Pith Number

pith:A663KSTU

pith:2016:A663KSTUIXKMXA5RMVYUTHOW3F

not attested not anchored not stored refs pending

Johnson-Schechtman inequalities for noncommutative martingales

Dejian Zhou, Dmitriy Zanin, Fedor Sukochev, Yong Jiao

arxiv:1612.04452 v1 · 2016-12-14 · 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{A663KSTUIXKMXA5RMVYUTHOW3F}

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	2026-05-18T00:54:59.506863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07bdb54a7445d4cb83b16571499dd6d94c0f834d054a87c1c14059f27ef967ae

Aliases

arxiv: 1612.04452 · arxiv_version: 1612.04452v1 · doi: 10.48550/arxiv.1612.04452 · pith_short_12: A663KSTUIXKM · pith_short_16: A663KSTUIXKMXA5R · pith_short_8: A663KSTU

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/A663KSTUIXKMXA5RMVYUTHOW3F \
  | 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: 07bdb54a7445d4cb83b16571499dd6d94c0f834d054a87c1c14059f27ef967ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab1ffb5e5e4829ca0413e4e6e2e826317b1bd7c6cdf7b5e0d417ca1e03652144",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-14T01:42:28Z",
    "title_canon_sha256": "891061b661bf712af8b6a62cf09122feb99f906e5792a6b81b52466157a273d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04452",
    "kind": "arxiv",
    "version": 1
  }
}