Pith Number

pith:TPE65RFG

pith:2017:TPE65RFG3OGU4B6EUFQ3H2NSOO

not attested not anchored not stored refs pending

Mean square of zeta function, circle problem and divisor problem revisited

Jean Bourgain, Nigel Watt

arxiv:1709.04340 v2 · 2017-09-13 · math.AP · 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{TPE65RFG3OGU4B6EUFQ3H2NSOO}

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.

Cited by

2 papers in Pith

The Weyl formula for planar annuli

On the Hyperbolic Fractional Sum of the Divisor Function

Receipt and verification

First computed	2026-07-05T06:31:00.864289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bc9eec4a6db8d4e07c4a161b3e9b2738019cf713617e899bc4d5fcb4ea29dba

Aliases

arxiv: 1709.04340 · arxiv_version: 1709.04340v2 · doi: 10.48550/arxiv.1709.04340 · pith_short_12: TPE65RFG3OGU · pith_short_16: TPE65RFG3OGU4B6E · pith_short_8: TPE65RFG

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/TPE65RFG3OGU4B6EUFQ3H2NSOO \
  | 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: 9bc9eec4a6db8d4e07c4a161b3e9b2738019cf713617e899bc4d5fcb4ea29dba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50387ddcdab01a10893882e9f3f12ab6d6e2603d0e199da76c89830e47412406",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-09-13T14:11:00Z",
    "title_canon_sha256": "562c3d2dd6b3abd66a5f40cb0ca10d790dbcace65334b7397b3e9ad59f12623a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.04340",
    "kind": "arxiv",
    "version": 2
  }
}