Pith Number

pith:CIMGY45M

pith:2012:CIMGY45MJ5QT7KZROWZ3PGWUK3

not attested not anchored not stored refs pending

Biharmonic maps into a Riemannian manifold of non-positive curvature

Hajime Urakawa, Nobumitsu Nakauchi, Sigmundur Gudmundsson

arxiv:1201.6457 v4 · 2012-01-31 · 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{CIMGY45MJ5QT7KZROWZ3PGWUK3}

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	2026-05-18T03:44:24.306968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12186c73ac4f613fab3175b3b79ad456f2c0ed944b9160ae09e1eec61cd5e4c2

Aliases

arxiv: 1201.6457 · arxiv_version: 1201.6457v4 · doi: 10.48550/arxiv.1201.6457 · pith_short_12: CIMGY45MJ5QT · pith_short_16: CIMGY45MJ5QT7KZR · pith_short_8: CIMGY45M

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/CIMGY45MJ5QT7KZROWZ3PGWUK3 \
  | 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: 12186c73ac4f613fab3175b3b79ad456f2c0ed944b9160ae09e1eec61cd5e4c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "558abfcfda45d41517bdba85e1aa7b048631bc538d5ea60710e3ddff524c30a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-01-31T06:47:40Z",
    "title_canon_sha256": "6160d0b3e5312269e977e394472210544e76de85dee027dda1c873a505a5e076"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.6457",
    "kind": "arxiv",
    "version": 4
  }
}