Pith Number

pith:3FNFRODC

pith:2011:3FNFRODC6FME74XU2M7W6X57R7

not attested not anchored not stored refs pending

John-Nirenberg inequality and atomic decomposition for noncommutative martingales

Guixiang Hong, Tao Mei

arxiv:1112.3187 v2 · 2011-12-14 · math.FA · math.CA · math.OA · 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{3FNFRODC6FME74XU2M7W6X57R7}

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	2026-05-18T02:38:37.632207Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d95a58b862f1584ff2f4d33f6f5fbf8ffbe88cab2475063a349d3c64f25340b8

Aliases

arxiv: 1112.3187 · arxiv_version: 1112.3187v2 · doi: 10.48550/arxiv.1112.3187 · pith_short_12: 3FNFRODC6FME · pith_short_16: 3FNFRODC6FME74XU · pith_short_8: 3FNFRODC

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/3FNFRODC6FME74XU2M7W6X57R7 \
  | 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: d95a58b862f1584ff2f4d33f6f5fbf8ffbe88cab2475063a349d3c64f25340b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "399a0d1b401ec618f35d2c5da47e88e0b21be992bea56d5dac81e60ba2f2038f",
    "cross_cats_sorted": [
      "math.CA",
      "math.OA",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-12-14T12:31:34Z",
    "title_canon_sha256": "5e69e17f38315a76aa64a77ae7bdccedae71ac4c5e910f701bc6eb1a28752017"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3187",
    "kind": "arxiv",
    "version": 2
  }
}