Pith Number

pith:DFD3LCCG

pith:2024:DFD3LCCGX42KJHRLWB44ZN46L4

not attested not anchored not stored refs pending

Every group-embeddable monoid arises as the bimorphism monoid of some graph

Isaac K. Dilley, Thomas D. H. Coleman

arxiv:2401.02775 v1 · 2024-01-05 · 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{DFD3LCCGX42KJHRLWB44ZN46L4}

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	2026-07-05T07:30:30.970198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1947b58846bf34a49e2bb079ccb79e5f01ccc89ce316ef151ff27ed25b3a3d39

Aliases

arxiv: 2401.02775 · arxiv_version: 2401.02775v1 · doi: 10.48550/arxiv.2401.02775 · pith_short_12: DFD3LCCGX42K · pith_short_16: DFD3LCCGX42KJHRL · pith_short_8: DFD3LCCG

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/DFD3LCCGX42KJHRLWB44ZN46L4 \
  | 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: 1947b58846bf34a49e2bb079ccb79e5f01ccc89ce316ef151ff27ed25b3a3d39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e6c2750bdee85eb05920a66a2fbca7b58313675ca08ffbad0e2b91d542d6610",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-01-05T12:24:04Z",
    "title_canon_sha256": "fb37431c8ca063b6b65b6bd3ae11a05603f760019b824c51aff354eb0dfe36dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2401.02775",
    "kind": "arxiv",
    "version": 1
  }
}