Pith Number

pith:WWXTTGTD

pith:2013:WWXTTGTDH6B7QU2M4TLDYIBVR4

not attested not anchored not stored refs pending

Liouville type theorems for transversally harmonic and biharmonic maps

Min Joo Jung, Seoung Dal Jung

arxiv:1307.3627 v3 · 2013-07-13 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WWXTTGTDH6B7QU2M4TLDYIBVR4}

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	2026-05-18T01:11:44.039289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5af399a633f83f8534ce4d63c20358f30f46a1e308cfea7d935fe9205e507ce

Aliases

arxiv: 1307.3627 · arxiv_version: 1307.3627v3 · doi: 10.48550/arxiv.1307.3627 · pith_short_12: WWXTTGTDH6B7 · pith_short_16: WWXTTGTDH6B7QU2M · pith_short_8: WWXTTGTD

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/WWXTTGTDH6B7QU2M4TLDYIBVR4 \
  | 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: b5af399a633f83f8534ce4d63c20358f30f46a1e308cfea7d935fe9205e507ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7732bd2872c30f8b293100a866d4c6b518ecc750bfd0ee906e788563e5d3b603",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-07-13T07:53:41Z",
    "title_canon_sha256": "e649142719de31ef5159d2e6e7b35ec80ef8541f366952cfa18027a4ef03ea29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.3627",
    "kind": "arxiv",
    "version": 3
  }
}