Pith Number

pith:L4OQGIR2

pith:2025:L4OQGIR2COOF2BT4FK5VSW53FS

not attested not anchored not stored refs pending

On the connection between zero-free regions and the error term in the Prime Number Theorem

Frederik Broucke

arxiv:2507.13780 v1 · 2025-07-18 · 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{L4OQGIR2COOF2BT4FK5VSW53FS}

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	2026-07-05T11:39:22.891703Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f1d03223a139c5d067c2abb595bbb2c9a65e96a5a1e2c4cecc545e54195f520

Aliases

arxiv: 2507.13780 · arxiv_version: 2507.13780v1 · doi: 10.48550/arxiv.2507.13780 · pith_short_12: L4OQGIR2COOF · pith_short_16: L4OQGIR2COOF2BT4 · pith_short_8: L4OQGIR2

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/L4OQGIR2COOF2BT4FK5VSW53FS \
  | 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: 5f1d03223a139c5d067c2abb595bbb2c9a65e96a5a1e2c4cecc545e54195f520

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55e176c0f63eeb66a02b19931eda8ba0ff165e2ea4a13c71ce90715378265526",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-07-18T09:46:12Z",
    "title_canon_sha256": "6fe1fcdaded596e4b0145674276dc03947cb747407a10c558246020d0146883e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.13780",
    "kind": "arxiv",
    "version": 1
  }
}