Pith Number

pith:7QI3SPH3

pith:2009:7QI3SPH3LJJQBV7Y2UNGD3FNOP

not attested not anchored not stored refs pending

John-Nirenberg lemmas for a doubling measure

Daniel Aalto, Hong Yue, Lauri Berkovits, Outi Elina Maasalo

arxiv:0910.1228 v2 · 2009-10-07 · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7QI3SPH3LJJQBV7Y2UNGD3FNOP}

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	2026-05-18T02:28:12.429428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc11b93cfb5a5300d7f8d51a61ecad73c3871a188cf3ebac24970d7122534158

Aliases

arxiv: 0910.1228 · arxiv_version: 0910.1228v2 · doi: 10.48550/arxiv.0910.1228 · pith_short_12: 7QI3SPH3LJJQ · pith_short_16: 7QI3SPH3LJJQBV7Y · pith_short_8: 7QI3SPH3

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/7QI3SPH3LJJQBV7Y2UNGD3FNOP \
  | 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: fc11b93cfb5a5300d7f8d51a61ecad73c3871a188cf3ebac24970d7122534158

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ae17d8e1cb79440e18373935bd2f8f5dfe5cdeac533c4965b947c26a587182e",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-10-07T12:05:57Z",
    "title_canon_sha256": "1445e22c0cf31fdab3f019291bbafd356927ecf7412a01ce07ccc19a0419d50c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.1228",
    "kind": "arxiv",
    "version": 2
  }
}