Pith Number

pith:D2TIULOX

pith:2025:D2TIULOXGHGLUJ6FMVALI6FCTV

not attested not anchored not stored refs pending

On divisibility relation graphs

J\'an Min\'a\v{c}, Jonathan L. Merzel, Nguyen Duy T\^an, Tung T. Nguyen

arxiv:2507.06873 v1 · 2025-07-09 · 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{D2TIULOXGHGLUJ6FMVALI6FCTV}

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	2026-07-05T11:34:24.351196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ea68a2dd731ccba27c56540b478a29d47e00b7519926359587076b6cd522b9e

Aliases

arxiv: 2507.06873 · arxiv_version: 2507.06873v1 · doi: 10.48550/arxiv.2507.06873 · pith_short_12: D2TIULOXGHGL · pith_short_16: D2TIULOXGHGLUJ6F · pith_short_8: D2TIULOX

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/D2TIULOXGHGLUJ6FMVALI6FCTV \
  | 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: 1ea68a2dd731ccba27c56540b478a29d47e00b7519926359587076b6cd522b9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19f0541963a19665d1ef23a8797e94e2c7bc08738690547f501279892cb16113",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-09T14:12:39Z",
    "title_canon_sha256": "d3efba53d4061b0cbe9160f5a4b0e114b35a402c3af2b2724e64b327d0083228"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.06873",
    "kind": "arxiv",
    "version": 1
  }
}