Pith Number

pith:52MAEILJ

pith:2005:52MAEILJE27OAZMEMMJA4VM224

not attested not anchored not stored refs pending

Large character sums: Pretentious characters and the Polya-Vinogradov Theorem

Andrew Granville, K. Soundararajan

arxiv:math/0503113 v1 · 2005-03-06 · 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{52MAEILJE27OAZMEMMJA4VM224}

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	2026-07-04T14:39:46.281381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee9802216926bee0658463120e559ad707c483dd09fbb0fae0f88545bfef4569

Aliases

arxiv: math/0503113 · arxiv_version: math/0503113v1 · doi: 10.48550/arxiv.math/0503113 · pith_short_12: 52MAEILJE27O · pith_short_16: 52MAEILJE27OAZME · pith_short_8: 52MAEILJ

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/52MAEILJE27OAZMEMMJA4VM224 \
  | 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: ee9802216926bee0658463120e559ad707c483dd09fbb0fae0f88545bfef4569

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3c8dfbe18e8a04dd0aacb9a4bd7c9b5cbd3304954967da1a938d3d1b5f5c40c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-03-06T18:34:04Z",
    "title_canon_sha256": "bccbd9eb5169f9eb1561a9a6e6fa466c994ea293530478f405166b68cba0a8af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0503113",
    "kind": "arxiv",
    "version": 1
  }
}