Pith Number

pith:L55DMTGF

pith:2023:L55DMTGFXVHTGA7WM6YH4NT5EC

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Tip growth in a strongly concentrated aggregation model follows local geodesics

Frankie Higgs

Starting from k needles, the small-particle limit of aggregate Loewner evolution is the Laplacian path model in which tips grow along geodesics to infinity.

arxiv:2304.04417 v3 · 2023-04-10 · math.PR · math.CV

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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

Started from a non-trivial initial configuration of k needles and the same parameters, we show that the small-particle scaling limit of ALE is the Laplacian path model, introduced by Carleson and Makarov in 2002, in which the tips grow along geodesics towards ∞.

C2weakest assumption

The result assumes the same parameters as the 2018 work (where ALE converges to a single slit) together with an initial configuration of exactly k needles; the scaling limit and geodesic behavior are shown only under these choices and may fail for other parameter regimes or initial data.

C3one line summary

The small-particle scaling limit of aggregate Loewner evolution from k needles is the Laplacian path model with geodesic tip growth.

References

16 extracted · 16 resolved · 0 Pith anchors

[1] Laplacian path mo dels 2002

[2] Petroﬀ, Hansj¨ org F 2012 · doi:10.1073/pnas.1215218109

[3] Seybold, and Daniel H 2017 · doi:10.1103/physreve.95.033113

[4] Richard M. Dudley. Real Analysis and Probability . Cambridge Studies in Advanced Mathematics. Cambridge University Press, seco nd edition, 2002. doi:10.1017/CBO9780511755347 2002 · doi:10.1017/cbo9780511755347

[5] Fingered growth in cha nnel geome- try: A Loewner-equation approach 2008 · doi:10.1103/physreve.77.041602

Receipt and verification

First computed	2026-05-27T01:05:31.674164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f7a364cc5bd4f3303f667b07e367d20890074aeee382bc5f0bf19cc6891325b

Aliases

arxiv: 2304.04417 · arxiv_version: 2304.04417v3 · doi: 10.48550/arxiv.2304.04417 · pith_short_12: L55DMTGFXVHT · pith_short_16: L55DMTGFXVHTGA7W · pith_short_8: L55DMTGF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/L55DMTGFXVHTGA7WM6YH4NT5EC \
  | 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: 5f7a364cc5bd4f3303f667b07e367d20890074aeee382bc5f0bf19cc6891325b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25cf164edf02508bbeba99040dd714b4118e0f09183785eedd5e2e46910c20b9",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-04-10T06:56:23Z",
    "title_canon_sha256": "1955e78164cfee1b225892fcf038bd701e5e644c914585fb7749f601880f44a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.04417",
    "kind": "arxiv",
    "version": 3
  }
}