Pith Number

pith:NMNSOKYH

pith:2021:NMNSOKYHWJKPUCWDNS7DP527DC

not attested not anchored not stored refs pending

A new theorem on quadratic residues modulo primes

Hao Pan, Qing-Hu Hou, Zhi-Wei Sun

arxiv:2107.08984 v3 · 2021-07-19 · 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{NMNSOKYHWJKPUCWDNS7DP527DC}

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	2026-07-05T05:04:02.193401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b1b272b07b254fa0ac36cbe37f75f18ab9693b01b878bbe521211c9dd6499f0

Aliases

arxiv: 2107.08984 · arxiv_version: 2107.08984v3 · doi: 10.48550/arxiv.2107.08984 · pith_short_12: NMNSOKYHWJKP · pith_short_16: NMNSOKYHWJKPUCWD · pith_short_8: NMNSOKYH

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/NMNSOKYHWJKPUCWDNS7DP527DC \
  | 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: 6b1b272b07b254fa0ac36cbe37f75f18ab9693b01b878bbe521211c9dd6499f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cf347966e27ae6f7b2f7e0c1c9d21b04cfb709024cf78a4431f6b59e2762fec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-07-19T15:58:31Z",
    "title_canon_sha256": "4c9310cc8f6a68f2e7c2356d8b69bcca2da3ed6a42156d1247567cd2764590a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.08984",
    "kind": "arxiv",
    "version": 3
  }
}