Pith Number

pith:32IPRTLV

pith:2007:32IPRTLVLRICKNAYIGOKXSXK6O

not attested not anchored not stored refs pending

Singular limits for the bi-laplacian operator with exponential nonlinearity in $\R^4$

Claudio Mu\~noz, M\'onica Clapp, Monica Musso

arxiv:0709.2878 v1 · 2007-09-18 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{32IPRTLVLRICKNAYIGOKXSXK6O}

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	2026-05-18T02:16:11.165232Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de90f8cd755c50253418419cabcaeaf3a9d7adc6c2c23f2c4b985a8764420645

Aliases

arxiv: 0709.2878 · arxiv_version: 0709.2878v1 · doi: 10.48550/arxiv.0709.2878 · pith_short_12: 32IPRTLVLRIC · pith_short_16: 32IPRTLVLRICKNAY · pith_short_8: 32IPRTLV

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/32IPRTLVLRICKNAYIGOKXSXK6O \
  | 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: de90f8cd755c50253418419cabcaeaf3a9d7adc6c2c23f2c4b985a8764420645

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5e6601f8b94121368c994c2922f1fe9633b128b8aebaf58400d366c9682b006",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-09-18T16:46:21Z",
    "title_canon_sha256": "549ea5fccc4d180fd0dc9a6666c86ba5d6ec99167fd2b795d772dcd676d552d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.2878",
    "kind": "arxiv",
    "version": 1
  }
}