Pith Number

pith:72O4MNAX

pith:2018:72O4MNAXCX2UTSM4VC5DAXFUHN

not attested not anchored not stored refs pending

Sharp inequalities for linear combinations of orthogonal martingales

Kai Zhu, Loukas Grafakos, Yong Ding

arxiv:1803.04570 v1 · 2018-03-12 · math.CA · 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{72O4MNAXCX2UTSM4VC5DAXFUHN}

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	2026-05-18T00:21:18.652989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe9dc6341715f549c99ca8ba305cb43b7044f93a388aee0b9e3d95ce8c4dc90a

Aliases

arxiv: 1803.04570 · arxiv_version: 1803.04570v1 · doi: 10.48550/arxiv.1803.04570 · pith_short_12: 72O4MNAXCX2U · pith_short_16: 72O4MNAXCX2UTSM4 · pith_short_8: 72O4MNAX

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/72O4MNAXCX2UTSM4VC5DAXFUHN \
  | 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: fe9dc6341715f549c99ca8ba305cb43b7044f93a388aee0b9e3d95ce8c4dc90a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fb97f49ee2517dde4a492d4efab84ab5fe58fcb7310d76da93c3c9302585800",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-03-12T23:17:00Z",
    "title_canon_sha256": "0241ff5bb491a7fcea9c660602062b707d744f21f6f3de4ea2305ea0a3639ac8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.04570",
    "kind": "arxiv",
    "version": 1
  }
}