Pith Number

pith:5QJCU5W7

pith:2018:5QJCU5W76E43PHYUKLILWAIS4D

not attested not anchored not stored refs pending

Multipliers between range spaces of co-analytic Toeplitz operators

Andreas Hartmann (IMB), Emmanuel Fricain (LPP), William Ross, William T. Ross

arxiv:1802.04026 v1 · 2018-02-12 · math.CV · 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{5QJCU5W76E43PHYUKLILWAIS4D}

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	2026-05-18T00:23:49.689812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec122a76dff139b79f1452d0bb0112e0cda040f43ba688beba45c384bf3c1fd4

Aliases

arxiv: 1802.04026 · arxiv_version: 1802.04026v1 · doi: 10.48550/arxiv.1802.04026 · pith_short_12: 5QJCU5W76E43 · pith_short_16: 5QJCU5W76E43PHYU · pith_short_8: 5QJCU5W7

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/5QJCU5W76E43PHYUKLILWAIS4D \
  | 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: ec122a76dff139b79f1452d0bb0112e0cda040f43ba688beba45c384bf3c1fd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d824d7e090e23cf251e70162e1480e33530f341a72f72604b14d7b1cb831f01",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2018-02-12T13:16:46Z",
    "title_canon_sha256": "5a7cb324cb7e58e9503c250e099a946ae498abbbd8494a9d031681c1f8179350"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.04026",
    "kind": "arxiv",
    "version": 1
  }
}