Pith Number

pith:IV4IQ3Q7

pith:2011:IV4IQ3Q7TCYRCINWDAZAY6C6QC

not attested not anchored not stored refs pending

L-functions associated with families of toric exponential sums

C. Douglas Haessig, Steven Sperber

arxiv:1109.3682 v2 · 2011-09-16 · 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{IV4IQ3Q7TCYRCINWDAZAY6C6QC}

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	2026-05-18T03:19:35.531100Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4578886e1f98b11121b618320c785e80860fd55599ab9c47a4e0df9e020d0efa

Aliases

arxiv: 1109.3682 · arxiv_version: 1109.3682v2 · doi: 10.48550/arxiv.1109.3682 · pith_short_12: IV4IQ3Q7TCYR · pith_short_16: IV4IQ3Q7TCYRCINW · pith_short_8: IV4IQ3Q7

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/IV4IQ3Q7TCYRCINWDAZAY6C6QC \
  | 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: 4578886e1f98b11121b618320c785e80860fd55599ab9c47a4e0df9e020d0efa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fca8b355fb01f524885b59a3b09502aef947cd2cbb90466d821f8bfab1d81ab4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-09-16T18:14:13Z",
    "title_canon_sha256": "35a230ff498b1e2082ae76304612313d2183f1f05dc1452f07869845df41de84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3682",
    "kind": "arxiv",
    "version": 2
  }
}