Pith Number

pith:4QTM5O7U

pith:2011:4QTM5O7UWTMO7MCZRYVNFGH47Y

not attested not anchored not stored refs pending

On the growth of vector-valued Fourier series

Fernando Soria, Javier Parcet, Quanhua Xu

arxiv:1109.4313 v2 · 2011-09-20 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4QTM5O7UWTMO7MCZRYVNFGH47Y}

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	2026-05-18T04:12:34.796145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e426cebbf4b4d8efb0598e2ad298fcfe28ba525a75a55243e41af386fd5a7464

Aliases

arxiv: 1109.4313 · arxiv_version: 1109.4313v2 · doi: 10.48550/arxiv.1109.4313 · pith_short_12: 4QTM5O7UWTMO · pith_short_16: 4QTM5O7UWTMO7MCZ · pith_short_8: 4QTM5O7U

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/4QTM5O7UWTMO7MCZRYVNFGH47Y \
  | 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: e426cebbf4b4d8efb0598e2ad298fcfe28ba525a75a55243e41af386fd5a7464

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26ded02d8987839279911e80608c9ca515d4637110a8e09b68eef3f1f7c321f7",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-09-20T15:00:39Z",
    "title_canon_sha256": "1aa8433c2fd324990996ca7c379f526db4c892b4dc7e8ef09c587ca46689870b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4313",
    "kind": "arxiv",
    "version": 2
  }
}