Pith Number

pith:G7QK72LH

pith:2013:G7QK72LHJX5MZ2LXEP6UNT2ZBC

not attested not anchored not stored refs pending

Additive and multiplicative structure of c$^{\star}$-sets

Dibyendu De

arxiv:1302.4270 v3 · 2013-02-18 · 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{G7QK72LHJX5MZ2LXEP6UNT2ZBC}

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	2026-05-18T02:42:15.126153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37e0afe9674dfacce97723fd46cf59089529ede46797555ff84f5b5a5a1b0169

Aliases

arxiv: 1302.4270 · arxiv_version: 1302.4270v3 · doi: 10.48550/arxiv.1302.4270 · pith_short_12: G7QK72LHJX5M · pith_short_16: G7QK72LHJX5MZ2LX · pith_short_8: G7QK72LH

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/G7QK72LHJX5MZ2LXEP6UNT2ZBC \
  | 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: 37e0afe9674dfacce97723fd46cf59089529ede46797555ff84f5b5a5a1b0169

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "337f3a97d875f4671cf7c31b7fe906420c61305f789430e14f4f47ea286e9bcf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-18T13:57:29Z",
    "title_canon_sha256": "8afa30f3dbe0bdb5205447585fb44b94a926cc2318f1f4d335d6798c7dc75d91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4270",
    "kind": "arxiv",
    "version": 3
  }
}