Pith Number

pith:WZOSBXWU

pith:2016:WZOSBXWUVR3SYCHBN45KKAQUIT

not attested not anchored not stored refs pending

On a problem by Shapozenko on Johnson graphs

Llu\'is Vena, Oriol Serra, V\'ictor Diego

arxiv:1604.05084 v2 · 2016-04-18 · 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{WZOSBXWUVR3SYCHBN45KKAQUIT}

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	2026-05-18T00:51:07.313042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b65d20ded4ac772c08e16f3aa5021444c151ba072bafb779ebadfc7ae05d878b

Aliases

arxiv: 1604.05084 · arxiv_version: 1604.05084v2 · doi: 10.48550/arxiv.1604.05084 · pith_short_12: WZOSBXWUVR3S · pith_short_16: WZOSBXWUVR3SYCHB · pith_short_8: WZOSBXWU

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/WZOSBXWUVR3SYCHBN45KKAQUIT \
  | 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: b65d20ded4ac772c08e16f3aa5021444c151ba072bafb779ebadfc7ae05d878b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ef242bfe2787bf846b4b394a2f8c7fb2e9b388c0b00670d3992cc678e469a04",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-04-18T11:05:53Z",
    "title_canon_sha256": "8a3f15f7eb1f985675b2b2d9e0c9aaca5f0a93e68720b9d29013e32f8458f0f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.05084",
    "kind": "arxiv",
    "version": 2
  }
}