Pith Number

pith:F3MROQ75

pith:2014:F3MROQ75IGKLHKIBMQKE55DKT4

not attested not anchored not stored refs pending

Inverse Jacobian multipliers and Hopf bifurcation on center manifolds

Xiang Zhang

arxiv:1407.7942 v1 · 2014-07-30 · math.CA · 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{F3MROQ75IGKLHKIBMQKE55DKT4}

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	2026-05-18T02:46:14.052618Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ed91743fd4194b3a90164144ef46a9f1cf838d24a99ae8df506d0d94a0881f4

Aliases

arxiv: 1407.7942 · arxiv_version: 1407.7942v1 · doi: 10.48550/arxiv.1407.7942 · pith_short_12: F3MROQ75IGKL · pith_short_16: F3MROQ75IGKLHKIB · pith_short_8: F3MROQ75

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/F3MROQ75IGKLHKIBMQKE55DKT4 \
  | 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: 2ed91743fd4194b3a90164144ef46a9f1cf838d24a99ae8df506d0d94a0881f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9e9049fbe920e88ea1a0520f960565c3b676aebdb426d5c9c9e6b54ba8ac39d",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-07-30T05:03:59Z",
    "title_canon_sha256": "0014706eff7399b3d8ec86cd87fa800e6e0c8e1e15350bec35b084c6c2cea09a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.7942",
    "kind": "arxiv",
    "version": 1
  }
}