Pith Number

pith:KBEEQ4R4

pith:2012:KBEEQ4R4XNZ625FOA2IGPHVBCI

not attested not anchored not stored refs pending

On the expansion of three-element subtraction sets

Nhan Bao Ho

arxiv:1202.2986 v3 · 2012-02-14 · 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{KBEEQ4R4XNZ625FOA2IGPHVBCI}

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	2026-05-18T02:30:33.999975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

504848723cbb73ed74ae0690679ea1121590894e29993a71ea3655ad3c4bc325

Aliases

arxiv: 1202.2986 · arxiv_version: 1202.2986v3 · doi: 10.48550/arxiv.1202.2986 · pith_short_12: KBEEQ4R4XNZ6 · pith_short_16: KBEEQ4R4XNZ625FO · pith_short_8: KBEEQ4R4

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/KBEEQ4R4XNZ625FOA2IGPHVBCI \
  | 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: 504848723cbb73ed74ae0690679ea1121590894e29993a71ea3655ad3c4bc325

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6dd23b306bac021492e7be782c6946a1d062af1d920e7610a79213a030e17ad2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-14T10:44:32Z",
    "title_canon_sha256": "49fc0353e98679c331b554cd67ef17a5d68276fb065d6cf47ba7d7dff7617e8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.2986",
    "kind": "arxiv",
    "version": 3
  }
}