Pith Number

pith:JWCBE64N

pith:2013:JWCBE64NL2WCHGQZTXK7OYC5YY

not attested not anchored not stored refs pending

A real p-homogeneous seminorm with square property is submultiplicative

M. El Azhari

arxiv:1301.2000 v3 · 2013-01-09 · 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{JWCBE64NL2WCHGQZTXK7OYC5YY}

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	2026-05-18T03:03:32.423088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d84127b8d5eac239a199dd5f7605dc61d5afe88aa4d39d3533cfba16096f446

Aliases

arxiv: 1301.2000 · arxiv_version: 1301.2000v3 · doi: 10.48550/arxiv.1301.2000 · pith_short_12: JWCBE64NL2WC · pith_short_16: JWCBE64NL2WCHGQZ · pith_short_8: JWCBE64N

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/JWCBE64NL2WCHGQZTXK7OYC5YY \
  | 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: 4d84127b8d5eac239a199dd5f7605dc61d5afe88aa4d39d3533cfba16096f446

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10e20d73acb846e7ff8709ff6ec5c8093901bd4f90669f8499b13d908f3bbe0a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-01-09T22:39:47Z",
    "title_canon_sha256": "28ac332bf73e3b3cf7f4ad138155e627529e2b03dcef8bd2ee3413d4caa45ff4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.2000",
    "kind": "arxiv",
    "version": 3
  }
}