Pith Number

pith:BN5YGCB7

pith:2004:BN5YGCB7LBSUPOGNCZ4BAVXUAZ

not attested not anchored not stored refs pending

On Euler numbers modulo powers of two

Zhi-Wei Sun

arxiv:math/0410085 v3 · 2004-10-05 · 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{BN5YGCB7LBSUPOGNCZ4BAVXUAZ}

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	2026-07-04T14:39:08.232486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b7b83083f586547b8cd16781056f406683ef6fa593e8e7f542c0b58273e883a

Aliases

arxiv: math/0410085 · arxiv_version: math/0410085v3 · doi: 10.48550/arxiv.math/0410085 · pith_short_12: BN5YGCB7LBSU · pith_short_16: BN5YGCB7LBSUPOGN · pith_short_8: BN5YGCB7

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/BN5YGCB7LBSUPOGNCZ4BAVXUAZ \
  | 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: 0b7b83083f586547b8cd16781056f406683ef6fa593e8e7f542c0b58273e883a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a54adfc37048410dcaa87f7c32f5d1c5aa14bee0ef9d0332f473f0291250e9e1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-10-05T10:00:27Z",
    "title_canon_sha256": "5485025bae95f09f56f7be78b6123d8aea5b633f230aee4a53f02258c9404706"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0410085",
    "kind": "arxiv",
    "version": 3
  }
}