Pith Number

pith:SET6WSEA

pith:2015:SET6WSEABKY2WNL44WB7LAHMKN

not attested not anchored not stored refs pending

Marcinkiewicz spaces, Garsia-Rodemich spaces and the scale of John-Nirenberg self improving inequalities

Mario Milman

arxiv:1508.05057 v2 · 2015-08-20 · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SET6WSEABKY2WNL44WB7LAHMKN}

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	2026-05-18T00:43:36.056582Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9127eb48800ab1ab357ce583f580ec537b3469bfc48ea002f122eac974cb410a

Aliases

arxiv: 1508.05057 · arxiv_version: 1508.05057v2 · doi: 10.48550/arxiv.1508.05057 · pith_short_12: SET6WSEABKY2 · pith_short_16: SET6WSEABKY2WNL4 · pith_short_8: SET6WSEA

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/SET6WSEABKY2WNL44WB7LAHMKN \
  | 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: 9127eb48800ab1ab357ce583f580ec537b3469bfc48ea002f122eac974cb410a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5710e53728a2a9af154c231296513342877f6ed3c22c7032b953e045e4b6bbb7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-08-20T17:58:16Z",
    "title_canon_sha256": "817fed232332e2bc464726a6f2b2b349b5dde1c6bf0b94bd087921fe80fa5bd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05057",
    "kind": "arxiv",
    "version": 2
  }
}