Pith Number

pith:LBB4KTGL

pith:2011:LBB4KTGLEZG2PRPXI4LOFMMHK6

not attested not anchored not stored refs pending

Asymptotic rays

Anastasiia Tsvietkova, Oleksii Kuchaiev

arxiv:1108.4092 v1 · 2011-08-20 · math.GT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LBB4KTGLEZG2PRPXI4LOFMMHK6}

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	2026-05-18T04:14:56.156658Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5843c54ccb264da7c5f74716e2b1875783991aa65d046ac1cc1278eba5e08a4b

Aliases

arxiv: 1108.4092 · arxiv_version: 1108.4092v1 · doi: 10.48550/arxiv.1108.4092 · pith_short_12: LBB4KTGLEZG2 · pith_short_16: LBB4KTGLEZG2PRPX · pith_short_8: LBB4KTGL

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/LBB4KTGLEZG2PRPXI4LOFMMHK6 \
  | 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: 5843c54ccb264da7c5f74716e2b1875783991aa65d046ac1cc1278eba5e08a4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42d81a620e09f4ee6ecc6d1e84c715fd099c2b3024239aac6910612e19f1b44c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-08-20T06:05:08Z",
    "title_canon_sha256": "c03b46a5377dc3ae586020f246e6bb8a138d05ac7391d057852e9f8ec9282aa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4092",
    "kind": "arxiv",
    "version": 1
  }
}