Pith Number

pith:4PJ4NTGM

pith:2025:4PJ4NTGMKLSCO3D24LKEC7YH54

not attested not anchored not stored refs pending

An equality for balanced digraphs

Benjamin Liber, Darij Grinberg

arxiv:2507.22388 v3 · 2025-07-30 · 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{4PJ4NTGMKLSCO3D24LKEC7YH54}

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	2026-06-23T02:13:16.236973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3d3c6cccc52e4276c7ae2d4417f07ef107de3fe1f9ca39d9cbecd1fb20b5315

Aliases

arxiv: 2507.22388 · arxiv_version: 2507.22388v3 · doi: 10.48550/arxiv.2507.22388 · pith_short_12: 4PJ4NTGMKLSC · pith_short_16: 4PJ4NTGMKLSCO3D2 · pith_short_8: 4PJ4NTGM

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/4PJ4NTGMKLSCO3D24LKEC7YH54 \
  | 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: e3d3c6cccc52e4276c7ae2d4417f07ef107de3fe1f9ca39d9cbecd1fb20b5315

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "306cabfef7a34698867edddedf816ca2684d44e6e398401a2ccf7e17da4d6362",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-30T05:21:45Z",
    "title_canon_sha256": "51d32b9c0b804be22f77db1156d7f4f9061ac5789f5edc07f1696a3b1422decb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.22388",
    "kind": "arxiv",
    "version": 3
  }
}