Pith Number

pith:MLZ4AZRP

pith:2012:MLZ4AZRPGOXWDMNDFZ3SM7AOZY

not attested not anchored not stored refs pending

Sharp Reverse H\"older property for A_\infty weights on spaces of homogeneous type

Carlos P\'erez, Ezequiel Rela, Tuomas Hyt\"onen

arxiv:1207.2394 v2 · 2012-07-10 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MLZ4AZRPGOXWDMNDFZ3SM7AOZY}

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	2026-05-18T03:48:26.682253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62f3c0662f33af61b1a32e77267c0ece0c55dd2c6c0fa5312b457f9dd1208419

Aliases

arxiv: 1207.2394 · arxiv_version: 1207.2394v2 · doi: 10.48550/arxiv.1207.2394 · pith_short_12: MLZ4AZRPGOXW · pith_short_16: MLZ4AZRPGOXWDMND · pith_short_8: MLZ4AZRP

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/MLZ4AZRPGOXWDMNDFZ3SM7AOZY \
  | 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: 62f3c0662f33af61b1a32e77267c0ece0c55dd2c6c0fa5312b457f9dd1208419

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "553dbabed132d8775bffdb21b72af9d41f38426fad0a70c47f54ea8685a58712",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-07-10T15:55:50Z",
    "title_canon_sha256": "412b12047026cc251b5fedbc874a5bf3dbb7d98fe844c2f3ba874b1ad5884221"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.2394",
    "kind": "arxiv",
    "version": 2
  }
}