Pith Number

pith:ZZWKPAJE

pith:2016:ZZWKPAJEEOTUOJL5MD3JDKTSOT

not attested not anchored not stored refs pending

Isometric embedding of $\ell_1$ into Lipschitz-free spaces and $\ell_\infty$ into their duals

Marek C\'uth, Michal Johanis

arxiv:1604.04131 v1 · 2016-04-14 · 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{ZZWKPAJEEOTUOJL5MD3JDKTSOT}

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	2026-05-18T00:29:05.906520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce6ca7812423a747257d60f691aa7274ca7bbe26090358f000cbef51aa94efe3

Aliases

arxiv: 1604.04131 · arxiv_version: 1604.04131v1 · doi: 10.48550/arxiv.1604.04131 · pith_short_12: ZZWKPAJEEOTU · pith_short_16: ZZWKPAJEEOTUOJL5 · pith_short_8: ZZWKPAJE

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/ZZWKPAJEEOTUOJL5MD3JDKTSOT \
  | 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: ce6ca7812423a747257d60f691aa7274ca7bbe26090358f000cbef51aa94efe3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b423ac177f1830553e617ea6aed2f1cdc1fa89fca6cd1d776cd20a583b0b411a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-04-14T12:21:55Z",
    "title_canon_sha256": "690b38105812a337e8493db4b2ea5942838a4c381d2f17d21a241a38d7f39605"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.04131",
    "kind": "arxiv",
    "version": 1
  }
}