Pith Number

pith:NQWMDLRV

pith:2026:NQWMDLRVVS3BOFFYPHCUXVQVDL

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A fast tree algorithm for multi-component coagulation equation

Akimasa Kataoka, Taichi K. Watanabe

A tree algorithm groups similar dust aggregates to cut multi-component coagulation costs from quadratic to near-linear scaling while matching direct-method results.

arxiv:2605.18353 v1 · 2026-05-18 · astro-ph.EP · astro-ph.IM

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3 Author claim open · sign in to claim

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Claims

C1strongest claim

The algorithm reduces the computational complexity from O(N^{2d}) to O(d N^d log N), considering N bins per d components, and calculates coagulation consistently with the conventional direct method.

C2weakest assumption

We assumed that two pairs of colliding aggregates reproduce a similar outcome if the dust properties are similar, and that the ratio of dust properties in logarithmic space gives the similarity as a distance. (Abstract, paragraph describing the assumptions that enable the tree algorithm.)

C3one line summary

A tree algorithm reduces multi-component coagulation complexity from O(N^{2d}) to O(d N^d log N) by grouping similar interactions and matches direct-method results in tests with analytic solutions.

References

189 extracted · 189 resolved · 2 Pith anchors

[1] 2015 , pages = 2014 · doi:10.1088/2041-8205/808/1/l3

[2] Journal of Geophysical Research: Planets , author = · doi:10.1002/2016je005088

[3] doi:10.3847/1538-4357/ac7d58 , url = 2022 · doi:10.3847/1538-4357/ac7d58

[4] doi:10.1088/0004-637X/752/2/106 2012 · doi:10.1088/0004-637x/752/2/106

[5] A&A , volume = · doi:10.1051/0004-6361/201322151

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:05:56.683556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c2cc1ae35acb61714b879c54bd6151ac48f8a6a60cbbcdcfdcd2e9a51438fd9

Aliases

arxiv: 2605.18353 · arxiv_version: 2605.18353v1 · doi: 10.48550/arxiv.2605.18353 · pith_short_12: NQWMDLRVVS3B · pith_short_16: NQWMDLRVVS3BOFFY · pith_short_8: NQWMDLRV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NQWMDLRVVS3BOFFYPHCUXVQVDL \
  | 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: 6c2cc1ae35acb61714b879c54bd6151ac48f8a6a60cbbcdcfdcd2e9a51438fd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37ea6ee6751d56cb3165c25c3354def51473263378e66d4279b8d8a4f45dfaa8",
    "cross_cats_sorted": [
      "astro-ph.IM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.EP",
    "submitted_at": "2026-05-18T13:09:33Z",
    "title_canon_sha256": "fb26dd081671f9d5c02b0d4d96e28ce27a88670714aa6224978540bb35f47445"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18353",
    "kind": "arxiv",
    "version": 1
  }
}