Pith Number

pith:LCCLJSEU

pith:2005:LCCLJSEUHKCX4KLJFU3MGW3YP3

not attested not anchored not stored refs pending

On the best constants in some non-commutative martingale inequalities

Marius Junge, Quanhua Xu

arxiv:math/0505309 v1 · 2005-05-14 · math.OA · math.FA · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LCCLJSEUHKCX4KLJFU3MGW3YP3}

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	2026-07-04T14:39:59.131966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5884b4c8943a857e29692d36c35b787ed3569796989525ec6f93151794fb261b

Aliases

arxiv: math/0505309 · arxiv_version: math/0505309v1 · doi: 10.48550/arxiv.math/0505309 · pith_short_12: LCCLJSEUHKCX · pith_short_16: LCCLJSEUHKCX4KLJ · pith_short_8: LCCLJSEU

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/LCCLJSEUHKCX4KLJFU3MGW3YP3 \
  | 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: 5884b4c8943a857e29692d36c35b787ed3569796989525ec6f93151794fb261b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36a1eee970d31b387e20326feada49ec95570289e4b7d72739eb6118e3e5d481",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2005-05-14T14:03:27Z",
    "title_canon_sha256": "76e5b92b6cdcd6b75df622aa591ed62f17879fef88a3c3523300ea1d6b62f540"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0505309",
    "kind": "arxiv",
    "version": 1
  }
}