Pith Number

pith:R3FT3NZK

pith:2011:R3FT3NZKBHWTL63HQ6YXJQ2GFC

not attested not anchored not stored refs pending

The Hopf bifurcation with bounded noise

Ale Jan Homburg, Ryan Botts, Todd Young

arxiv:1108.4053 v1 · 2011-08-19 · 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{R3FT3NZKBHWTL63HQ6YXJQ2GFC}

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	2026-05-18T04:14:56.278270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ecb3db72a09ed35fb6787b174c34628ac89168fdd938c71c93a27f7932de813

Aliases

arxiv: 1108.4053 · arxiv_version: 1108.4053v1 · doi: 10.48550/arxiv.1108.4053 · pith_short_12: R3FT3NZKBHWT · pith_short_16: R3FT3NZKBHWTL63H · pith_short_8: R3FT3NZK

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/R3FT3NZKBHWTL63HQ6YXJQ2GFC \
  | 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: 8ecb3db72a09ed35fb6787b174c34628ac89168fdd938c71c93a27f7932de813

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29b9d873982ec14cc6f3452ef3e6c5d4dafb502b1e04129b2b3f8e87595bf74e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-08-19T21:43:20Z",
    "title_canon_sha256": "d7504458b2c4ac0364b4cc53e90d00deaaeb12077ffe3aaef0b309a609159aa3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4053",
    "kind": "arxiv",
    "version": 1
  }
}