Pith Number

pith:V5WZI2UP

pith:2017:V5WZI2UPAAXANUB2CWM4SIZW3N

not attested not anchored not stored refs pending

The Essential Spectrum of Toeplitz Operators on the Unit Ball

Raffael Hagger

arxiv:1705.04553 v2 · 2017-05-12 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V5WZI2UPAAXANUB2CWM4SIZW3N}

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	2026-05-18T00:18:46.515117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af6d946a8f002e06d03a1599c92336db65b8aa133612cbacc34fbd029f4c3da9

Aliases

arxiv: 1705.04553 · arxiv_version: 1705.04553v2 · doi: 10.48550/arxiv.1705.04553 · pith_short_12: V5WZI2UPAAXA · pith_short_16: V5WZI2UPAAXANUB2 · pith_short_8: V5WZI2UP

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/V5WZI2UPAAXANUB2CWM4SIZW3N \
  | 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: af6d946a8f002e06d03a1599c92336db65b8aa133612cbacc34fbd029f4c3da9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "863c4fb283aa0ba6c65fcdd0a614cf576990744625273b5d8b8b69262cfa4520",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-05-12T13:08:30Z",
    "title_canon_sha256": "33668f877a31e853a667187dac9cf1cbcecf9e7462569786e0f079a7ec4e7507"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.04553",
    "kind": "arxiv",
    "version": 2
  }
}