Pith Number

pith:KCZYJGD2

pith:2016:KCZYJGD2D5WLCHFNDZDP442Z6O

not attested not anchored not stored refs pending

Torsion type invariants of singularities

Hao Fang, Huijun Fan

arxiv:1603.06530 v1 · 2016-03-21 · math-ph · math.DG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KCZYJGD2D5WLCHFNDZDP442Z6O}

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	2026-05-18T01:18:48.351481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50b384987a1f6cb11cad1e46fe7359f3ab6bb5f098e85a2ec8156579a6dd22ce

Aliases

arxiv: 1603.06530 · arxiv_version: 1603.06530v1 · doi: 10.48550/arxiv.1603.06530 · pith_short_12: KCZYJGD2D5WL · pith_short_16: KCZYJGD2D5WLCHFN · pith_short_8: KCZYJGD2

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/KCZYJGD2D5WLCHFNDZDP442Z6O \
  | 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: 50b384987a1f6cb11cad1e46fe7359f3ab6bb5f098e85a2ec8156579a6dd22ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3785ba76fbaba5c487990a5f8d8f8c00b3c455f9f9356f51211a102fb35ae67b",
    "cross_cats_sorted": [
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-03-21T18:31:24Z",
    "title_canon_sha256": "86d261b0f8086c0c517a33b692b6d70a22ec81104b2377a195dbb9407412f6e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06530",
    "kind": "arxiv",
    "version": 1
  }
}