Pith Number

pith:C3VKLMV5

pith:2012:C3VKLMV5F6725T376R42NOO4SM

not attested not anchored not stored refs pending

Threshold phenomenon for the quintic wave equation in three dimensions

Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag

arxiv:1209.0347 v2 · 2012-09-03 · 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{C3VKLMV5F6725T376R42NOO4SM}

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	2026-05-18T03:46:16.288810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16eaa5b2bd2fbfaecf7ff479a6b9dc931f51247a5cd171a1b632a019b9c71222

Aliases

arxiv: 1209.0347 · arxiv_version: 1209.0347v2 · doi: 10.48550/arxiv.1209.0347 · pith_short_12: C3VKLMV5F672 · pith_short_16: C3VKLMV5F6725T37 · pith_short_8: C3VKLMV5

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/C3VKLMV5F6725T376R42NOO4SM \
  | 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: 16eaa5b2bd2fbfaecf7ff479a6b9dc931f51247a5cd171a1b632a019b9c71222

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67467d78a6d3269fae70d50de925e6c2a3707909cecddf9ce9c45d813715f44b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-09-03T13:29:17Z",
    "title_canon_sha256": "41c579d370281034313a26a2b9a9f0ebcc7c32307a77c0e8dadf406c714a4b10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0347",
    "kind": "arxiv",
    "version": 2
  }
}