Pith Number

pith:6MP5SON7

pith:2025:6MP5SON7HCBIGOZMTYERD6JAES

not attested not anchored not stored refs pending

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $

Michael Revers

arxiv:2501.04488 v2 · 2025-01-08 · 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{6MP5SON7HCBIGOZMTYERD6JAES}

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	2026-07-05T10:07:29.342573Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f31fd939bf3882833b2c9e0911f920248cd761af7b71719b5f2e037ae62c0367

Aliases

arxiv: 2501.04488 · arxiv_version: 2501.04488v2 · doi: 10.48550/arxiv.2501.04488 · pith_short_12: 6MP5SON7HCBI · pith_short_16: 6MP5SON7HCBIGOZM · pith_short_8: 6MP5SON7

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/6MP5SON7HCBIGOZMTYERD6JAES \
  | 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: f31fd939bf3882833b2c9e0911f920248cd761af7b71719b5f2e037ae62c0367

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "810d5c0c30531f5b246ba4a75b8f839b8f08811bdeb6bd0562e369a3fa75e8ae",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-01-08T13:14:54Z",
    "title_canon_sha256": "d4f56c2d9eabf1c0a842e92549626f129ffd1fd425b5e6e2559a9cd096d21336"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.04488",
    "kind": "arxiv",
    "version": 2
  }
}