Pith Number

pith:4XQ5FEG3

pith:2013:4XQ5FEG34XXX3K5BAPSKV5E4Z5

not attested not anchored not stored refs pending

Bernoulli, Ramanujan, Toeplitz and the triangular matrices

C. Di Fiore, F. Tudisco, P. Zellini

arxiv:1307.3108 v1 · 2013-07-11 · math.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4XQ5FEG34XXX3K5BAPSKV5E4Z5}

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	2026-05-18T03:18:41.173881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5e1d290dbe5ef7daba103e4aaf49ccf4bb2c5a0a1b4ffd033217b6c985bf517

Aliases

arxiv: 1307.3108 · arxiv_version: 1307.3108v1 · doi: 10.48550/arxiv.1307.3108 · pith_short_12: 4XQ5FEG34XXX · pith_short_16: 4XQ5FEG34XXX3K5B · pith_short_8: 4XQ5FEG3

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/4XQ5FEG34XXX3K5BAPSKV5E4Z5 \
  | 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: e5e1d290dbe5ef7daba103e4aaf49ccf4bb2c5a0a1b4ffd033217b6c985bf517

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c768408f1a3c2413cddd2882602551cba461e2106575256bb0c80e3c50dbcf73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-07-11T13:41:12Z",
    "title_canon_sha256": "6d10dba7efa9a0112b0fb7a54e85a65e4641f9b9a920680022627b0a0cdbf0d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.3108",
    "kind": "arxiv",
    "version": 1
  }
}