Pith Number

pith:OSZ3WZMF

pith:2019:OSZ3WZMFPNOAZZE45UXQYZORIB

not attested not anchored not stored refs pending

Some congruences related to a congruence of Van Hamme

Ji-Cai Liu, Victor J. W. Guo

arxiv:1903.03766 v1 · 2019-03-09 · math.CO · 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{OSZ3WZMFPNOAZZE45UXQYZORIB}

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	2026-05-17T23:51:40.990241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74b3bb65857b5c0ce49ced2f0c65d1405f58f3be8e572490e43c6eb14e279257

Aliases

arxiv: 1903.03766 · arxiv_version: 1903.03766v1 · doi: 10.48550/arxiv.1903.03766 · pith_short_12: OSZ3WZMFPNOA · pith_short_16: OSZ3WZMFPNOAZZE4 · pith_short_8: OSZ3WZMF

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/OSZ3WZMFPNOAZZE45UXQYZORIB \
  | 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: 74b3bb65857b5c0ce49ced2f0c65d1405f58f3be8e572490e43c6eb14e279257

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "baa7c7730401b01e6fbc3775005546a1d72a2e069abc5f36ea9d502f7b718453",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-03-09T08:57:30Z",
    "title_canon_sha256": "d2203d827d76d901a501df1857b647e4188050916b53a8f834eb8b56b08251d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.03766",
    "kind": "arxiv",
    "version": 1
  }
}