Pith Number

pith:DTY62HY3

pith:2001:DTY62HY3NTFH2OCPPRTR2CBAAK

not attested not anchored not stored refs pending

p-adic variation of L-functions of exponential sums, I

Hui June Zhu

arxiv:math/0111194 v2 · 2001-11-18 · math.AG · 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{DTY62HY3NTFH2OCPPRTR2CBAAK}

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	2026-05-18T01:08:29.370696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1cf1ed1f1b6cca7d384f7c671d0820029fa1de382f6886ea1bc7cba4f1751fe6

Aliases

arxiv: math/0111194 · arxiv_version: math/0111194v2 · doi: 10.48550/arxiv.math/0111194 · pith_short_12: DTY62HY3NTFH · pith_short_16: DTY62HY3NTFH2OCP · pith_short_8: DTY62HY3

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/DTY62HY3NTFH2OCPPRTR2CBAAK \
  | 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: 1cf1ed1f1b6cca7d384f7c671d0820029fa1de382f6886ea1bc7cba4f1751fe6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a711c3a1f7cde0d12e60a3a9fdef160a78d386d66b9d1119773c10f61a9a6759",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2001-11-18T01:46:25Z",
    "title_canon_sha256": "ae0fbb7f7d379a92a4a633204697b52174c1f5c079aef3829974afad542e21ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0111194",
    "kind": "arxiv",
    "version": 2
  }
}