Pith Number

pith:P33KMP7U

pith:2011:P33KMP7U55X2UTCR2G2VBQSB42

not attested not anchored not stored refs pending

Unfoldings of singular Hopf bifurcation

John Guckenheimer, Philipp Meerkamp

arxiv:1107.3185 v1 · 2011-07-16 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P33KMP7U55X2UTCR2G2VBQSB42}

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	2026-05-18T04:18:03.728010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ef6a63ff4ef6faa4c51d1b550c241e6b0d8f39f9e760815f799cb27b3ffd3e2

Aliases

arxiv: 1107.3185 · arxiv_version: 1107.3185v1 · doi: 10.48550/arxiv.1107.3185 · pith_short_12: P33KMP7U55X2 · pith_short_16: P33KMP7U55X2UTCR · pith_short_8: P33KMP7U

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/P33KMP7U55X2UTCR2G2VBQSB42 \
  | 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: 7ef6a63ff4ef6faa4c51d1b550c241e6b0d8f39f9e760815f799cb27b3ffd3e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5dee2f76ea325b1229a71b24b917ccab9f78600d4111148abcd76ee0fe6b2813",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-07-16T00:06:54Z",
    "title_canon_sha256": "419a72528415cc6c0cfed7a19e93a5bd6bf832de300c9d7cbaef521de1282821"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3185",
    "kind": "arxiv",
    "version": 1
  }
}