Pith Number

pith:XKEJUDVI

pith:2026:XKEJUDVIAZP5F3FOPT2ESK7X5H

not attested not anchored not stored refs pending

Dimension and Order Bounds for Isometric Embeddings of Graphs into Abelian Cayley Graphs, and the Abelian Dividend

Bitjoka Laurent, Fokam Souop Rigobert

arxiv:2607.07939 v1 · 2026-07-08 · 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{XKEJUDVIAZP5F3FOPT2ESK7X5H}

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	2026-07-10T00:19:05.391447Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba889a0ea8065fd2ecae7cf4492bf7e9e2b0950f2babfaeed217e872aafe4c14

Aliases

arxiv: 2607.07939 · arxiv_version: 2607.07939v1 · doi: 10.48550/arxiv.2607.07939 · pith_short_12: XKEJUDVIAZP5 · pith_short_16: XKEJUDVIAZP5F3FO · pith_short_8: XKEJUDVI

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/XKEJUDVIAZP5F3FOPT2ESK7X5H \
  | 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: ba889a0ea8065fd2ecae7cf4492bf7e9e2b0950f2babfaeed217e872aafe4c14

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80b7143c3f9323325c4f97d2a47cfd65e1fd4ee0f5c93ba1465668874fe11e8b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-08T21:35:08Z",
    "title_canon_sha256": "c13e1507a34ba7c3aeef9996956bb6dd673b5f96583a779ec9e865a18fced474"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.07939",
    "kind": "arxiv",
    "version": 1
  }
}