Pith Number

pith:HCUZUPA4

pith:2017:HCUZUPA4LUGNSQIZXGK2ESR57K

not attested not anchored not stored refs pending

Popular differences and generalized Sidon sets

Max Wenqiang Xu

arxiv:1706.05969 v5 · 2017-06-19 · math.NT · 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{HCUZUPA4LUGNSQIZXGK2ESR57K}

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	2026-07-05T00:44:35.389378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38a99a3c1c5d0cd94119b995a24a3dfaa8c39dd8644391c0d1ed778b5f9b3df7

Aliases

arxiv: 1706.05969 · arxiv_version: 1706.05969v5 · doi: 10.48550/arxiv.1706.05969 · pith_short_12: HCUZUPA4LUGN · pith_short_16: HCUZUPA4LUGNSQIZ · pith_short_8: HCUZUPA4

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/HCUZUPA4LUGNSQIZXGK2ESR57K \
  | 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: 38a99a3c1c5d0cd94119b995a24a3dfaa8c39dd8644391c0d1ed778b5f9b3df7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0fb8a0c3e166f08fa5f9a85f01c7cc7466cc736fe28735261a19154593c66d66",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-06-19T14:13:16Z",
    "title_canon_sha256": "0c2c4924f0c0afc5db3db72547518d22cd0f5513273a4c3f21cbbd8f123084ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.05969",
    "kind": "arxiv",
    "version": 5
  }
}