Pith Number

pith:X7JQYHKR

pith:2011:X7JQYHKRGAPPBVEDFK5WPUYWUV

not attested not anchored not stored refs pending

New Bounds on the Minimum Density of a Vertex Identifying Code for the Infinite Hexagonal Grid

Ari Cukierman, Gexin Yu

arxiv:1110.1097 v1 · 2011-10-05 · 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{X7JQYHKRGAPPBVEDFK5WPUYWUV}

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	2026-05-18T04:11:39.301372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfd30c1d51301ef0d4832abb67d316a56afa18a85325e572e9cf5719c6b3770f

Aliases

arxiv: 1110.1097 · arxiv_version: 1110.1097v1 · doi: 10.48550/arxiv.1110.1097 · pith_short_12: X7JQYHKRGAPP · pith_short_16: X7JQYHKRGAPPBVED · pith_short_8: X7JQYHKR

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/X7JQYHKRGAPPBVEDFK5WPUYWUV \
  | 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: bfd30c1d51301ef0d4832abb67d316a56afa18a85325e572e9cf5719c6b3770f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca7c7eedca25dbd59bf4ea045ad9a0c5bd3e177af792b57909b0a68d7b0fa463",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-10-05T20:28:53Z",
    "title_canon_sha256": "f0b41e4d3f135d000d5664a8b574bcc1bcbcd7ca0601d2c67bb92d7aacb8c783"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1097",
    "kind": "arxiv",
    "version": 1
  }
}