Pith Number

pith:Q3EKVY4Z

pith:2015:Q3EKVY4ZZOMLV4NVWJP2R7KE4Y

not attested not anchored not stored refs pending

Harmonic analysis operators related to symmetrized Jacobi expansions for all admissible parameters

Bartosz Langowski

arxiv:1512.08948 v1 · 2015-12-30 · 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{Q3EKVY4ZZOMLV4NVWJP2R7KE4Y}

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	2026-05-18T01:23:34.402762Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86c8aae399cb98baf1b5b25fa8fd44e607fa557511ce1582adf424b2d95396dc

Aliases

arxiv: 1512.08948 · arxiv_version: 1512.08948v1 · doi: 10.48550/arxiv.1512.08948 · pith_short_12: Q3EKVY4ZZOML · pith_short_16: Q3EKVY4ZZOMLV4NV · pith_short_8: Q3EKVY4Z

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/Q3EKVY4ZZOMLV4NVWJP2R7KE4Y \
  | 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: 86c8aae399cb98baf1b5b25fa8fd44e607fa557511ce1582adf424b2d95396dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "474bc27b03af3517cb494feb5367ac6837ec1df3df97d9dfc0847ec4db8ee2d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-30T14:22:24Z",
    "title_canon_sha256": "c469229a4d56a7ed1d120756c8b2e65fe36559de3b18b58f68fb2dd2f291b9af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08948",
    "kind": "arxiv",
    "version": 1
  }
}