Pith Number

pith:KNJFRTFW

pith:2017:KNJFRTFWZLHNADR5G5RUSG4FBR

not attested not anchored not stored refs pending

On the Azuma inequality in spaces of subgaussian of rank $p$ random variables

Krzysztof Zajkowski

arxiv:1701.03099 v1 · 2017-01-11 · 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{KNJFRTFWZLHNADR5G5RUSG4FBR}

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	2026-05-18T00:52:59.330639Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

535258ccb6caced00e3d3763491b850c7eca7cdbcb61345696780b86c443792f

Aliases

arxiv: 1701.03099 · arxiv_version: 1701.03099v1 · doi: 10.48550/arxiv.1701.03099 · pith_short_12: KNJFRTFWZLHN · pith_short_16: KNJFRTFWZLHNADR5 · pith_short_8: KNJFRTFW

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/KNJFRTFWZLHNADR5G5RUSG4FBR \
  | 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: 535258ccb6caced00e3d3763491b850c7eca7cdbcb61345696780b86c443792f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "701f7381b1068143a4ede9233123f4a73c1d6cb13df3b95cbb6e63ba5a71bbfd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-01-11T18:58:44Z",
    "title_canon_sha256": "55a365ef7dde8f7f0b14140bee7ec71922b7de8d88cb38549a445f218383689d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.03099",
    "kind": "arxiv",
    "version": 1
  }
}