Pith Number

pith:ATKXVCEJ

pith:2023:ATKXVCEJAUG5SM5I5D7N3NW4VX

not attested not anchored not stored refs pending

Waring's problem with restricted digits

Ben Green

arxiv:2309.09383 v3 · 2023-09-17 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ATKXVCEJAUG5SM5I5D7N3NW4VX}

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.

Cited by

1 paper in Pith

Sharp Lower Bounds for Sumsets in Hypercubes

Receipt and verification

First computed	2026-07-05T09:36:36.904416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04d57a8889050dd933a8e8feddb6dcade89b65190709805b77412aec4f8a3fda

Aliases

arxiv: 2309.09383 · arxiv_version: 2309.09383v3 · doi: 10.48550/arxiv.2309.09383 · pith_short_12: ATKXVCEJAUG5 · pith_short_16: ATKXVCEJAUG5SM5I · pith_short_8: ATKXVCEJ

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/ATKXVCEJAUG5SM5I5D7N3NW4VX \
  | 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: 04d57a8889050dd933a8e8feddb6dcade89b65190709805b77412aec4f8a3fda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c166c30d1e540f0a0b41757dbb4c2dcd68a0eaa32157d8671e22b816337513be",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2023-09-17T21:42:53Z",
    "title_canon_sha256": "36a17a2657ceead2f140872e0b0559f3b61adb4e37fc6a58153160945b7fd2de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2309.09383",
    "kind": "arxiv",
    "version": 3
  }
}