Pith Number

pith:PKB2PYQB

pith:2010:PKB2PYQB7RKLWX6HFC5Z3RYHFU

not attested not anchored not stored refs pending

Vector-valued non-homogeneous Tb theorem on metric measure spaces

Henri Martikainen

arxiv:1004.3176 v1 · 2010-04-19 · 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{PKB2PYQB7RKLWX6HFC5Z3RYHFU}

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	2026-05-18T03:36:37.344843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a83a7e201fc54bb5fc728bb9dc7072d019a5415a3ac4dd0e4028d1854e4a4dd

Aliases

arxiv: 1004.3176 · arxiv_version: 1004.3176v1 · doi: 10.48550/arxiv.1004.3176 · pith_short_12: PKB2PYQB7RKL · pith_short_16: PKB2PYQB7RKLWX6H · pith_short_8: PKB2PYQB

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/PKB2PYQB7RKLWX6HFC5Z3RYHFU \
  | 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: 7a83a7e201fc54bb5fc728bb9dc7072d019a5415a3ac4dd0e4028d1854e4a4dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2e5f0d78de08d8e7a0dea6d9bc052ec69fac68ff42253cfb5825066d2a211a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-04-19T12:44:00Z",
    "title_canon_sha256": "c84f582db3a329d15cdc3cdb3f7bc5d95cde63e57aeb1c0c0bf59162bd40bbc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.3176",
    "kind": "arxiv",
    "version": 1
  }
}