Pith Number

pith:UHVNDNNE

pith:2010:UHVNDNNEKNJIHVDTR2XEWT36SY

not attested not anchored not stored refs pending

A Counting Proof of the Graham Pollak Theorem

Sundar Vishwanathan

arxiv:1007.1553 v2 · 2010-07-09 · 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{UHVNDNNEKNJIHVDTR2XEWT36SY}

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	2026-05-18T04:31:42.171848Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a1ead1b5a4535283d4738eae4b4f7e9603ec32552520ae367d14d3e4cc37f666

Aliases

arxiv: 1007.1553 · arxiv_version: 1007.1553v2 · doi: 10.48550/arxiv.1007.1553 · pith_short_12: UHVNDNNEKNJI · pith_short_16: UHVNDNNEKNJIHVDT · pith_short_8: UHVNDNNE

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/UHVNDNNEKNJIHVDTR2XEWT36SY \
  | 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: a1ead1b5a4535283d4738eae4b4f7e9603ec32552520ae367d14d3e4cc37f666

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2b8c003c44a8f57813adcff26302880c6cd2249501cbe23dd828101ed3a2099",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-07-09T10:35:25Z",
    "title_canon_sha256": "dac02afaedcf5321f9bdd8fe95c1d946258f8b2f0756d6605c685278ba933701"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1553",
    "kind": "arxiv",
    "version": 2
  }
}