Pith Number

pith:XP6D7SW3

pith:2010:XP6D7SW3TGJ3QYKHMEAF6V5Q2C

not attested not anchored not stored refs pending

A new series for $\pi^3$ and related congruences

Zhi-Wei Sun

arxiv:1009.5375 v8 · 2010-09-27 · 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{XP6D7SW3TGJ3QYKHMEAF6V5Q2C}

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	2026-05-18T01:29:51.796378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbfc3fcadb9993b8614761005f57b0d09a4a183d99cedb5e1442b7dcb20f46d5

Aliases

arxiv: 1009.5375 · arxiv_version: 1009.5375v8 · doi: 10.48550/arxiv.1009.5375 · pith_short_12: XP6D7SW3TGJ3 · pith_short_16: XP6D7SW3TGJ3QYKH · pith_short_8: XP6D7SW3

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/XP6D7SW3TGJ3QYKHMEAF6V5Q2C \
  | 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: bbfc3fcadb9993b8614761005f57b0d09a4a183d99cedb5e1442b7dcb20f46d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfe9d43009b900dc04afa93ccf35ccb572b8966ac332ce83be0a13a033c7334b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-09-27T19:56:59Z",
    "title_canon_sha256": "8596bf604c35f0176905dfb4f7d0a4eb5c577ebcea7a76a321b564d84c670fb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5375",
    "kind": "arxiv",
    "version": 8
  }
}