Pith Number

pith:23GRXNCE

pith:2025:23GRXNCEZLA7CSVGHCSXUKW5QA

not attested not anchored not stored refs pending

Circular sorting, strong complete mappings and wreath product constructions

Anurag Bishnoi, Carla Groenland, Dion Gijswijt, Paul Bastide, Rohinee Joshi

arxiv:2510.18529 v3 · 2025-10-21 · 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{23GRXNCEZLA7CSVGHCSXUKW5QA}

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	2026-06-19T16:11:14.245685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6cd1bb444cac1f14aa638a57a2add800bf1f7412535461ef32206d7fb14a7d8

Aliases

arxiv: 2510.18529 · arxiv_version: 2510.18529v3 · doi: 10.48550/arxiv.2510.18529 · pith_short_12: 23GRXNCEZLA7 · pith_short_16: 23GRXNCEZLA7CSVG · pith_short_8: 23GRXNCE

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/23GRXNCEZLA7CSVGHCSXUKW5QA \
  | 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: d6cd1bb444cac1f14aa638a57a2add800bf1f7412535461ef32206d7fb14a7d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4489d8842117347eecbab134d2c33cee2d784bf9eed70abc556d658b2e891fd1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-10-21T11:16:05Z",
    "title_canon_sha256": "9435af2bd802cdabfb9ccbff86437d20fff90900468c45b783b4ea507b44444c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.18529",
    "kind": "arxiv",
    "version": 3
  }
}