Pith Number

pith:3RY7L5XU

pith:2015:3RY7L5XUYSYZEOCTPCFVN4LV3B

not attested not anchored not stored refs pending

Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions

Bartosz Langowski

arxiv:1505.01653 v3 · 2015-05-07 · 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{3RY7L5XUYSYZEOCTPCFVN4LV3B}

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	2026-05-18T01:15:58.633719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc71f5f6f4c4b1923853788b56f175d87ccbeef975d10031b11b5eb153cfa599

Aliases

arxiv: 1505.01653 · arxiv_version: 1505.01653v3 · doi: 10.48550/arxiv.1505.01653 · pith_short_12: 3RY7L5XUYSYZ · pith_short_16: 3RY7L5XUYSYZEOCT · pith_short_8: 3RY7L5XU

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/3RY7L5XUYSYZEOCTPCFVN4LV3B \
  | 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: dc71f5f6f4c4b1923853788b56f175d87ccbeef975d10031b11b5eb153cfa599

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19be9fc5c27fd15080c6bf33eca078bf469d341ab2db2fbc338c78a86e5bfaf4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-05-07T10:26:01Z",
    "title_canon_sha256": "cdb7f08dbf25714b118c9c78bca416004f2acbefd12dbdbe1a200ecdc81e6fa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.01653",
    "kind": "arxiv",
    "version": 3
  }
}