Pith Number

pith:L5CQFZ6K

pith:2009:L5CQFZ6K2FKBA76XMFV33CKNLX

not attested not anchored not stored refs pending

Character sums with division polynomials

Igor E Shparlinski, Katherine E. Stange

arxiv:0912.5246 v4 · 2009-12-29 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L5CQFZ6K2FKBA76XMFV33CKNLX}

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	2026-05-18T02:30:32.984910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f4502e7cad154107fd7616bbd894d5dedc9f4c52052e9ff92cc8141995c988b

Aliases

arxiv: 0912.5246 · arxiv_version: 0912.5246v4 · doi: 10.48550/arxiv.0912.5246 · pith_short_12: L5CQFZ6K2FKB · pith_short_16: L5CQFZ6K2FKBA76X · pith_short_8: L5CQFZ6K

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/L5CQFZ6K2FKBA76XMFV33CKNLX \
  | 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: 5f4502e7cad154107fd7616bbd894d5dedc9f4c52052e9ff92cc8141995c988b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1357c880eee93f8aeb83e0e06ced0d89348d44e5bacdc830aef4bbc398d76422",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-12-29T03:43:16Z",
    "title_canon_sha256": "bac447b32730c6c69d7e7329ca684236ce86ccc0b105aff35060af6816c80f81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.5246",
    "kind": "arxiv",
    "version": 4
  }
}