Pith Number

pith:IFTZLSMP

pith:2013:IFTZLSMPBA7S64BN3J3UILCYGY

not attested not anchored not stored refs pending

The proof of non-homogeneous T1 theorem via averaging of dyadic shifts

Alexander Volberg

arxiv:1303.0367 v1 · 2013-03-02 · math.AP · math.CA · 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{IFTZLSMPBA7S64BN3J3UILCYGY}

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	2026-05-18T03:31:56.335109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

416795c98f083f2f702dda77442c58360500c21e386d5b6a4f9a0686bfd4d7d0

Aliases

arxiv: 1303.0367 · arxiv_version: 1303.0367v1 · doi: 10.48550/arxiv.1303.0367 · pith_short_12: IFTZLSMPBA7S · pith_short_16: IFTZLSMPBA7S64BN · pith_short_8: IFTZLSMP

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/IFTZLSMPBA7S64BN3J3UILCYGY \
  | 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: 416795c98f083f2f702dda77442c58360500c21e386d5b6a4f9a0686bfd4d7d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "248d48f21a9c46b27e9a8b7f497588057e9e4cb085d76b97475bc461b7b785ef",
    "cross_cats_sorted": [
      "math.CA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-03-02T09:48:56Z",
    "title_canon_sha256": "0a27e819f6b671ca68f90e50c992978205a31114c33877bdc19e74fcb216108b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.0367",
    "kind": "arxiv",
    "version": 1
  }
}