Pith Number

pith:2HTN6L2G

pith:2024:2HTN6L2GOLM2GCJQFDU2EH5ZPD

not attested not anchored not stored refs pending

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals

Glenn Bruda

arxiv:2412.19866 v1 · 2024-12-27 · math.CO · 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{2HTN6L2GOLM2GCJQFDU2EH5ZPD}

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	2026-07-05T09:54:50.789103Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1e6df2f4672d9a3093028e9a21fb978de2bbf2f10f253933a317624987b97fb

Aliases

arxiv: 2412.19866 · arxiv_version: 2412.19866v1 · doi: 10.48550/arxiv.2412.19866 · pith_short_12: 2HTN6L2GOLM2 · pith_short_16: 2HTN6L2GOLM2GCJQ · pith_short_8: 2HTN6L2G

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/2HTN6L2GOLM2GCJQFDU2EH5ZPD \
  | 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: d1e6df2f4672d9a3093028e9a21fb978de2bbf2f10f253933a317624987b97fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "feb9e4fc1836d571d983d5af00fba6cfc68ec8c7b71c1b9e829dbdc5d8111233",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-27T04:32:55Z",
    "title_canon_sha256": "a1f5ab775166681e2c692f16872c2c3b31af5a6fa215fa1034b45122056aa0de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.19866",
    "kind": "arxiv",
    "version": 1
  }
}