Pith Number

pith:W3PXV4RB

pith:2016:W3PXV4RBY6DL2ILOMKQXOTMHY6

not attested not anchored not stored refs pending

Applications of some exponential sums on prime powers: a survey

Alessandro Languasco

arxiv:1606.00860 v1 · 2016-06-02 · 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{W3PXV4RBY6DL2ILOMKQXOTMHY6}

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	2026-05-18T00:44:42.555442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6df7af221c786bd216e62a1774d87c7b7e97aa4eaf69df913e27f4f4a0f962b

Aliases

arxiv: 1606.00860 · arxiv_version: 1606.00860v1 · doi: 10.48550/arxiv.1606.00860 · pith_short_12: W3PXV4RBY6DL · pith_short_16: W3PXV4RBY6DL2ILO · pith_short_8: W3PXV4RB

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/W3PXV4RBY6DL2ILOMKQXOTMHY6 \
  | 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: b6df7af221c786bd216e62a1774d87c7b7e97aa4eaf69df913e27f4f4a0f962b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "697ac370eb61dc5f39d165ae2cc8b2ac322041ead0cd0a258738467ce10b15a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-06-02T20:36:03Z",
    "title_canon_sha256": "4622fc2f296e2da41c761846fcf0baeaa13b8a6cea6b6bbe8f869a44becee0c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.00860",
    "kind": "arxiv",
    "version": 1
  }
}