Pith Number

pith:5UPYNPM2

pith:2026:5UPYNPM233DHQZXFHRLOQBHV23

not attested not anchored not stored refs resolved

Self-gravity in thin protoplanetary discs: 2. Numerical convergence solved and revealing the overestimation in mass of formed planets with softening

S. Rendon Restrepo

The 2D Bessel kernel for self-gravity resolves numerical convergence in thin disc simulations and shows that softening overestimates planet masses by a factor of two to three.

arxiv:2605.13461 v1 · 2026-05-13 · astro-ph.EP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5UPYNPM233DHQZXFHRLOQBHV23}

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

The 2D Bessel formalism of gravity effectively resolves the convergence issues encountered in 2D simulations. When compared to simulations employing softened or unsoftened potentials, a small softening parameter tends to overestimate gravitational effects. This results in an artificially high number of fragments, leading to final fragment masses that are overestimated by a factor of 2-3.

C2weakest assumption

That the first-principles Bessel kernel accurately represents the vertical structure and 3D-to-2D transition in real thin discs without requiring direct validation against full 3D simulations.

C3one line summary

A new Bessel kernel for 2D disc gravity fixes convergence in GI simulations and reveals that softening prescriptions overestimate formed planet masses by a factor of 2-3.

References

57 extracted · 57 resolved · 0 Pith anchors

[1] Adams, F. C., Ruden, S. P., & Shu, F. H. 1989, ApJ, 347, 959 1989

[2] 2011, in Advances in Imaging and Electron Physics, V ol 2011

[3] Baehr, H. & Klahr, H. 2015, The Astrophysical Journal, 814, 155 2015

[4] Baehr, H., Klahr, H., & Kratter, K. M. 2017, ApJ, 848, 40 2017

[5] Baruteau, C. & Masset, F. 2008, ApJ, 678, 483 2008

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:41.702950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed1f86bd9adec67866e53c56e804f5d6f453a2646a1af6da271594054f922279

Aliases

arxiv: 2605.13461 · arxiv_version: 2605.13461v1 · doi: 10.48550/arxiv.2605.13461 · pith_short_12: 5UPYNPM233DH · pith_short_16: 5UPYNPM233DHQZXF · pith_short_8: 5UPYNPM2

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/5UPYNPM233DHQZXFHRLOQBHV23 \
  | 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: ed1f86bd9adec67866e53c56e804f5d6f453a2646a1af6da271594054f922279

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "435e7230bef4ec772eb518c0a764e60a865520b20d9439a9b994fb6ae8da2833",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.EP",
    "submitted_at": "2026-05-13T12:53:08Z",
    "title_canon_sha256": "da0d96d38d095f76083500e7b94e57afe97b23c81ae27113f2cec360ee0e797a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13461",
    "kind": "arxiv",
    "version": 1
  }
}