Pith Number

pith:CIYY7Y2R

pith:2012:CIYY7Y2RHZ7WWU3VXSBT2KXCI3

not attested not anchored not stored refs pending

Biharmonic Pseudo-Riemannian submersions from 3-manifolds

Cengizhan Murathan, Irem K\"upeli Erken

arxiv:1206.1768 v3 · 2012-06-08 · 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{CIYY7Y2RHZ7WWU3VXSBT2KXCI3}

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	2026-05-18T00:50:36.176310Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12318fe3513e7f6b5375bc833d2ae246fb86e0a3e500f047e7cf21402227fc58

Aliases

arxiv: 1206.1768 · arxiv_version: 1206.1768v3 · doi: 10.48550/arxiv.1206.1768 · pith_short_12: CIYY7Y2RHZ7W · pith_short_16: CIYY7Y2RHZ7WWU3V · pith_short_8: CIYY7Y2R

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/CIYY7Y2RHZ7WWU3VXSBT2KXCI3 \
  | 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: 12318fe3513e7f6b5375bc833d2ae246fb86e0a3e500f047e7cf21402227fc58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4e9e954b39d81257467f0da6ed641e66ab3e441d89cb73ed966d99774dcc132",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-06-08T14:12:21Z",
    "title_canon_sha256": "9d5da57c90847c2d14bdd7ae10172ffa2dd584b9349f3f0b8b63b735dbb28cd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1768",
    "kind": "arxiv",
    "version": 3
  }
}