Pith Number

pith:TYIB4SND

pith:2019:TYIB4SNDGS3ZVSMN7DKVWKINHL

not attested not anchored not stored refs pending

Approaching Cusick's conjecture on the sum-of-digits function

Lukas Spiegelhofer

arxiv:1904.08646 v1 · 2019-04-18 · 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{TYIB4SNDGS3ZVSMN7DKVWKINHL}

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	2026-05-17T23:48:13.555896Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e101e49a334b79ac98df8d55b290d3ae36737bf3cd75710a06ee7f46d56944f

Aliases

arxiv: 1904.08646 · arxiv_version: 1904.08646v1 · doi: 10.48550/arxiv.1904.08646 · pith_short_12: TYIB4SNDGS3Z · pith_short_16: TYIB4SNDGS3ZVSMN · pith_short_8: TYIB4SND

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/TYIB4SNDGS3ZVSMN7DKVWKINHL \
  | 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: 9e101e49a334b79ac98df8d55b290d3ae36737bf3cd75710a06ee7f46d56944f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "132b1265703d4ac358e445fc13582857551307e2fbed4a848a499b4efe179be2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-04-18T09:14:17Z",
    "title_canon_sha256": "ba787642c0906cded5225b75f08d1e2cc7793714fa5141a7b9c88bf1228c5517"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.08646",
    "kind": "arxiv",
    "version": 1
  }
}