Pith Number

pith:MBBQ5OIJ

pith:2013:MBBQ5OIJIRCZ3MISVIHE76T4AF

not attested not anchored not stored refs pending

A model for the nonautonomous Hopf bifurcation

Gerhard Keller, Tobias J\"ager, Vasso Anagnostopoulou

arxiv:1305.1579 v1 · 2013-05-07 · math.DS · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MBBQ5OIJIRCZ3MISVIHE76T4AF}

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	2026-05-18T03:26:21.305411Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60430eb90944459db112aa0e4ffa7c0161bed3ca14118b8fb921b61932092653

Aliases

arxiv: 1305.1579 · arxiv_version: 1305.1579v1 · doi: 10.48550/arxiv.1305.1579 · pith_short_12: MBBQ5OIJIRCZ · pith_short_16: MBBQ5OIJIRCZ3MIS · pith_short_8: MBBQ5OIJ

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/MBBQ5OIJIRCZ3MISVIHE76T4AF \
  | 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: 60430eb90944459db112aa0e4ffa7c0161bed3ca14118b8fb921b61932092653

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca2a529da205fc93122aa9dbef959630532de22d92ae9af5acc8701e1bcc93b6",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-05-07T16:45:35Z",
    "title_canon_sha256": "21a3fd372b5a9185ab1c01a70842927ac5a7404f2f3ddd08a70c1689162e42bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.1579",
    "kind": "arxiv",
    "version": 1
  }
}