Pith Number

pith:DZB5SNII

pith:2011:DZB5SNIIC6JDE2QWJLGDVWHVJV

not attested not anchored not stored refs pending

Multi-norms and the injectivity of $L^p(G)$

H. Garth Dales, Hung Le Pham, Matthew Daws, Paul Ramsden

arxiv:1101.4320 v2 · 2011-01-22 · 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{DZB5SNIIC6JDE2QWJLGDVWHVJV}

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	2026-05-18T04:01:26.397902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e43d935081792326a164acc3ad8f54d5a98a925aba4d607f4c8b9db9b039020

Aliases

arxiv: 1101.4320 · arxiv_version: 1101.4320v2 · doi: 10.48550/arxiv.1101.4320 · pith_short_12: DZB5SNIIC6JD · pith_short_16: DZB5SNIIC6JDE2QW · pith_short_8: DZB5SNII

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/DZB5SNIIC6JDE2QWJLGDVWHVJV \
  | 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: 1e43d935081792326a164acc3ad8f54d5a98a925aba4d607f4c8b9db9b039020

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f9e2e3c0725efc4f45135ad3f56d8d17f50dd574a223f1c236115f4f30c6767",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-01-22T20:32:59Z",
    "title_canon_sha256": "9a9cee1c79264b3e311f534ecb8051b8f1705f1142e510576fca7a61dd73d5e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.4320",
    "kind": "arxiv",
    "version": 2
  }
}