Pith Number

pith:ZGZMBK7O

pith:2019:ZGZMBK7OH5MLEMQSXDW72N4XSO

not attested not anchored not stored refs pending

Congruences with intervals and arbitrary sets

Igor Shparlinski, William Banks

arxiv:1907.03943 v1 · 2019-07-09 · 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{ZGZMBK7OH5MLEMQSXDW72N4XSO}

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	2026-05-17T23:41:06.293102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9b2c0abee3f58b23212b8edfd379793a6788354659d690589b294f03e545fc9

Aliases

arxiv: 1907.03943 · arxiv_version: 1907.03943v1 · doi: 10.48550/arxiv.1907.03943 · pith_short_12: ZGZMBK7OH5ML · pith_short_16: ZGZMBK7OH5MLEMQS · pith_short_8: ZGZMBK7O

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/ZGZMBK7OH5MLEMQSXDW72N4XSO \
  | 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: c9b2c0abee3f58b23212b8edfd379793a6788354659d690589b294f03e545fc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5411a1b92cecc6536fff94d685d9bf26456e51c3059cff618d64471fd470ef7b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-07-09T02:13:18Z",
    "title_canon_sha256": "beee23e752ed6a3021a225af842e25535c1a48f8378e7c460c08b9483a61c372"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.03943",
    "kind": "arxiv",
    "version": 1
  }
}