Pith Number

pith:IJ7UTUJK

pith:2018:IJ7UTUJKIXW5F3ONACOYIDO5RK

not attested not anchored not stored refs pending

Spectrum of composition operators on ${\mathcal S}({\mathbb R})$ with polynomial symbols

Antonio Galbis, Carmen Fern\'andez, Enrique Jord\'a

arxiv:1810.13208 v1 · 2018-10-31 · 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{IJ7UTUJKIXW5F3ONACOYIDO5RK}

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	2026-05-18T00:01:51.927649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

427f49d12a45edd2edcd009d840ddd8a9682b6eb4bfeb335494ea477f17b5713

Aliases

arxiv: 1810.13208 · arxiv_version: 1810.13208v1 · doi: 10.48550/arxiv.1810.13208 · pith_short_12: IJ7UTUJKIXW5 · pith_short_16: IJ7UTUJKIXW5F3ON · pith_short_8: IJ7UTUJK

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/IJ7UTUJKIXW5F3ONACOYIDO5RK \
  | 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: 427f49d12a45edd2edcd009d840ddd8a9682b6eb4bfeb335494ea477f17b5713

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2992757286a2b5d294519aff51052757955b85ff746febc30a96046b731c8f20",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-10-31T10:49:14Z",
    "title_canon_sha256": "fe26498baabcb788106daf5f174a086aa0f708ff9e53b19942a36ddcf67c3612"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.13208",
    "kind": "arxiv",
    "version": 1
  }
}