Pith Number

pith:4NWARQ2O

pith:2014:4NWARQ2OV5GS3TNB4CU5D6UDIB

not attested not anchored not stored refs pending

Koppelman formulas on the A_1-singularity

Jean Ruppenthal, Richard L\"ark\"ang

arxiv:1407.5703 v3 · 2014-07-22 · 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{4NWARQ2OV5GS3TNB4CU5D6UDIB}

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	2026-05-18T00:43:36.264669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e36c08c34eaf4d2dcda1e0a9d1fa834074837807a26cb3c36242550d8663092a

Aliases

arxiv: 1407.5703 · arxiv_version: 1407.5703v3 · doi: 10.48550/arxiv.1407.5703 · pith_short_12: 4NWARQ2OV5GS · pith_short_16: 4NWARQ2OV5GS3TNB · pith_short_8: 4NWARQ2O

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/4NWARQ2OV5GS3TNB4CU5D6UDIB \
  | 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: e36c08c34eaf4d2dcda1e0a9d1fa834074837807a26cb3c36242550d8663092a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec8fa12e70828a85db29f8b8c86e5b373c3469bc8cd54eded73935ab9856dace",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2014-07-22T01:01:06Z",
    "title_canon_sha256": "04d51b32e6a9aceeb1834cd54f5069510fecedf23839e477da29ad3758b92438"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.5703",
    "kind": "arxiv",
    "version": 3
  }
}