Pith Number

pith:IF3T6T2Y

pith:2018:IF3T6T2YNA6KPRG26P2HVLYTEA

not attested not anchored not stored refs pending

Entropy numbers and spectral radius type formula for composition operators on the polydisk

Daniel Li (LML), Herv\'e Queff\'elec (LPP), Luis Rodr\'iguez-Piazza

arxiv:1812.02060 v1 · 2018-12-05 · 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{IF3T6T2YNA6KPRG26P2HVLYTEA}

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	2026-05-17T23:58:59.819266Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41773f4f58683ca7c4daf3f47aaf1320146c46f6cc7869174369e84a84e0142b

Aliases

arxiv: 1812.02060 · arxiv_version: 1812.02060v1 · doi: 10.48550/arxiv.1812.02060 · pith_short_12: IF3T6T2YNA6K · pith_short_16: IF3T6T2YNA6KPRG2 · pith_short_8: IF3T6T2Y

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/IF3T6T2YNA6KPRG26P2HVLYTEA \
  | 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: 41773f4f58683ca7c4daf3f47aaf1320146c46f6cc7869174369e84a84e0142b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2549945828eac2b5ba1d7e3295d25e660c0a5c427094bc82814387f0ec9a06bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-12-05T15:49:27Z",
    "title_canon_sha256": "98bf42b7310e18d2de5fc807859ff62f3334211fc2d47b946e8a240579aec210"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.02060",
    "kind": "arxiv",
    "version": 1
  }
}