Pith Number

pith:MBZ6FUGT

pith:2017:MBZ6FUGT4FYHDI64IDOC2MVRMW

not attested not anchored not stored refs pending

Bounds of triple exponential sums with mixed exponential and linear terms

Kam Hung Yau

arxiv:1707.09707 v5 · 2017-07-31 · 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{MBZ6FUGT4FYHDI64IDOC2MVRMW}

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	2026-05-18T00:07:18.553777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6073e2d0d3e17071a3dc40dc2d32b1659a0017fae51a56a0e88c6ce628dc7c9f

Aliases

arxiv: 1707.09707 · arxiv_version: 1707.09707v5 · doi: 10.48550/arxiv.1707.09707 · pith_short_12: MBZ6FUGT4FYH · pith_short_16: MBZ6FUGT4FYHDI64 · pith_short_8: MBZ6FUGT

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/MBZ6FUGT4FYHDI64IDOC2MVRMW \
  | 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: 6073e2d0d3e17071a3dc40dc2d32b1659a0017fae51a56a0e88c6ce628dc7c9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd63e27c327aaa0dcd30e5bdf1ffc1fa48d5306d2857f8d30bed7faec8b5de8b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-07-31T03:21:01Z",
    "title_canon_sha256": "69e1a0b611e3bd8ae91a0b1aed5dfbc6f19454f40b4b8b810903a7b8178c01a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.09707",
    "kind": "arxiv",
    "version": 5
  }
}