurcation the- ory in Bifurcation theory and catastrophe theory. Translated from the 1986 Russian original by N. D. Kazarinoff 1986

[2] Large bifurcation supports 2018 · arXiv:1804.04596

[3] Global bifurcations in generic one-parameter families with a parabolic cycle on S2

[4] Germs of bifurcation diagrams and SN-SN families 2021 · doi:10.1063/5.0030742

[5] Global bifurcations in the two-sphere: a new perspective, Invent 2018

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:10:00.065463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fd43c19aeaa13d3eab11912b01aae2384e20c974eb13dde06273f797f535149

Aliases

arxiv: 2605.12636 · arxiv_version: 2605.12636v1 · doi: 10.48550/arxiv.2605.12636 · pith_short_12: B7KDYGNOVIJ5 · pith_short_16: B7KDYGNOVIJ5H2VR · pith_short_8: B7KDYGNO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/B7KDYGNOVIJ5H2VRDEJLAGVOEO \
  | 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: 0fd43c19aeaa13d3eab11912b01aae2384e20c974eb13dde06273f797f535149

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4342a439a42ff3304a44b05649f996deb1c363a3a9b1e86f46e854067bcf3e59",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-12T18:25:16Z",
    "title_canon_sha256": "528209ba9a79f6f6761d309f3ff172f34be8084f604dd1dcd26eaaba98202a8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12636",
    "kind": "arxiv",
    "version": 1
  }
}