Pith Number

pith:5GRJPXDW

pith:2004:5GRJPXDWNLJN3RBWPRFUYBNODK

not attested not anchored not stored refs pending

$\ell_p$ (p>2) does not coarsely embed into a Hilbert space

N. L. Randrianarivony, W. B. Johnson

arxiv:math/0410427 v1 · 2004-10-19 · 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{5GRJPXDWNLJN3RBWPRFUYBNODK}

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	2026-05-18T01:05:25.719181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9a297dc766ad2ddc4367c4b4c05ae1ab0bb2794f62e7f1ebcdc63ab81afbe41

Aliases

arxiv: math/0410427 · arxiv_version: math/0410427v1 · doi: 10.48550/arxiv.math/0410427 · pith_short_12: 5GRJPXDWNLJN · pith_short_16: 5GRJPXDWNLJN3RBW · pith_short_8: 5GRJPXDW

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/5GRJPXDWNLJN3RBWPRFUYBNODK \
  | 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: e9a297dc766ad2ddc4367c4b4c05ae1ab0bb2794f62e7f1ebcdc63ab81afbe41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a06cf64c828ecb2f1c6bc12dfdac550ea764d70212eb06db3f8588727a3cbde",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2004-10-19T19:20:48Z",
    "title_canon_sha256": "3d545aacdc32437b2f00c2b5e2759b971cc7f73619d3dd045d20c9dc6dd7b041"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0410427",
    "kind": "arxiv",
    "version": 1
  }
}