Pith Number

pith:XZK5YT5J

pith:2015:XZK5YT5J6H5OSMMCRKPFTS2E3H

not attested not anchored not stored refs pending

An analytic method for bounding $\psi(x)$

Jan B\"uthe

arxiv:1511.02032 v2 · 2015-11-06 · math.NT · math.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XZK5YT5J6H5OSMMCRKPFTS2E3H}

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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

An Efficient Algorithm for Estimating Prime Counts

Receipt and verification

First computed	2026-05-18T00:32:21.607991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be55dc4fa9f1fae931828a9e59cb44d9dd853215326be1a7745e0467591bda3b

Aliases

arxiv: 1511.02032 · arxiv_version: 1511.02032v2 · doi: 10.48550/arxiv.1511.02032 · pith_short_12: XZK5YT5J6H5O · pith_short_16: XZK5YT5J6H5OSMMC · pith_short_8: XZK5YT5J

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/XZK5YT5J6H5OSMMCRKPFTS2E3H \
  | 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: be55dc4fa9f1fae931828a9e59cb44d9dd853215326be1a7745e0467591bda3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a89daea114b8e3a4f6cf301e2a5e01891566e69eca694fd348b939d15c6ecb78",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-11-06T11:10:12Z",
    "title_canon_sha256": "d41755419d5e8b4d333ed006764fe2afe5091f62161fe1fb8938d3f714957608"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.02032",
    "kind": "arxiv",
    "version": 2
  }
}