Pith Number

pith:JPNKXEGG

pith:2011:JPNKXEGGFMYZFA7PVAPGSXFKXR

not attested not anchored not stored refs pending

Finite Element Error Estimates for Critical Growth Semilinear Problems without Angle Conditions

Michael Holst, Randolph E. Bank, Ryan Szypowski, Yunrong Zhu

arxiv:1108.3661 v2 · 2011-08-18 · math.NA · 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{JPNKXEGGFMYZFA7PVAPGSXFKXR}

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	2026-05-18T04:05:57.491672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bdaab90c62b319283efa81e695caabc65a3f87a41e03dad57314a8ccfc4546b

Aliases

arxiv: 1108.3661 · arxiv_version: 1108.3661v2 · doi: 10.48550/arxiv.1108.3661 · pith_short_12: JPNKXEGGFMYZ · pith_short_16: JPNKXEGGFMYZFA7P · pith_short_8: JPNKXEGG

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/JPNKXEGGFMYZFA7PVAPGSXFKXR \
  | 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: 4bdaab90c62b319283efa81e695caabc65a3f87a41e03dad57314a8ccfc4546b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e340e3b0047a731e10c36c287d6f72538e7ccb429239820c706358b76a7f26ba",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2011-08-18T06:54:25Z",
    "title_canon_sha256": "1bddcfd59c930fb61a0347040a527d34f2919a393135ca9fbfe0c871dcc729b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3661",
    "kind": "arxiv",
    "version": 2
  }
}