Pith Number

pith:WFBYUHZ4

pith:2013:WFBYUHZ4L6EZGQM2ZKELEI2TIB

not attested not anchored not stored refs pending

On the Atkin Polynomials

Ahmad El-Guindy, Mourad E.H. Ismail

arxiv:1309.2123 v1 · 2013-09-09 · math.NT · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WFBYUHZ4L6EZGQM2ZKELEI2TIB}

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	2026-05-18T01:22:24.958502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1438a1f3c5f8993419aca88b223534055d5ed6cdd4ba077b77f4f31a1b7492f

Aliases

arxiv: 1309.2123 · arxiv_version: 1309.2123v1 · doi: 10.48550/arxiv.1309.2123 · pith_short_12: WFBYUHZ4L6EZ · pith_short_16: WFBYUHZ4L6EZGQM2 · pith_short_8: WFBYUHZ4

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/WFBYUHZ4L6EZGQM2ZKELEI2TIB \
  | 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: b1438a1f3c5f8993419aca88b223534055d5ed6cdd4ba077b77f4f31a1b7492f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b5f28f7bd09f75c676dcba7827f13630e0ed096ecdd42d17246776c609f135b",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-09-09T11:52:20Z",
    "title_canon_sha256": "f724fe2033539abe6441860b36d78c701d5ab74d7a3509a756e9f3c2442bb595"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.2123",
    "kind": "arxiv",
    "version": 1
  }
}