Pith Number

pith:4YPMNO4E

pith:2026:4YPMNO4EXW6X4AI33YJRDMRLQJ

not attested not anchored not stored refs pending

Poincar\'e-Einstein 4-manifolds with cusps

Hongyi Liu, Mingyang Li

arxiv:2605.25462 v1 · 2026-05-25 · math.DG · math-ph · math.AP · 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{4YPMNO4EXW6X4AI33YJRDMRLQJ}

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	2026-05-26T02:04:37.123345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e61ec6bb84bdbd7e011bde1311b22b824636040fc1cf461d22ca1930e3d86961

Aliases

arxiv: 2605.25462 · arxiv_version: 2605.25462v1 · doi: 10.48550/arxiv.2605.25462 · pith_short_12: 4YPMNO4EXW6X · pith_short_16: 4YPMNO4EXW6X4AI3 · pith_short_8: 4YPMNO4E

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/4YPMNO4EXW6X4AI33YJRDMRLQJ \
  | 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: e61ec6bb84bdbd7e011bde1311b22b824636040fc1cf461d22ca1930e3d86961

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02b2004787d9dbc952c936ae44fde0092cdddcb462be3e73e79b68ddb59a75fa",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-25T06:14:19Z",
    "title_canon_sha256": "8fb1cb3b55ec8e29292eb8c3f225a24f7ba4dc9a046a407097732fe69bdb203c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.25462",
    "kind": "arxiv",
    "version": 1
  }
}