Pith Number

pith:PBZ2P3BK

pith:2015:PBZ2P3BKO3QX7X6VD5APJDY4PG

not attested not anchored not stored refs pending

Note on super congruences modulo $p^2$

Zhi-Hong Sun

arxiv:1503.03418 v1 · 2015-03-11 · 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{PBZ2P3BKO3QX7X6VD5APJDY4PG}

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	2026-05-18T02:24:58.930553Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7873a7ec2a76e17fdfd51f40f48f1c79a289ba2f4003a677bd4d83042096a431

Aliases

arxiv: 1503.03418 · arxiv_version: 1503.03418v1 · doi: 10.48550/arxiv.1503.03418 · pith_short_12: PBZ2P3BKO3QX · pith_short_16: PBZ2P3BKO3QX7X6V · pith_short_8: PBZ2P3BK

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/PBZ2P3BKO3QX7X6VD5APJDY4PG \
  | 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: 7873a7ec2a76e17fdfd51f40f48f1c79a289ba2f4003a677bd4d83042096a431

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfa7ce7ab99f09d5d335eb78209b63111e8aee73d4d950c12b1858a150b59ac2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-03-11T16:59:16Z",
    "title_canon_sha256": "719e9e61ab3101bc77c591c87ed25cff9ab58af2de72af463bd3f9d741b5c51f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.03418",
    "kind": "arxiv",
    "version": 1
  }
}