Pith Number

pith:VQG4CBIY

pith:2011:VQG4CBIYVY2H2ORPT2A5RKGP57

not attested not anchored not stored refs pending

Exact observability, square functions and spectral theory

Bernhard Hermann Haak (IMB), El-Maati Ouhabaz (IMB)

arxiv:1102.3268 v1 · 2011-02-16 · math.FA · cs.SY · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VQG4CBIYVY2H2ORPT2A5RKGP57}

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	2026-05-18T04:28:36.729148Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac0dc10518ae347d3a2f9e81d8a8cfeff8ccceaa6aa0d8d41c53630bb444d600

Aliases

arxiv: 1102.3268 · arxiv_version: 1102.3268v1 · doi: 10.48550/arxiv.1102.3268 · pith_short_12: VQG4CBIYVY2H · pith_short_16: VQG4CBIYVY2H2ORP · pith_short_8: VQG4CBIY

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/VQG4CBIYVY2H2ORPT2A5RKGP57 \
  | 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: ac0dc10518ae347d3a2f9e81d8a8cfeff8ccceaa6aa0d8d41c53630bb444d600

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7310f0e693afb7c7683bc3e7e383e9d7a5fecedc886da65d15138a586baa0692",
    "cross_cats_sorted": [
      "cs.SY",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-02-16T09:07:52Z",
    "title_canon_sha256": "4bd6e5204d8ffd21906afe01cd156ae54e5c14771a21d8fef0ae5dc3f6833621"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.3268",
    "kind": "arxiv",
    "version": 1
  }
}