Pith Number

pith:B3HHFXLF

pith:2021:B3HHFXLFPHHRFNUQUWTWN2HLCL

not attested not anchored not stored refs pending

Number of singular points on projective surfaces

Jihao Liu, Lingyao Xie

arxiv:2103.04522 v1 · 2021-03-08 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B3HHFXLFPHHRFNUQUWTWN2HLCL}

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	2026-07-05T02:21:06.581327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ece72dd6579cf12b690a5a766e8eb12c811a924dfb3ef7b166cd0cda2171a6d

Aliases

arxiv: 2103.04522 · arxiv_version: 2103.04522v1 · doi: 10.48550/arxiv.2103.04522 · pith_short_12: B3HHFXLFPHHR · pith_short_16: B3HHFXLFPHHRFNUQ · pith_short_8: B3HHFXLF

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/B3HHFXLFPHHRFNUQUWTWN2HLCL \
  | 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: 0ece72dd6579cf12b690a5a766e8eb12c811a924dfb3ef7b166cd0cda2171a6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a42cdc95f65e84208f7b4ca664d52b2f68ce7167aed8c25e33b0ce83185e8b4a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2021-03-08T02:55:12Z",
    "title_canon_sha256": "b839fd24de047813d56ceaa8850239e90469b920fc6b4bd2af335514f1103afc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.04522",
    "kind": "arxiv",
    "version": 1
  }
}