Pith Number

pith:2X7KNAIL

pith:2012:2X7KNAILJYES6OHSOIQYTNBTPJ

not attested not anchored not stored refs pending

Note on the harmonic index of a graph

Aleksandar Ilic

arxiv:1204.3313 v1 · 2012-04-15 · 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{2X7KNAILJYES6OHSOIQYTNBTPJ}

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	2026-05-18T03:57:51.866872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5fea6810b4e092f38f2722189b4337a7b8a64dec9b6ac7fe3909994f75418e8

Aliases

arxiv: 1204.3313 · arxiv_version: 1204.3313v1 · doi: 10.48550/arxiv.1204.3313 · pith_short_12: 2X7KNAILJYES · pith_short_16: 2X7KNAILJYES6OHS · pith_short_8: 2X7KNAIL

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/2X7KNAILJYES6OHSOIQYTNBTPJ \
  | 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: d5fea6810b4e092f38f2722189b4337a7b8a64dec9b6ac7fe3909994f75418e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1fa377160d445fbe05a86d15b7f15284c83f8562d98c8f9aa8d46d1a4613585",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-04-15T19:18:03Z",
    "title_canon_sha256": "c9ada87199a1587d89bb6e5dac099592e9b0009d112033cb09609eee1949e2f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3313",
    "kind": "arxiv",
    "version": 1
  }
}