Pith Number

pith:RDX54MFQ

pith:2009:RDX54MFQ7QVOCEU2BUSM37BSKD

not attested not anchored not stored refs pending

Removable singularities and bubbling of harmonic maps and biharmonic maps

Hajime Urakawa, Nabumitsu Nakauchi

arxiv:0912.4086 v4 · 2009-12-21 · math.DG · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RDX54MFQ7QVOCEU2BUSM37BSKD}

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	2026-05-18T03:57:25.479695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88efde30b0fc2ae1129a0d24cdfc3250dfba0100703053d3bc0c5c506770dbd2

Aliases

arxiv: 0912.4086 · arxiv_version: 0912.4086v4 · doi: 10.48550/arxiv.0912.4086 · pith_short_12: RDX54MFQ7QVO · pith_short_16: RDX54MFQ7QVOCEU2 · pith_short_8: RDX54MFQ

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/RDX54MFQ7QVOCEU2BUSM37BSKD \
  | 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: 88efde30b0fc2ae1129a0d24cdfc3250dfba0100703053d3bc0c5c506770dbd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d92b097b239d29ddafc1a351972c90ce488e449c455d68b8d2041acdf776e02",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-12-21T06:45:06Z",
    "title_canon_sha256": "e38bcbe0b38c8e92446d69d5cf61f33f88f0e28add0064868add34e4602ad3b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.4086",
    "kind": "arxiv",
    "version": 4
  }
}