Pith Number

pith:3KFWZUS6

pith:1998:3KFWZUS6KMSAFIBSH6W6ROBGAO

not attested not anchored not stored refs pending

Interactions of Andronov-Hopf and Bogdamov-Takens bifurcations

Kaijun Zhan (University of Guelph), University of Guelph), William F. Langford (Fields Institute

arxiv:math/9811178 v1 · 1998-11-08 · 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{3KFWZUS6KMSAFIBSH6W6ROBGAO}

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	2026-05-18T01:05:33.538623Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da8b6cd25e532402a0323fade8b8260384ff186bc6daa51e42692c4c9c782776

Aliases

arxiv: math/9811178 · arxiv_version: math/9811178v1 · doi: 10.48550/arxiv.math/9811178 · pith_short_12: 3KFWZUS6KMSA · pith_short_16: 3KFWZUS6KMSAFIBS · pith_short_8: 3KFWZUS6

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/3KFWZUS6KMSAFIBSH6W6ROBGAO \
  | 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: da8b6cd25e532402a0323fade8b8260384ff186bc6daa51e42692c4c9c782776

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f73d7efed11133e77f9a0c4ed47f0a51e0c1d0d196c232e3db896839daa5002",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "1998-11-08T00:00:00Z",
    "title_canon_sha256": "3c4c793584cb927fece6ba97293cefbf1bfb983dc9181a66419fc0dca0e14d9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9811178",
    "kind": "arxiv",
    "version": 1
  }
}