Pith Number

pith:VBCHZ4IA

pith:2026:VBCHZ4IA6IGVAOSSO4RDO2TZGU

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Star-collision in random hypergraphs

Kartick Adhikari, Samiron Parui

Nontrivial units disappear with high probability in random hypergraphs under specific regimes.

arxiv:2605.16856 v1 · 2026-05-16 · math.CO · math.PR

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\pithnumber{VBCHZ4IA6IGVAOSSO4RDO2TZGU}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

nontrivial units disappear with high probability as the number of vertices grows. As a consequence, star-dependent matrices exhibit asymptotically trivial local structure, and their spectral behavior, invariant subspaces, and associated linear dynamics are governed by a reduced quotient object obtained by contracting vertex stars.

C2weakest assumption

The disappearance holds only in some particular regimes of the random k-uniform hypergraph model (specific ranges of uniformity k and edge probability).

C3one line summary

In random k-uniform hypergraphs, star collisions cause nontrivial units to disappear with high probability, yielding asymptotically trivial local structure for star-dependent matrices governed by a quotient object.

References

38 extracted · 38 resolved · 0 Pith anchors

[1] K. Adhikari and A. Khatun , On the diameter of random uniform hypergraphs in dense regime , arXiv preprint arXiv:2512.04544, (2025) 2025

[2] K. Adhikari and S. Parui , Spectrum and local weak convergence of sparse random uniform hypergraphs , arXiv preprint arXiv:2509.05102, (2025) 2025

[3] D. Aldous and J. M. Steele , The objective method: probabilistic combinatorial optimization and local weak convergence , in Probability on discrete structures, Springer, 2004, pp. 1--72 2004

[4] Banerjee , On the spectrum of hypergraphs , Linear Algebra and its Applications, 614 (2021), pp 2021

[5] A. Banerjee, A. Char, and B. Mondal , Spectra of general hypergraphs , Linear Algebra Appl., 518 (2017), pp. 14--30 2017

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:26.473582Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8447cf100f20d503a527722376a7935169529c2e8b8b9a8918c1cde61363ae8

Aliases

arxiv: 2605.16856 · arxiv_version: 2605.16856v1 · doi: 10.48550/arxiv.2605.16856 · pith_short_12: VBCHZ4IA6IGV · pith_short_16: VBCHZ4IA6IGVAOSS · pith_short_8: VBCHZ4IA

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/VBCHZ4IA6IGVAOSSO4RDO2TZGU \
  | 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: a8447cf100f20d503a527722376a7935169529c2e8b8b9a8918c1cde61363ae8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebb3c1ecc8e24c93d68c2149de3b9407f704c4666b349c604673dc990d997f93",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-16T07:41:14Z",
    "title_canon_sha256": "b46a2b967bbc93e5b152123904c4c0acf396ee2a02a43dd6d5519aa1a3b04ca9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16856",
    "kind": "arxiv",
    "version": 1
  }
}