Pith Number

pith:ZMYWXQ2X

pith:2026:ZMYWXQ2XDJNLMEZFPWF6PQBMQQ

not attested not anchored not stored refs resolved

Self-focusing of helicity drives finite-time singularities in inviscid flows

Mokhtar Adda-Bedia, Sergio Rica

Helicity self-focuses inside a shrinking tube to create finite-time singularities in inviscid flows.

arxiv:2605.17569 v1 · 2026-05-17 · physics.flu-dyn

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZMYWXQ2XDJNLMEZFPWF6PQBMQQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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 find that the helicity is the driving mechanism of the blow-up through a self-focusing mechanism. The flow near the singularity separates into two phases. A first phase is within a tubular region that shrinks as a power-law (t_c-t)^ν, with t_c the blow-up time, where the helicity is focused. This region is separated by a sharp interface from an outer region where the vorticity, and thus helicity, is identically zero.

C2weakest assumption

The assumption that a Leray-inspired self-similar velocity field permits an exact separation of variables that reduces the full Euler PDEs to a closed nonlinear ODE system whose solutions accurately capture the local structure of any actual finite-time singularity.

C3one line summary

Helicity self-focusing in a power-law shrinking tube drives finite-time singularities in Euler flows, yielding point-like or line-like blow-ups whose exponents are selected by conservation laws.

References

32 extracted · 32 resolved · 1 Pith anchors

[1] Amauger, J. , Josserand, C. , Pomeau, Y. & Rica, S. 2023 Two dimensional singularity turbulence . Physica D: Nonlinear Phenomena 443 , 133532 2023

[2] Anderson, J. D. 1995 Computational Fluid Dynamics: The Basics with Applications\/ . McGraw-Hill 1995

[3] Barenblatt, G. I. 1996 Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics\/ . Cambridge University Press 1996

[4] 2020 A fluid mechanic's analysis of the teacup singularity 2020

[5] Brachet, M. E. 1991 Direct simulation of three-dimensional turbulence in the T aylor- G reen vortex . Fluid Dynamics Research 8 (1), 1--8 1991

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:46.438925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb316bc3571a5ab613257d8be7c02c841f62f45dd7408b0b3b8d796eddf05237

Aliases

arxiv: 2605.17569 · arxiv_version: 2605.17569v1 · doi: 10.48550/arxiv.2605.17569 · pith_short_12: ZMYWXQ2XDJNL · pith_short_16: ZMYWXQ2XDJNLMEZF · pith_short_8: ZMYWXQ2X

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZMYWXQ2XDJNLMEZFPWF6PQBMQQ \
  | 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: cb316bc3571a5ab613257d8be7c02c841f62f45dd7408b0b3b8d796eddf05237

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e46004a394aeaee9c6107ed1c7128f60a41135b7cca6a83a03421b1a648069ad",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2026-05-17T17:58:39Z",
    "title_canon_sha256": "51d57dce25bd0ef2d8546a0ed69754f313ae50ad6cebe6f00c62e8d4d6dcbd15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17569",
    "kind": "arxiv",
    "version": 1
  }
}