Pith Number

pith:X5H5LUKB

pith:2015:X5H5LUKBT66H5UHN6SIQX3LZOT

not attested not anchored not stored refs pending

Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

Hung-Lin Chiu, Jenn-Fang Hwang, Jih-Hsin Cheng, Paul Yang

arxiv:1512.05859 v1 · 2015-12-18 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X5H5LUKBT66H5UHN6SIQX3LZOT}

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	2026-05-18T01:24:06.047188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf4fd5d1419fbc7ed0edf4910bed7974cec431c00b13bb41d63da4224cc51c67

Aliases

arxiv: 1512.05859 · arxiv_version: 1512.05859v1 · doi: 10.48550/arxiv.1512.05859 · pith_short_12: X5H5LUKBT66H · pith_short_16: X5H5LUKBT66H5UHN · pith_short_8: X5H5LUKB

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/X5H5LUKBT66H5UHN6SIQX3LZOT \
  | 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: bf4fd5d1419fbc7ed0edf4910bed7974cec431c00b13bb41d63da4224cc51c67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8d42ae66d7af404821e5194fd96a0e5c91e00def7499dea2e96e50d97281892",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-12-18T06:27:38Z",
    "title_canon_sha256": "1c760f150dbc636ea92f40315ca8cbbb123a490bfa1e8950419ad7fb0561d764"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05859",
    "kind": "arxiv",
    "version": 1
  }
}