Pith Number

pith:7XKKE3XQ

pith:2017:7XKKE3XQ2CIXKGZJ3JI3BCKEHO

not attested not anchored not stored refs pending

Gaussian martingale inequality applies to random functions and maxima of empirical processes

Xiequan Fan

arxiv:1706.03916 v2 · 2017-06-13 · 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{7XKKE3XQ2CIXKGZJ3JI3BCKEHO}

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	2026-05-18T00:32:50.565838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdd4a26ef0d091751b29da51b089443bb305a5f4b23ba9f360465740106dac02

Aliases

arxiv: 1706.03916 · arxiv_version: 1706.03916v2 · doi: 10.48550/arxiv.1706.03916 · pith_short_12: 7XKKE3XQ2CIX · pith_short_16: 7XKKE3XQ2CIXKGZJ · pith_short_8: 7XKKE3XQ

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/7XKKE3XQ2CIXKGZJ3JI3BCKEHO \
  | 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: fdd4a26ef0d091751b29da51b089443bb305a5f4b23ba9f360465740106dac02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23d89cc3e41fd69da6d6019a21d5ed82dcd3cfdda2d2d01cf3e25a49baf71096",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-06-13T06:16:40Z",
    "title_canon_sha256": "0ee574a4649d72b71e5a22117891120145334a84a55e9219d85f2d73aac814d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.03916",
    "kind": "arxiv",
    "version": 2
  }
}