Pith Number

pith:SR4SPDM6

pith:2012:SR4SPDM6IQQO64UY7SBMBJAW2Y

not attested not anchored not stored refs pending

New Lower Bounds for the Least Common Multiples of Arithmetic Progressions

Qianrong Tan, Rongjun Wu, Shaofang Hong

arxiv:1211.4468 v1 · 2012-11-19 · 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{SR4SPDM6IQQO64UY7SBMBJAW2Y}

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	2026-05-18T03:08:14.430391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9479278d9e4420ef7298fc82c0a416d62df0e11b6eb9f2d59f5d0021aba2617d

Aliases

arxiv: 1211.4468 · arxiv_version: 1211.4468v1 · doi: 10.48550/arxiv.1211.4468 · pith_short_12: SR4SPDM6IQQO · pith_short_16: SR4SPDM6IQQO64UY · pith_short_8: SR4SPDM6

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/SR4SPDM6IQQO64UY7SBMBJAW2Y \
  | 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: 9479278d9e4420ef7298fc82c0a416d62df0e11b6eb9f2d59f5d0021aba2617d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3105328ce24a61f28d7b09b93d8785991c0bd6079e09cd6b65c7ef9117911b91",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-19T15:45:03Z",
    "title_canon_sha256": "5b6da642178712597cd48bdf98fd592f397f3d22ca4883940ed1d8f06220c557"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4468",
    "kind": "arxiv",
    "version": 1
  }
}