Pith Number

pith:52AHTQQO

pith:2011:52AHTQQOTMJX24R3DH6OSIRNA7

not attested not anchored not stored refs pending

The crossing number of locally twisted cubes

Bao Liu, Guoqing Wang, Haoli Wang, Wenping Zheng, Xirong Xu, Yuansheng Yang

arxiv:1103.4227 v1 · 2011-03-22 · 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{52AHTQQOTMJX24R3DH6OSIRNA7}

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	2026-05-18T02:22:11.793597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee8079c20e9b137d723b19fce9222d07cfd5d8f5ce1a5f362d04a5344ff73c41

Aliases

arxiv: 1103.4227 · arxiv_version: 1103.4227v1 · doi: 10.48550/arxiv.1103.4227 · pith_short_12: 52AHTQQOTMJX · pith_short_16: 52AHTQQOTMJX24R3 · pith_short_8: 52AHTQQO

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/52AHTQQOTMJX24R3DH6OSIRNA7 \
  | 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: ee8079c20e9b137d723b19fce9222d07cfd5d8f5ce1a5f362d04a5344ff73c41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e6b6f6b4af0ece0f25ce953cdd487167591222f797cfac36404bfd2dad216d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-22T08:06:27Z",
    "title_canon_sha256": "dd1db40bb97f5aff3ab4962fae0213310c8e088f785cac314194d4e88d395ab3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4227",
    "kind": "arxiv",
    "version": 1
  }
}