Pith Number

pith:2ITBEWG4

pith:2015:2ITBEWG4BCYX33BLRQPCGG3TLK

not attested not anchored not stored refs pending

Spherical Designs and Generalized Sum-Free Sets in Abelian Groups

B\'ela Bajnok

arxiv:1512.02991 v1 · 2015-12-09 · 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{2ITBEWG4BCYX33BLRQPCGG3TLK}

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	2026-05-18T01:24:39.085576Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2261258dc08b17dec2b8c1e231b735a9a17da384342ff9d2a75923e3a0fa41f

Aliases

arxiv: 1512.02991 · arxiv_version: 1512.02991v1 · doi: 10.48550/arxiv.1512.02991 · pith_short_12: 2ITBEWG4BCYX · pith_short_16: 2ITBEWG4BCYX33BL · pith_short_8: 2ITBEWG4

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/2ITBEWG4BCYX33BLRQPCGG3TLK \
  | 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: d2261258dc08b17dec2b8c1e231b735a9a17da384342ff9d2a75923e3a0fa41f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7507d3a742dc364d3fb4ef0b7f82f74a6ecf1c06ab313392df8d55e1a5e1fc70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-09T18:54:50Z",
    "title_canon_sha256": "60d6395aacf0bbc2c3bbd649c09dd60772524698ef72c22e2d97d869790dc20c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02991",
    "kind": "arxiv",
    "version": 1
  }
}