Pith Number

pith:NPDPQV5C

pith:2026:NPDPQV5CW3CCRAZ5LTZ65RKCAO

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A survey on normal forms of real submanifolds with CR singularity

Laurent Stolovitch, Xianghong Gong

Normal forms reduce real submanifolds with CR singularities to model equations starting from Bishop's invariant.

arxiv:2605.13157 v1 · 2026-05-13 · math.CV · math.DS

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Record completeness

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3 Author claim open · sign in to claim

4 Citations 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

We survey results dating back from the seminal works of Bishop and Moser-Webster as well as more recent advances.

C2weakest assumption

The survey accurately and comprehensively represents the key results in the literature on normal forms for real submanifolds with CR singularities.

C3one line summary

A survey of normal forms for real submanifolds with CR singularities from Bishop and Moser-Webster to recent results.

References

31 extracted · 31 resolved · 0 Pith anchors

[1] [AG05] P. R. Ahern and X. Gong, A complete classification for pairs of real analytic curves in the complex plane with tangential intersection, J. Dyn. Control Syst.11(2005), no. 1, 1–71; MR2122466. Er 2005

[2] [BER97] M. S. Baouendi, P. Ebenfelt and L. P. Rothschild, Parametrization of local biholomorphisms of real analytic hypersurfaces, Asian J. Math.1(1997), no. 1, 1–16; MR1480988. [BMR02] M. S. Baouendi 1997

[3] [Be97] V. K. Beloshapka, Math. Notes61(1997), no. 5-6, 777–779; translated from Mat. Zametki61 (1997), no. 6, 931–934; MR1629829. [Bi15] G.D. Birkhoff, The Restricted Problem of Three Bodies, Rendi. d 1997

[4] [Brj71] A. D. Brjuno. Analytic form of differential equations. I, II.Trudy Moskov. Mat. Obˇ sˇ c., 25:119–262 (1971); ibid. 26 (1972), 199–239, 1971

[5] [CM88] D. Cerveau and R. Moussu. Groupes d’automorphismes de (C,0) et ´ equations diff´ erentielles ydy+· · ·= 0.Bull. S.M.F, 116 (4):459–488,1988. [Cha86] M. Chaperon. G´ eom´ etrie diff´ erentielle 1988

Receipt and verification

First computed	2026-05-18T03:08:56.963601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bc6f857a2b6c428833d5cf3eec54203bd6e21e7ad74677914d776eb11c0e74a

Aliases

arxiv: 2605.13157 · arxiv_version: 2605.13157v1 · doi: 10.48550/arxiv.2605.13157 · pith_short_12: NPDPQV5CW3CC · pith_short_16: NPDPQV5CW3CCRAZ5 · pith_short_8: NPDPQV5C

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NPDPQV5CW3CCRAZ5LTZ65RKCAO \
  | 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: 6bc6f857a2b6c428833d5cf3eec54203bd6e21e7ad74677914d776eb11c0e74a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79d1b9c1595e7a264f66329c4ba5ad42558934f053639633bffc32799d65bddf",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2026-05-13T08:20:46Z",
    "title_canon_sha256": "f7f715c2c266d0f13e1d7c4bddc2f1f5b4fbcb4ad736bdcc207d94410efb03af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13157",
    "kind": "arxiv",
    "version": 1
  }
}