Pith Number

pith:VA4XSBLC

pith:2011:VA4XSBLCILAMSGUIU7RDGVEJ54

not attested not anchored not stored refs pending

Topological symmetry groups and mapping class groups for spatial graphs

Sangbum Cho, Yuya Koda

arxiv:1111.2668 v2 · 2011-11-11 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VA4XSBLCILAMSGUIU7RDGVEJ54}

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	2026-05-18T03:52:54.778218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a83979056242c0c91a88a7e2335489ef07bfe4628f4175e3870b43fed94a8609

Aliases

arxiv: 1111.2668 · arxiv_version: 1111.2668v2 · doi: 10.48550/arxiv.1111.2668 · pith_short_12: VA4XSBLCILAM · pith_short_16: VA4XSBLCILAMSGUI · pith_short_8: VA4XSBLC

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/VA4XSBLCILAMSGUIU7RDGVEJ54 \
  | 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: a83979056242c0c91a88a7e2335489ef07bfe4628f4175e3870b43fed94a8609

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cc20c55573a47c7fa83f447709a74ac8395a6c0e75ae2679bfffd492fa2f255",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-11-11T06:04:30Z",
    "title_canon_sha256": "04ccace389b59968f3fa7978a56cd9845a9dbbc6e50cd064e5a4fcf449920be0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2668",
    "kind": "arxiv",
    "version": 2
  }
}