Pith Number

pith:ILGKJC3Y

pith:2025:ILGKJC3YM4FP26MTAJT3XACIX7

not attested not anchored not stored refs pending

Symmetric Central Configurations in the Concave 4-Body Problem with Two Pairs of Equal Masses

Yangshanshan Liu, Zhifu Xie

arxiv:2510.25638 v2 · 2025-10-29 · math.DS · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ILGKJC3YM4FP26MTAJT3XACIX7}

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.

Receipt and verification

First computed	2026-06-19T16:12:15.964874Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42cca48b78670afd79930267bb8048bff86ebc36d7290de2d9c2cd4f139bf289

Aliases

arxiv: 2510.25638 · arxiv_version: 2510.25638v2 · doi: 10.48550/arxiv.2510.25638 · pith_short_12: ILGKJC3YM4FP · pith_short_16: ILGKJC3YM4FP26MT · pith_short_8: ILGKJC3Y

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/ILGKJC3YM4FP26MTAJT3XACIX7 \
  | 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: 42cca48b78670afd79930267bb8048bff86ebc36d7290de2d9c2cd4f139bf289

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d492282c8fc9014a23eb2e46896d2beec2d52f1abfb23fd8c8588004d9f1e8e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-10-29T15:57:58Z",
    "title_canon_sha256": "8204f219dcb9acac9ca79bffdb4d2f0cc40ff9bd2374b141fb348f68791e5d8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.25638",
    "kind": "arxiv",
    "version": 2
  }
}