Pith Number

pith:LMY5SWN5

pith:2025:LMY5SWN5EZ6JW7CYZQURB5GZCY

not attested not anchored not stored refs pending

When Are Standard Graph Products Isomorphic?

Fouzul Atik, M. Rajesh Kannan, Priti Prasanna Mondal

arxiv:2508.04137 v1 · 2025-08-06 · 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{LMY5SWN5EZ6JW7CYZQURB5GZCY}

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	2026-07-05T11:49:21.190967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b31d959bd267c9b7c58cc2910f4d9160242ce1a3d1e2d39f9b28d40457f6781

Aliases

arxiv: 2508.04137 · arxiv_version: 2508.04137v1 · doi: 10.48550/arxiv.2508.04137 · pith_short_12: LMY5SWN5EZ6J · pith_short_16: LMY5SWN5EZ6JW7CY · pith_short_8: LMY5SWN5

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/LMY5SWN5EZ6JW7CYZQURB5GZCY \
  | 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: 5b31d959bd267c9b7c58cc2910f4d9160242ce1a3d1e2d39f9b28d40457f6781

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0d8fec369aafeef6f53db837b6777d1c33d7f6f98421082c5941e9adfec2a7f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-06T07:04:38Z",
    "title_canon_sha256": "142886d4804ce76d14e9145e5a28d0c22ed67fac96f03995872861ad70ee0481"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.04137",
    "kind": "arxiv",
    "version": 1
  }
}