Pith Number

pith:NTP3EQ7K

pith:2026:NTP3EQ7KMP7OSXDCYLSMLAKETW

not attested not anchored not stored refs pending

On graph products and multi-word-representability

Benny George Kenkireth, Gopalan Sajith, Sreyas Sasidharan

arxiv:2603.29629 v3 · 2026-03-31 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NTP3EQ7KMP7OSXDCYLSMLAKETW}

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	2026-06-04T01:09:49.218427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cdfb243ea63fee95c62c2e4c581449d96f2c0c9d6037c54ba29dc1889247851

Aliases

arxiv: 2603.29629 · arxiv_version: 2603.29629v3 · doi: 10.48550/arxiv.2603.29629 · pith_short_12: NTP3EQ7KMP7O · pith_short_16: NTP3EQ7KMP7OSXDC · pith_short_8: NTP3EQ7K

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/NTP3EQ7KMP7OSXDCYLSMLAKETW \
  | 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: 6cdfb243ea63fee95c62c2e4c581449d96f2c0c9d6037c54ba29dc1889247851

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5499d0e4b3e29afed5884f669836fee22b9dd2d5752ab8e927679f21bdaa1d38",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-03-31T11:52:38Z",
    "title_canon_sha256": "59cce3fa5d457e07caf85910498393cf06c94e32fdefd2d75d22aba18def7052"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.29629",
    "kind": "arxiv",
    "version": 3
  }
}