Pith Number

pith:43WRAB64

pith:2005:43WRAB64HLN63SZSPR4Z25QRXF

not attested not anchored not stored refs pending

Negative values of truncations to $L(1,\chi)$

Andrew Granville, K. Soundararajan

arxiv:math/0508361 v1 · 2005-08-18 · 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{43WRAB64HLN63SZSPR4Z25QRXF}

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	2026-07-04T14:40:18.984994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6ed1007dc3adbedcb327c799d7611b97e342693366dbe082d84297e32e74f3d

Aliases

arxiv: math/0508361 · arxiv_version: math/0508361v1 · doi: 10.48550/arxiv.math/0508361 · pith_short_12: 43WRAB64HLN6 · pith_short_16: 43WRAB64HLN63SZS · pith_short_8: 43WRAB64

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/43WRAB64HLN63SZSPR4Z25QRXF \
  | 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: e6ed1007dc3adbedcb327c799d7611b97e342693366dbe082d84297e32e74f3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46465de29274d358a778cac3bb5d201f8427450c3fb38f871be16f772db07c82",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-08-18T23:17:42Z",
    "title_canon_sha256": "b357098b2bc03efe7d2da36ecfbd78af3ca64873714386f14be40e9b21203eb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508361",
    "kind": "arxiv",
    "version": 1
  }
}