Pith Number

pith:DQJAWOYH

pith:2015:DQJAWOYHQNYFZMSEFU4QEG6B6F

not attested not anchored not stored refs pending

A multiplicative analogue of Schnirelmann's theorem

Aled Walker

arxiv:1505.03328 v4 · 2015-05-13 · 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{DQJAWOYHQNYFZMSEFU4QEG6B6F}

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	2026-05-17T23:52:24.886170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c120b3b0783705cb2442d39021bc1f1798286c8628a455c0ea632e643f42756

Aliases

arxiv: 1505.03328 · arxiv_version: 1505.03328v4 · doi: 10.48550/arxiv.1505.03328 · pith_short_12: DQJAWOYHQNYF · pith_short_16: DQJAWOYHQNYFZMSE · pith_short_8: DQJAWOYH

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/DQJAWOYHQNYFZMSEFU4QEG6B6F \
  | 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: 1c120b3b0783705cb2442d39021bc1f1798286c8628a455c0ea632e643f42756

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a7d6ed5f42e6435dff4e404d46b0b38c00c92922ba8b7a0406bccee0ed54683",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-05-13T11:01:24Z",
    "title_canon_sha256": "0944427307a04adf5fb3731e4f629357a038b5c5526cf9138c7f74683eb9be28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.03328",
    "kind": "arxiv",
    "version": 4
  }
}