Pith Number

pith:XINMDVGA

pith:2011:XINMDVGA5SAZZUR3FRBI64MU7H

not attested not anchored not stored refs pending

Some new series for $1/\pi$ and related congruences

Zhi-Wei Sun

arxiv:1104.3856 v9 · 2011-04-19 · math.NT · math.CA · 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{XINMDVGA5SAZZUR3FRBI64MU7H}

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	2026-05-18T00:27:22.876507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba1ac1d4c0ec819cd23b2c428f7194f9fb71c6a9cf9b35c7bb84953d0239e35f

Aliases

arxiv: 1104.3856 · arxiv_version: 1104.3856v9 · doi: 10.48550/arxiv.1104.3856 · pith_short_12: XINMDVGA5SAZ · pith_short_16: XINMDVGA5SAZZUR3 · pith_short_8: XINMDVGA

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/XINMDVGA5SAZZUR3FRBI64MU7H \
  | 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: ba1ac1d4c0ec819cd23b2c428f7194f9fb71c6a9cf9b35c7bb84953d0239e35f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20eeb823c917ea14d0107b753c1f38465386b381c01ce60f62b2a0c47d80f4d2",
    "cross_cats_sorted": [
      "math.CA",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-04-19T19:59:00Z",
    "title_canon_sha256": "632e41c5ff9f0333a905e456b71bfb217bff108bf645a27f17658b013399d5f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3856",
    "kind": "arxiv",
    "version": 9
  }
}