Pith Number

pith:3VGJXQBK

pith:2025:3VGJXQBK4V4WW2PL76CI3TTMB3

not attested not anchored not stored refs pending

Existence of minimizers for interaction energies with external potentials

Ruiwen Shu

arxiv:2509.08761 v1 · 2025-09-10 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3VGJXQBK4V4WW2PL76CI3TTMB3}

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	2026-07-05T12:08:35.804495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd4c9bc02ae5796b69ebff848dce6c0ef87f95be6fb25768003a5d3b27683d5a

Aliases

arxiv: 2509.08761 · arxiv_version: 2509.08761v1 · doi: 10.48550/arxiv.2509.08761 · pith_short_12: 3VGJXQBK4V4W · pith_short_16: 3VGJXQBK4V4WW2PL · pith_short_8: 3VGJXQBK

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/3VGJXQBK4V4WW2PL76CI3TTMB3 \
  | 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: dd4c9bc02ae5796b69ebff848dce6c0ef87f95be6fb25768003a5d3b27683d5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b4a675d215cf25bc514a1593c47001295125a8ca36310aec0155e6878a07571",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-09-10T16:50:09Z",
    "title_canon_sha256": "296d3b4381d3904e02d295db06c54a3e868ad4d1ee76c8a2ab294ef58850e397"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.08761",
    "kind": "arxiv",
    "version": 1
  }
}