Pith Number

pith:72PQ7KI6

pith:2013:72PQ7KI6CAVVQTYXYCDP4IIMUX

not attested not anchored not stored refs pending

Sobolev spaces associated with Jacobi expansions

Bartosz Langowski

arxiv:1312.7285 v1 · 2013-12-27 · 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{72PQ7KI6CAVVQTYXYCDP4IIMUX}

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	2026-05-18T02:39:25.568921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe9f0fa91e102b584f17c086fe210ca5d449ff25233f8246067dd711ebf2b8f1

Aliases

arxiv: 1312.7285 · arxiv_version: 1312.7285v1 · doi: 10.48550/arxiv.1312.7285 · pith_short_12: 72PQ7KI6CAVV · pith_short_16: 72PQ7KI6CAVVQTYX · pith_short_8: 72PQ7KI6

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/72PQ7KI6CAVVQTYXYCDP4IIMUX \
  | 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: fe9f0fa91e102b584f17c086fe210ca5d449ff25233f8246067dd711ebf2b8f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed903fd725fe4b73ff135c0615319df50484c2812e765cfabec07e722c8289eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-12-27T15:41:11Z",
    "title_canon_sha256": "1698851b526d1b70c84b159b8aca29d81faf20b2dc2d7761c48b51655b507bc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7285",
    "kind": "arxiv",
    "version": 1
  }
}