Pith Number

pith:3JWLMYMX

pith:2022:3JWLMYMXA4HWSS7ABFJK7G6D4Q

not attested not anchored not stored refs pending

Maximal estimates for the Weyl sums on $\mathbb{T}^{d}$ (with an appendix by Alex Barron)

Changxing Miao, Jiye Yuan, Tengfei Zhao

arxiv:2201.12840 v4 · 2022-01-30 · math.NT · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3JWLMYMXA4HWSS7ABFJK7G6D4Q}

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	2026-07-05T06:04:49.317789Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da6cb66197070f694be00952af9bc3e4011a0fdd83bdf42029b1a01d054e7351

Aliases

arxiv: 2201.12840 · arxiv_version: 2201.12840v4 · doi: 10.48550/arxiv.2201.12840 · pith_short_12: 3JWLMYMXA4HW · pith_short_16: 3JWLMYMXA4HWSS7A · pith_short_8: 3JWLMYMX

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/3JWLMYMXA4HWSS7ABFJK7G6D4Q \
  | 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: da6cb66197070f694be00952af9bc3e4011a0fdd83bdf42029b1a01d054e7351

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebc12248b74d9be77953c6b5429b03fc3b19173063069fc5fc0311747418574c",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-01-30T15:10:33Z",
    "title_canon_sha256": "83cfeaf739cdc97f5efd74415a37e40747f972d8db24bbde22018f9e1da89fe6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2201.12840",
    "kind": "arxiv",
    "version": 4
  }
}