Pith Number

pith:6ZWMOUB2

pith:2019:6ZWMOUB24TMEJEQQDSAQNMW62Y

not attested not anchored not stored refs pending

The structure of multiplicative functions with small partial sums

Dimitris Koukoulopoulos, K. Soundararajan

arxiv:1909.13105 v2 · 2019-09-28 · 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{6ZWMOUB24TMEJEQQDSAQNMW62Y}

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	2026-07-05T01:02:04.594134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f66cc7503ae4d84492101c8106b2ded63eba583fd381175c04cd310e976193fe

Aliases

arxiv: 1909.13105 · arxiv_version: 1909.13105v2 · doi: 10.48550/arxiv.1909.13105 · pith_short_12: 6ZWMOUB24TME · pith_short_16: 6ZWMOUB24TMEJEQQ · pith_short_8: 6ZWMOUB2

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/6ZWMOUB24TMEJEQQDSAQNMW62Y \
  | 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: f66cc7503ae4d84492101c8106b2ded63eba583fd381175c04cd310e976193fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e92fcadeb07f429560ded0d21b682f6415479e99358edb63c2db0e0757874e0c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-09-28T14:41:10Z",
    "title_canon_sha256": "e8d0b51ddcdfd26f3c20eaadb13fd5d71c19dc522eb33b3d91ce3d621574b2e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.13105",
    "kind": "arxiv",
    "version": 2
  }
}