Pith Number

pith:WFPRDH7N

pith:2013:WFPRDH7NFDJKPFG6PHVWDR7OEY

not attested not anchored not stored refs pending

The sliding-sum method for short exponential sums

\'E. Fouvry, E. Kowalski, Ph. Michel

arxiv:1307.0135 v2 · 2013-06-29 · 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{WFPRDH7NFDJKPFG6PHVWDR7OEY}

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	2026-05-18T01:35:57.579016Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b15f119fed28d2a794de79eb61c7ee2621c5e68978139597eaabb6a52217aeec

Aliases

arxiv: 1307.0135 · arxiv_version: 1307.0135v2 · doi: 10.48550/arxiv.1307.0135 · pith_short_12: WFPRDH7NFDJK · pith_short_16: WFPRDH7NFDJKPFG6 · pith_short_8: WFPRDH7N

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/WFPRDH7NFDJKPFG6PHVWDR7OEY \
  | 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: b15f119fed28d2a794de79eb61c7ee2621c5e68978139597eaabb6a52217aeec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8ee23543cb2713f2fbfb1bc191d5ec852854f77f25bc9231a6da1c0f1b2b88d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-06-29T17:54:10Z",
    "title_canon_sha256": "9954c0158748264a31975ed4fc6219fbb037cb50fb080ed683e9f615737cb752"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.0135",
    "kind": "arxiv",
    "version": 2
  }
}