Pith Number

pith:2Y7COQN6

pith:2013:2Y7COQN64XODE2TDJS4Z5IE7OO

not attested not anchored not stored refs pending

A Condition for Hopf bifurcation to occur in Equations of Lotka - Volterra Type with Delay

Chol Kim

arxiv:1309.0953 v2 · 2013-09-04 · 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{2Y7COQN64XODE2TDJS4Z5IE7OO}

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	2026-05-18T03:07:33.861384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d63e2741bee5dc326a634cb99ea09f73b94a943cb710569c851c18a2f906ff64

Aliases

arxiv: 1309.0953 · arxiv_version: 1309.0953v2 · doi: 10.48550/arxiv.1309.0953 · pith_short_12: 2Y7COQN64XOD · pith_short_16: 2Y7COQN64XODE2TD · pith_short_8: 2Y7COQN6

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/2Y7COQN64XODE2TDJS4Z5IE7OO \
  | 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: d63e2741bee5dc326a634cb99ea09f73b94a943cb710569c851c18a2f906ff64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15493e682c4753e2143458a6a840317ec21663d3bfdb63b1b2a84948d0499fa1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-09-04T09:36:12Z",
    "title_canon_sha256": "b381150781d57d028f87356911fa50b0b3af4b0ab6f27cf1387ef07da677e47f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0953",
    "kind": "arxiv",
    "version": 2
  }
}