Pith Number

pith:J4OESV5R

pith:2015:J4OESV5R5VUMYGCPBCHFHER6C6

not attested not anchored not stored refs pending

Blowup behavior of harmonic maps with finite index

Lei Liu, Youde Wang, Yuxiang Li

arxiv:1512.05970 v1 · 2015-12-18 · 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{J4OESV5R5VUMYGCPBCHFHER6C6}

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	2026-05-18T01:24:05.755301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f1c4957b1ed68cc184f088e53923e17bc8c7df108dda02a3962cb2eea6cdb54

Aliases

arxiv: 1512.05970 · arxiv_version: 1512.05970v1 · doi: 10.48550/arxiv.1512.05970 · pith_short_12: J4OESV5R5VUM · pith_short_16: J4OESV5R5VUMYGCP · pith_short_8: J4OESV5R

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/J4OESV5R5VUMYGCPBCHFHER6C6 \
  | 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: 4f1c4957b1ed68cc184f088e53923e17bc8c7df108dda02a3962cb2eea6cdb54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1011e5d0d14b20dcca202777dca2869790b11a565c07a48191c1911061f45c06",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-12-18T14:27:00Z",
    "title_canon_sha256": "d66f66cc9454d126ea6c9cd26d5d8528619b157ed12a5b984b7550cf67fb65ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05970",
    "kind": "arxiv",
    "version": 1
  }
}