Pith Number

pith:5QNR5EQ3

pith:2016:5QNR5EQ3NFU5ZUQHSEEATJR2NW

not attested not anchored not stored refs pending

Closed and asymptotic formulas for energy of some circulant graphs

Carlos Alberto Mar\'in arango, David Bl\'azquez-Sanz

arxiv:1602.07730 v2 · 2016-02-24 · 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{5QNR5EQ3NFU5ZUQHSEEATJR2NW}

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	2026-05-18T01:19:40.218358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec1b1e921b6969dcd207910809a63a6db9e3b56c3e11afa10c497017b3307304

Aliases

arxiv: 1602.07730 · arxiv_version: 1602.07730v2 · doi: 10.48550/arxiv.1602.07730 · pith_short_12: 5QNR5EQ3NFU5 · pith_short_16: 5QNR5EQ3NFU5ZUQH · pith_short_8: 5QNR5EQ3

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/5QNR5EQ3NFU5ZUQHSEEATJR2NW \
  | 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: ec1b1e921b6969dcd207910809a63a6db9e3b56c3e11afa10c497017b3307304

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6962dfd0e4017d04ac6c492b7fc1ee31661212577381b4ce238132fb13f6fddb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-02-24T22:16:17Z",
    "title_canon_sha256": "09a79d5cb74b7383277b4e25755c5ebedb78c4bdaa0204278fc85cedced29c99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.07730",
    "kind": "arxiv",
    "version": 2
  }
}