Pith Number

pith:BEARAVH4

pith:2013:BEARAVH4DA6KAEJLJG3AALLXMR

not attested not anchored not stored refs pending

On the Products $(1^\ell+1)(2^\ell+1)\cdots (n^\ell +1)$, II

Ming-Liang Gong, Yong-Gao Chen

arxiv:1311.5646 v1 · 2013-11-22 · 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{BEARAVH4DA6KAEJLJG3AALLXMR}

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	2026-05-18T02:42:53.962564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09011054fc183ca0112b49b6002d77647524b527008fdcd263094047ba711753

Aliases

arxiv: 1311.5646 · arxiv_version: 1311.5646v1 · doi: 10.48550/arxiv.1311.5646 · pith_short_12: BEARAVH4DA6K · pith_short_16: BEARAVH4DA6KAEJL · pith_short_8: BEARAVH4

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/BEARAVH4DA6KAEJLJG3AALLXMR \
  | 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: 09011054fc183ca0112b49b6002d77647524b527008fdcd263094047ba711753

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f11b87405867c0bf73db3d4c38487a1ed43304f04aa995b0b6968bcffa2cd353",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-22T03:32:59Z",
    "title_canon_sha256": "87d3e62b86374c3a07196f51127146f803051f05a146bfa40f25aa07ec079b96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5646",
    "kind": "arxiv",
    "version": 1
  }
}