Pith Number

pith:TPFI2HLF

pith:2026:TPFI2HLFYEHXV26ZOGOS75LU5M

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Identification of Non-Transversal Bifurcations of Linkages

Andreas Mueller, J. S. Dai, P. C. L\'opez Custodio

The kinematic tangent cone already contains all information needed to separate non-transversal motion branches in linkages.

arxiv:2605.13094 v1 · 2026-05-13 · cs.RO

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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

It is shown in this paper that the constructive definition of the kinematic tangent cone already involves all information necessary to separate different motion branches.

C2weakest assumption

That amending the algorithmic framework from previous publications is sufficient to extract branch-separation information directly from the kinematic tangent cone without requiring additional external data or geometric assumptions.

C3one line summary

The constructive definition of the kinematic tangent cone contains all information necessary to separate different motion branches at non-transversal bifurcations, enabling an amended computational identification method.

References

42 extracted · 42 resolved · 0 Pith anchors

[1] K. Wohlhart, “Kinematotropic linkages,” ser. Recent Ad - vances in Robot Kinematics, V . P .-C. J. Lenarˇ ciˇ c, Ed. Kluwer, 1996, pp. 359–368 1996

[2] A variable-dof single-loop 7R spatial mechani sm with ﬁve motion modes, 2018

[3] On Implicitization of Kine- matic Constraint Equations, 2010

[4] Mechanism constraints and singularities—the algebraic formulation, 2019

[5] Analysing sin - gularities of a benchmark problem, 2008

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:08:58.403230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bca8d1d65c10f7aebd9719d2ff574eb10be30e6c811b919e21d392651bce858

Aliases

arxiv: 2605.13094 · arxiv_version: 2605.13094v1 · doi: 10.48550/arxiv.2605.13094 · pith_short_12: TPFI2HLFYEHX · pith_short_16: TPFI2HLFYEHXV26Z · pith_short_8: TPFI2HLF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TPFI2HLFYEHXV26ZOGOS75LU5M \
  | 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: 9bca8d1d65c10f7aebd9719d2ff574eb10be30e6c811b919e21d392651bce858

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8530dfe7bb54a45ce66e609a326fe6e1e299ea998f673b2c550263e7889bd62d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.RO",
    "submitted_at": "2026-05-13T07:05:41Z",
    "title_canon_sha256": "c634a35e859f1b518e9dce72c72ed8eb8e742c6167042bb33a41ff8a48e497fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13094",
    "kind": "arxiv",
    "version": 1
  }
}