Pith Number

pith:ABCMKA3F

pith:2011:ABCMKA3F5JHJNMICAG76KDVVKB

not attested not anchored not stored refs pending

Normal forms for Hopf-Zero singularities with nonconservative nonlinear part

Fahimeh Mokhtari, Jan A. Sanders, Majid Gazor

arxiv:1112.2544 v3 · 2011-12-12 · 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{ABCMKA3F5JHJNMICAG76KDVVKB}

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	2026-05-18T03:12:33.439674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0044c50365ea4e96b10201bfe50eb5505894bc6453cef243b89b3efbcf8cdf5f

Aliases

arxiv: 1112.2544 · arxiv_version: 1112.2544v3 · doi: 10.48550/arxiv.1112.2544 · pith_short_12: ABCMKA3F5JHJ · pith_short_16: ABCMKA3F5JHJNMIC · pith_short_8: ABCMKA3F

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/ABCMKA3F5JHJNMICAG76KDVVKB \
  | 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: 0044c50365ea4e96b10201bfe50eb5505894bc6453cef243b89b3efbcf8cdf5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e96b0fa292323d56a13e915fb52354d1436633d4a38e1103034f103ebc16991",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-12-12T13:38:56Z",
    "title_canon_sha256": "1b8961045442c048d9fc1f1f460e1bb3a001cdb7dad48647534581679dc77f2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2544",
    "kind": "arxiv",
    "version": 3
  }
}