Pith Number

pith:BKBNNJN2

pith:2011:BKBNNJN2YYFADGSOL6BQKPKJDA

not attested not anchored not stored refs pending

Liouville theorems for F-harmonic maps and their applications

Guilin Yang, Hezi Lin, Yuxin Dong

arxiv:1111.1882 v1 · 2011-11-08 · 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{BKBNNJN2YYFADGSOL6BQKPKJDA}

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	2026-05-18T04:09:24.520366Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a82d6a5bac60a019a4e5f83053d491826ba03a0b8b3929f6b334ddaceeb7002

Aliases

arxiv: 1111.1882 · arxiv_version: 1111.1882v1 · doi: 10.48550/arxiv.1111.1882 · pith_short_12: BKBNNJN2YYFA · pith_short_16: BKBNNJN2YYFADGSO · pith_short_8: BKBNNJN2

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/BKBNNJN2YYFADGSOL6BQKPKJDA \
  | 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: 0a82d6a5bac60a019a4e5f83053d491826ba03a0b8b3929f6b334ddaceeb7002

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a795fd6ee9eb9b71c7688055b6efe116ed1fa002e9974fcf0b48c3ab98164e15",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-11-08T12:15:59Z",
    "title_canon_sha256": "3a832e4800570395ae10c2edc8c59930e4455b021e613ac5784c224801956a37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1882",
    "kind": "arxiv",
    "version": 1
  }
}