Pith Number

pith:JOBE4IVE

pith:2019:JOBE4IVEQBBXAY3DX3Q5XLKJ5J

not attested not anchored not stored refs pending

A minimax principle to the injectivity of the Jacobian conjecture

Quan Xu, Wei Liu

arxiv:1902.03615 v1 · 2019-02-10 · math.AG · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JOBE4IVEQBBXAY3DX3Q5XLKJ5J}

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	2026-05-17T23:54:06.657211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b824e22a48043706363bee1dbad49ea6ff6b3883c6d322a230b300c2b38bd84

Aliases

arxiv: 1902.03615 · arxiv_version: 1902.03615v1 · doi: 10.48550/arxiv.1902.03615 · pith_short_12: JOBE4IVEQBBX · pith_short_16: JOBE4IVEQBBXAY3D · pith_short_8: JOBE4IVE

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/JOBE4IVEQBBXAY3DX3Q5XLKJ5J \
  | 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: 4b824e22a48043706363bee1dbad49ea6ff6b3883c6d322a230b300c2b38bd84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85d7e419bd0c31bf41ff707d6366c9fa43abc568eafeef827e1c07a37e2ad88f",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-02-10T15:02:49Z",
    "title_canon_sha256": "0a8d159d090b4c5a379bd1ae922b7c5e707b51d437d230b0375e3d3301f002f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.03615",
    "kind": "arxiv",
    "version": 1
  }
}