Pith Number

pith:4LMBU4CE

pith:2012:4LMBU4CERLIIMKG5VNSRULJ4Q3

not attested not anchored not stored refs pending

High-order Green Operators on the Disk and the Polydisc

Yang Liu, Yifei Pan, Zhihua Chen

arxiv:1205.3055 v2 · 2012-05-14 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4LMBU4CERLIIMKG5VNSRULJ4Q3}

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	2026-05-18T03:55:36.764670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2d81a70448ad08628ddab651a2d3c86dcc86c3522d345636b3e8a2e9821fff1

Aliases

arxiv: 1205.3055 · arxiv_version: 1205.3055v2 · doi: 10.48550/arxiv.1205.3055 · pith_short_12: 4LMBU4CERLII · pith_short_16: 4LMBU4CERLIIMKG5 · pith_short_8: 4LMBU4CE

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/4LMBU4CERLIIMKG5VNSRULJ4Q3 \
  | 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: e2d81a70448ad08628ddab651a2d3c86dcc86c3522d345636b3e8a2e9821fff1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73c0608261e8c48f9e386ec829ae2e6cffe4f252187922b7b8a5a517d82e44d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2012-05-14T15:04:45Z",
    "title_canon_sha256": "40a61d39462cd232c6aa1dcc507a5d74aa86af9ae26595bff5d7c287949dadf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.3055",
    "kind": "arxiv",
    "version": 2
  }
}