Pith Number

pith:PIPBQJDX

pith:2017:PIPBQJDXVWPTNKWTBMID5FUCLK

not attested not anchored not stored refs pending

Integrals containing the logarithm of the Airy Function Ai'(x)

Bernard J. Laurenzi

arxiv:1712.10332 v1 · 2017-12-21 · math.CA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PIPBQJDXVWPTNKWTBMID5FUCLK}

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	2026-05-18T00:27:03.387617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a1e182477ad9f36aad30b103e96825aac878a9988d1dd6763f42ff749b9d937

Aliases

arxiv: 1712.10332 · arxiv_version: 1712.10332v1 · doi: 10.48550/arxiv.1712.10332 · pith_short_12: PIPBQJDXVWPT · pith_short_16: PIPBQJDXVWPTNKWT · pith_short_8: PIPBQJDX

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/PIPBQJDXVWPTNKWTBMID5FUCLK \
  | 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: 7a1e182477ad9f36aad30b103e96825aac878a9988d1dd6763f42ff749b9d937

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47e688d7b09155e2448695bb398590a0c52e070bfd726535c6d6424c322de49d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-12-21T19:03:14Z",
    "title_canon_sha256": "20b68d2e2458c2be0103803e2244c0517ae42a1f02160c11262d5e73963eab74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.10332",
    "kind": "arxiv",
    "version": 1
  }
}