Pith Number

pith:WVYR4MII

pith:2012:WVYR4MIIGEZ4TDYVAHBEWAOKLF

not attested not anchored not stored refs pending

On Enflo and narrow operators acting on $L_p$

B. Randrianantoanina, M. Popov, V. Mykhaylyuk

arxiv:1201.4041 v3 · 2012-01-19 · 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{WVYR4MIIGEZ4TDYVAHBEWAOKLF}

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	2026-05-18T04:00:15.230867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5711e31083133c98f1501c24b01ca5949be7600f358a9738a20e11e4fa962ba

Aliases

arxiv: 1201.4041 · arxiv_version: 1201.4041v3 · doi: 10.48550/arxiv.1201.4041 · pith_short_12: WVYR4MIIGEZ4 · pith_short_16: WVYR4MIIGEZ4TDYV · pith_short_8: WVYR4MII

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/WVYR4MIIGEZ4TDYVAHBEWAOKLF \
  | 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: b5711e31083133c98f1501c24b01ca5949be7600f358a9738a20e11e4fa962ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b09a9e1826312ecd4a5946c5eeee24fa9ec40a03b461d58730d60359e0549792",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-01-19T12:32:54Z",
    "title_canon_sha256": "1d5bd94852991fb5c4924cd2a0cc2b0c0a035f94ace4cd4eda77f659e86e635c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4041",
    "kind": "arxiv",
    "version": 3
  }
}