Pith Number

pith:JLGPLQ3G

pith:2021:JLGPLQ3GJDEIAHBHQFXXTOPWDH

not attested not anchored not stored refs pending

On the error term in the explicit formula of Riemann--von Mangoldt

Daniel R. Johnston, Michaela Cully-Hugill

arxiv:2111.10001 v5 · 2021-11-19 · 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{JLGPLQ3GJDEIAHBHQFXXTOPWDH}

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

1 paper in Pith

Effective short intervals containing primes

Receipt and verification

First computed	2026-07-05T07:30:42.470880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4accf5c36648c8801c27816f79b9f619eeb60b150057e877499286c7eeb8f913

Aliases

arxiv: 2111.10001 · arxiv_version: 2111.10001v5 · doi: 10.48550/arxiv.2111.10001 · pith_short_12: JLGPLQ3GJDEI · pith_short_16: JLGPLQ3GJDEIAHBH · pith_short_8: JLGPLQ3G

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/JLGPLQ3GJDEIAHBHQFXXTOPWDH \
  | 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: 4accf5c36648c8801c27816f79b9f619eeb60b150057e877499286c7eeb8f913

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "140157462d561a6420563c29f3cd2a6a4bf466f73593ca902c14b5e015f01388",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-11-19T01:36:50Z",
    "title_canon_sha256": "5f361db7d7e42a4a4549b4e9f8096ba9a416c6de6e73d7b0a8a0c8d068b8611e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.10001",
    "kind": "arxiv",
    "version": 5
  }
}