Pith Number

pith:6HDWNU3J

pith:2017:6HDWNU3JN3ELU7MJJ3K3PEYUOR

not attested not anchored not stored refs pending

Remarks on the Crouzeix-Palencia proof that the numerical range is a $(1+\sqrt2)$-spectral set

Felix Schwenninger, Thomas Ransford

arxiv:1708.08633 v2 · 2017-08-29 · math.FA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6HDWNU3JN3ELU7MJJ3K3PEYUOR}

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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	2026-05-17T23:54:56.708180Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1c766d3696ec8ba7d894ed5b79314745d2f19b9b4ec6d1698c5fe981b647263

Aliases

arxiv: 1708.08633 · arxiv_version: 1708.08633v2 · doi: 10.48550/arxiv.1708.08633 · pith_short_12: 6HDWNU3JN3EL · pith_short_16: 6HDWNU3JN3ELU7MJ · pith_short_8: 6HDWNU3J

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/6HDWNU3JN3ELU7MJJ3K3PEYUOR \
  | 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: f1c766d3696ec8ba7d894ed5b79314745d2f19b9b4ec6d1698c5fe981b647263

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d844fbd11a9b8e773b92078cc709090463d0ee23c8249e6383cfb8eb73990f61",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-08-29T08:14:46Z",
    "title_canon_sha256": "dc58176046dced898cec48490803ca50b644c75c21d8d0efc77e394e7303c4bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.08633",
    "kind": "arxiv",
    "version": 2
  }
}