Pith Number

pith:FHY7OOYB

pith:2026:FHY7OOYBTNMNFDZTAWLVHBL3MV

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Surface Growth Driven by an Optimality Criterion

Marco Picchi Scardaoni, Roberto Paroni, Rohan Abeyaratne

Surface growth is determined by minimizing structural mean compliance subject to a global mass constraint at each discrete step.

arxiv:2605.13602 v1 · 2026-05-13 · math-ph · math.MP

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\pithnumber{FHY7OOYBTNMNFDZTAWLVHBL3MV}

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Record completeness

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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

Through a formal limiting procedure, we derive from the time-discrete formulation a time-continuous limit in the form of a constrained gradient flow.

C2weakest assumption

The driving mechanism is encoded in an objective functional, here taken to be the structural mean compliance; growth is modeled as an irreversible surface deposition process subject to a global mass constraint.

C3one line summary

A time-discrete variational model for accretive surface growth minimizes mean compliance subject to a global mass constraint and yields a constrained gradient flow in the continuous-time limit.

References

38 extracted · 38 resolved · 0 Pith anchors

[1] Akerson, A., Bourdin, B., Bhattacharya, K. (2022). Optimal design of responsive structures.Structural and Multidisciplinary Optimization, 65. doi:10.1007/s00158-022- 03202-0 2022 · doi:10.1007/s00158-022-

[2] doi:10.1016/bs.hna.2020.10.004 , author = 2021 · doi:10.1016/bs.hna.2020.10.004

[3] Ambrosi, D., Mollica, F. (2002). On the mechanics of a growing tumor.International Journal of Engineering Science, 40(12), 1297–1316 2002

[4] Ambrosi, D., Guana, F. (2007). Stress-modulated growth.Mathematics and Mechanics of Solids, 12(3), 319–342. doi:10.1177/1081286505059739 2007 · doi:10.1177/1081286505059739

[5] Gradient Flows: In Metric Spaces and in the Space of Probability Measures 2005 · doi:10.1007/978-3-7643-8722-8

Receipt and verification

First computed	2026-05-18T02:44:22.905695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29f1f73b019b58d28f33059753857b654ee86fb0168648c9c1779b0c2b2bf555

Aliases

arxiv: 2605.13602 · arxiv_version: 2605.13602v1 · doi: 10.48550/arxiv.2605.13602 · pith_short_12: FHY7OOYBTNMN · pith_short_16: FHY7OOYBTNMNFDZT · pith_short_8: FHY7OOYB

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/FHY7OOYBTNMNFDZTAWLVHBL3MV \
  | 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: 29f1f73b019b58d28f33059753857b654ee86fb0168648c9c1779b0c2b2bf555

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94abf35e585cde190bbc2403cb87b3aa59e7efc3f9146f7642c4678681b3d017",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-13T14:36:19Z",
    "title_canon_sha256": "711f8960cd2fc6e9830af1cea4a88b69cd946668407432da9fc4601e48946802"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13602",
    "kind": "arxiv",
    "version": 1
  }
}