Pith Number

pith:JCTNQCMZ

pith:2014:JCTNQCMZLSXWKEKROQOF3S457G

not attested not anchored not stored refs pending

Proof of some conjectures of Z.-W. Sun on the divisibility of certain double-sums

Ji-Cai Liu, Victor J. W. Guo

arxiv:1412.5415 v1 · 2014-12-10 · 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{JCTNQCMZLSXWKEKROQOF3S457G}

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	2026-05-18T02:31:03.042042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48a6d809995caf651151741c5dcb9df984ae4222ae6183441074bd292087c729

Aliases

arxiv: 1412.5415 · arxiv_version: 1412.5415v1 · doi: 10.48550/arxiv.1412.5415 · pith_short_12: JCTNQCMZLSXW · pith_short_16: JCTNQCMZLSXWKEKR · pith_short_8: JCTNQCMZ

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/JCTNQCMZLSXWKEKROQOF3S457G \
  | 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: 48a6d809995caf651151741c5dcb9df984ae4222ae6183441074bd292087c729

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbb1186e999ceae561966f72a151dec972f05e0e6c15a1865f570915cd962b0c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-12-10T00:38:55Z",
    "title_canon_sha256": "2986904a9c22e9713ffbb8dfa12b6445766a040bd28c68b18ef44b79bac0d73f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.5415",
    "kind": "arxiv",
    "version": 1
  }
}