Pith Number

pith:Y4WZT4N7

pith:2015:Y4WZT4N7RPXW2BH4WTYL2LQK4K

not attested not anchored not stored refs pending

Large character sums: Burgess's theorem and zeros of $L$-functions

Andrew Granville, Kannan Soundararajan

arxiv:1501.01804 v2 · 2015-01-08 · 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{Y4WZT4N7RPXW2BH4WTYL2LQK4K}

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	2026-05-18T00:42:07.998556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c72d99f1bf8bef6d04fcb4f0bd2e0ae2a664dac98f88da9570360f9aefd5bfa0

Aliases

arxiv: 1501.01804 · arxiv_version: 1501.01804v2 · doi: 10.48550/arxiv.1501.01804 · pith_short_12: Y4WZT4N7RPXW · pith_short_16: Y4WZT4N7RPXW2BH4 · pith_short_8: Y4WZT4N7

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/Y4WZT4N7RPXW2BH4WTYL2LQK4K \
  | 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: c72d99f1bf8bef6d04fcb4f0bd2e0ae2a664dac98f88da9570360f9aefd5bfa0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ce41c79a0a56ec5abfd61fd85f490e02c566cd77a7215f0df0c5c1833d94925",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-01-08T11:47:04Z",
    "title_canon_sha256": "6596000c6dfd25fd98bb5f9c11ce38b47741eb02884d6dc6a7e25cf5240540bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.01804",
    "kind": "arxiv",
    "version": 2
  }
}