Pith Number

pith:LTV5XZUM

pith:2017:LTV5XZUMQ5KBEDO6JRPIVJ46IL

not attested not anchored not stored refs pending

New estimates for some functions defined over primes

Christian Axler

arxiv:1703.08032 v2 · 2017-03-23 · 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{LTV5XZUMQ5KBEDO6JRPIVJ46IL}

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	2026-05-18T00:44:18.647347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cebdbe68c8754120dde4c5e8aa79e42c1c2fc49c336f1c0c3cafeca15dd464a

Aliases

arxiv: 1703.08032 · arxiv_version: 1703.08032v2 · doi: 10.48550/arxiv.1703.08032 · pith_short_12: LTV5XZUMQ5KB · pith_short_16: LTV5XZUMQ5KBEDO6 · pith_short_8: LTV5XZUM

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/LTV5XZUMQ5KBEDO6JRPIVJ46IL \
  | 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: 5cebdbe68c8754120dde4c5e8aa79e42c1c2fc49c336f1c0c3cafeca15dd464a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "403bff34dece5a33f93d8d1b88a26535f11724dfa0c21ca3645fff0973aeb58c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-03-23T12:18:29Z",
    "title_canon_sha256": "09955e4c7e179113e16fa3d17d63dc27c39f02f2aff9c0ae62622dc44fffb589"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.08032",
    "kind": "arxiv",
    "version": 2
  }
}