Pith Number

pith:5PGLKXVA

pith:2012:5PGLKXVAALUNRRTTZKCS6OFGHN

not attested not anchored not stored refs pending

Series Expansion of Generalized Fresnel Integrals

Richard J. Mathar

arxiv:1211.3963 v2 · 2012-11-16 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5PGLKXVAALUNRRTTZKCS6OFGHN}

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	2026-05-18T03:39:15.969359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebccb55ea002e8d8c673ca852f38a63b69441a75634cab0ee9db1a8933d2a5ca

Aliases

arxiv: 1211.3963 · arxiv_version: 1211.3963v2 · doi: 10.48550/arxiv.1211.3963 · pith_short_12: 5PGLKXVAALUN · pith_short_16: 5PGLKXVAALUNRRTT · pith_short_8: 5PGLKXVA

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/5PGLKXVAALUNRRTTZKCS6OFGHN \
  | 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: ebccb55ea002e8d8c673ca852f38a63b69441a75634cab0ee9db1a8933d2a5ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba3e4519789544467989327ab7fdcebf8568ebb232fc445504ba6e7e22f9fd3a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-11-16T17:38:48Z",
    "title_canon_sha256": "15a1200321bc154b799470313af2b42315ff3015151e214037e03322f9c0e3e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3963",
    "kind": "arxiv",
    "version": 2
  }
}