Pith Number

pith:JXLQV6BQ

pith:2026:JXLQV6BQHRZ7UR6LR7MTYUY5UI

not attested not anchored not stored refs resolved

On Generic Linearly Constrained Frameworks

Anthony Nixon, Hakan Guler, Zakir Deniz

Extending rigidity characterizations to matroid rank functions provides sufficient conditions for global rigidity of looped simple graphs in any dimension.

arxiv:2605.17544 v1 · 2026-05-17 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JXLQV6BQHRZ7UR6LR7MTYUY5UI}

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

By extending the characterisation of rigidity to characterise the rank function of the linearly constrained rigidity matroid (under the same loop hypothesis), sufficient conditions for a looped simple graph to be (globally) rigid in R^d are obtained.

C2weakest assumption

The generic case assumption together with the hypothesis that each vertex is incident to sufficiently many loops, which is required for the prior rigidity characterisation by Jackson, Nixon and Tanigawa to extend to the matroid rank function.

C3one line summary

Extends rigidity characterizations for linearly constrained generic frameworks to the matroid rank function and obtains sufficient conditions for global rigidity in R^d, with a sharper 2D result via discharging.

References

20 extracted · 20 resolved · 0 Pith anchors

[1] Abbot, Generalizations of Kempe’s Universality Theorem 2008

[2] D. Antolini, S. Dewar and S.-I. Tanigawa, Dilworth truncations and Hadamard products of linear spaces to appear in: SIAM Journal on Disc. Math., https://arxiv.org/pdf/2508.04798

[3] L. Asimow and B. Roth, The rigidity of graphs, Trans. Am. Math. Soc. 245 (1978), 279-289 1978

[4] J. Cruickshank, H. Guler, B. Jackson and A. Nixon, Rigidity of Linearly Constrained Frameworks, International Mathematics Research Notices 12 (2020), 3824–3840 2020

[5] J. Cruickshank, F. Mohammadi, H. J. Motwani, A. Nixon, and S.-I. Tanigawa, Global Rigidity of Line Constrained Frameworks, SIAM Journal on Disc. Math. 38 (2024), 743-763 2024

Receipt and verification

First computed	2026-05-20T00:04:45.042193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4dd70af8303c73fa47cb8fd93c531da23792fdf04f8553afecdd7e4b2b114e77

Aliases

arxiv: 2605.17544 · arxiv_version: 2605.17544v1 · doi: 10.48550/arxiv.2605.17544 · pith_short_12: JXLQV6BQHRZ7 · pith_short_16: JXLQV6BQHRZ7UR6L · pith_short_8: JXLQV6BQ

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/JXLQV6BQHRZ7UR6LR7MTYUY5UI \
  | 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: 4dd70af8303c73fa47cb8fd93c531da23792fdf04f8553afecdd7e4b2b114e77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b09181ca65146bca4046a50cc93cde7473f11a9bbf02c5a2925e83b65c1497c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-17T16:53:49Z",
    "title_canon_sha256": "69d4552ae27b17349f72787bedea74a498166cfd3e57204f08e1e33db82cdd5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17544",
    "kind": "arxiv",
    "version": 1
  }
}