Pith Number

pith:424PH4XC

pith:2015:424PH4XCHNMCSERHI4HUMDI6BN

not attested not anchored not stored refs pending

The bifurcation diagram of cubic polynomial vector fields on $\mathbb{C}\mathbb{P}^1$

Christiane Rousseau

arxiv:1506.07120 v1 · 2015-06-23 · 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{424PH4XCHNMCSERHI4HUMDI6BN}

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	2026-05-18T01:40:55.101520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6b8f3f2e23b58291227470f460d1e0b7166ed6288bf92599e6fee9696978ce9

Aliases

arxiv: 1506.07120 · arxiv_version: 1506.07120v1 · doi: 10.48550/arxiv.1506.07120 · pith_short_12: 424PH4XCHNMC · pith_short_16: 424PH4XCHNMCSERH · pith_short_8: 424PH4XC

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/424PH4XCHNMCSERHI4HUMDI6BN \
  | 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: e6b8f3f2e23b58291227470f460d1e0b7166ed6288bf92599e6fee9696978ce9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d94d48d67105baf2e3a1f62531eef7a5cf60207a1cf80dec24c951cd170905b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-06-23T18:24:50Z",
    "title_canon_sha256": "ca0f1f0843950862474cc70024e1e2a4b0cabc33cee6c8813cbbafd987d2ae01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.07120",
    "kind": "arxiv",
    "version": 1
  }
}