Pith Number

pith:LZVWP7RI

pith:2011:LZVWP7RIIDL4XZ7IYY4DO472G7

not attested not anchored not stored refs pending

The classification of four end solutions of the Allen-Cahn equation on the plane

Frank Pacard, Michal Kowalczyk, Yong Liu

arxiv:1109.5604 v2 · 2011-09-26 · 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{LZVWP7RIIDL4XZ7IYY4DO472G7}

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	2026-05-18T04:12:01.809972Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e6b67fe2840d7cbe7e8c6383773fa37ebdeb65abd5abb4a22f5069d236a22d9

Aliases

arxiv: 1109.5604 · arxiv_version: 1109.5604v2 · doi: 10.48550/arxiv.1109.5604 · pith_short_12: LZVWP7RIIDL4 · pith_short_16: LZVWP7RIIDL4XZ7I · pith_short_8: LZVWP7RI

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/LZVWP7RIIDL4XZ7IYY4DO472G7 \
  | 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: 5e6b67fe2840d7cbe7e8c6383773fa37ebdeb65abd5abb4a22f5069d236a22d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fec66ada627e9e8d3bfcc128ea0749786c40bc78e04b200e9149cfa081094dc1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-09-26T15:31:26Z",
    "title_canon_sha256": "5ffa0faa5755369fdbf3a5bf10a3cbb8dd3c5410be96c73de383c7234e1a0272"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5604",
    "kind": "arxiv",
    "version": 2
  }
}