Pith Number

pith:LTFPJNB4

pith:2012:LTFPJNB4VO54KUJ5VQQ4XZSKF2

not attested not anchored not stored refs pending

Asymptotic variation of L-functions of exponential sums

Hui June Zhu

arxiv:1211.5875 v2 · 2012-11-26 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LTFPJNB4VO54KUJ5VQQ4XZSKF2}

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	2026-05-18T03:39:52.550163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ccaf4b43cabbbc5513dac21cbe64a2e9568e3e58ca26d344a347da06e629381

Aliases

arxiv: 1211.5875 · arxiv_version: 1211.5875v2 · doi: 10.48550/arxiv.1211.5875 · pith_short_12: LTFPJNB4VO54 · pith_short_16: LTFPJNB4VO54KUJ5 · pith_short_8: LTFPJNB4

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/LTFPJNB4VO54KUJ5VQQ4XZSKF2 \
  | 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: 5ccaf4b43cabbbc5513dac21cbe64a2e9568e3e58ca26d344a347da06e629381

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfe0d1f4e85652375c689689d92c2672ed68ed57066a1f33cbcaf230967cdc5d",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-26T08:03:41Z",
    "title_canon_sha256": "945b12c1ecbd4315cbf7a03d0188bc03221bd5f3afd0ae5c5a8c9d2408a43066"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5875",
    "kind": "arxiv",
    "version": 2
  }
}