Pith Number

pith:IVNT2PCR

pith:2013:IVNT2PCRUJTMYGDQWIHHALJJZ4

not attested not anchored not stored refs pending

Super-Critical and Sub-Critical Hopf bifurcations in two and three dimensions

Debapriya Das, Dhruba Banerjee, Jayanta K. Bhattacharjee

arxiv:1309.5470 v1 · 2013-09-21 · nlin.CD · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IVNT2PCRUJTMYGDQWIHHALJJZ4}

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	2026-05-18T03:12:36.335993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

455b3d3c51a266cc1870b20e702d29cf31b7635562510d68b251e7f1c201fbd8

Aliases

arxiv: 1309.5470 · arxiv_version: 1309.5470v1 · doi: 10.48550/arxiv.1309.5470 · pith_short_12: IVNT2PCRUJTM · pith_short_16: IVNT2PCRUJTMYGDQ · pith_short_8: IVNT2PCR

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/IVNT2PCRUJTMYGDQWIHHALJJZ4 \
  | 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: 455b3d3c51a266cc1870b20e702d29cf31b7635562510d68b251e7f1c201fbd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5b47962d3fce38ed97eda9c0cd0c40a3bc5f6c17410b959cff84e2c13b9b392",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.CD",
    "submitted_at": "2013-09-21T12:42:15Z",
    "title_canon_sha256": "73bfa0dcd4611b4208dc4e0133e0689b4d03a1387de12a13f66d8fb119449b63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.5470",
    "kind": "arxiv",
    "version": 1
  }
}