Pith Number

pith:RHGQF46L

pith:2019:RHGQF46L6AFJQA7DNQ2GYDWBND

not attested not anchored not stored refs pending

Busemann functions on the Wasserstein space

Guomin Zhu, Wen-Long Li, Xiaojun Cui

arxiv:1905.05544 v3 · 2019-05-14 · math.DS · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RHGQF46L6AFJQA7DNQ2GYDWBND}

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	2026-07-05T00:11:33.884776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89cd02f3cbf00a9803e36c346c0ec168f69064bd0b0588a12868617e28898704

Aliases

arxiv: 1905.05544 · arxiv_version: 1905.05544v3 · doi: 10.48550/arxiv.1905.05544 · pith_short_12: RHGQF46L6AFJ · pith_short_16: RHGQF46L6AFJQA7D · pith_short_8: RHGQF46L

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/RHGQF46L6AFJQA7DNQ2GYDWBND \
  | 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: 89cd02f3cbf00a9803e36c346c0ec168f69064bd0b0588a12868617e28898704

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29ef943d4eda8b0325960aeb8fa6aaa82d7f11e61e4d7cc764966c11e95f69db",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-05-14T12:17:12Z",
    "title_canon_sha256": "1764ce8e00a202dd7a1d31484b72923822b6ee823b0d2b682b5447e4c5e04408"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.05544",
    "kind": "arxiv",
    "version": 3
  }
}