Pith Number

pith:PMOAI5WO

pith:2002:PMOAI5WOPRVJ22CPJGLHTY2Z7Z

not attested not anchored not stored refs pending

Doob's inequality for non-commutative martingales

M. Junge

arxiv:math/0206062 v1 · 2002-06-06 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PMOAI5WOPRVJ22CPJGLHTY2Z7Z}

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.

Cited by

1 paper in Pith

A general proof of integer R\'enyi QNEC

Receipt and verification

First computed	2026-07-04T14:36:15.198827Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b1c0476ce7c6a9d684f499679e359fe72c749a5dce22f41d1cb88beb0d0c825

Aliases

arxiv: math/0206062 · arxiv_version: math/0206062v1 · doi: 10.48550/arxiv.math/0206062 · pith_short_12: PMOAI5WOPRVJ · pith_short_16: PMOAI5WOPRVJ22CP · pith_short_8: PMOAI5WO

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/PMOAI5WOPRVJ22CPJGLHTY2Z7Z \
  | 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: 7b1c0476ce7c6a9d684f499679e359fe72c749a5dce22f41d1cb88beb0d0c825

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79543dcec792b07cbb12a394a9445ccdd80065f3c38528ebcb917e1c7078aa85",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2002-06-06T23:15:07Z",
    "title_canon_sha256": "99e5d836b6f8fd57af68be5dce26a09d38e1f845ef5e54b6515339a9ac3c817d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0206062",
    "kind": "arxiv",
    "version": 1
  }
}