Pith Number

pith:3QQY4KKB

pith:2014:3QQY4KKBYZ3C7FDBXRNGVQCCPB

not attested not anchored not stored refs pending

Systoles and kissing numbers of finite area hyperbolic surfaces

Federica Fanoni, Hugo Parlier

arxiv:1408.6048 v2 · 2014-08-26 · math.GT · 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{3QQY4KKBYZ3C7FDBXRNGVQCCPB}

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	2026-05-18T01:21:55.940225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc218e2941c6762f9461bc5a6ac04278525c6dd836823119e5f186e73d77cfc0

Aliases

arxiv: 1408.6048 · arxiv_version: 1408.6048v2 · doi: 10.48550/arxiv.1408.6048 · pith_short_12: 3QQY4KKBYZ3C · pith_short_16: 3QQY4KKBYZ3C7FDB · pith_short_8: 3QQY4KKB

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/3QQY4KKBYZ3C7FDBXRNGVQCCPB \
  | 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: dc218e2941c6762f9461bc5a6ac04278525c6dd836823119e5f186e73d77cfc0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "468646c511c3cc452cf35347369c1ee8d9e9fc69f0fd0b7a50d40385859795f4",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-08-26T08:31:09Z",
    "title_canon_sha256": "6c5dd801f721c3634404e70b4eea0c59b6009da3d02705ef04950b08307043a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.6048",
    "kind": "arxiv",
    "version": 2
  }
}