Pith Number

pith:ZGBSCYYF

pith:2017:ZGBSCYYF43C25FYIZ75AXQN5LG

not attested not anchored not stored refs pending

Some Extensions of the Crouzeix-Palencia Result

Anne Greenbaum, Kenan Li, Trevor Caldwell

arxiv:1707.08603 v2 · 2017-07-26 · 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{ZGBSCYYF43C25FYIZ75AXQN5LG}

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.

Cited by

1 paper in Pith

A Schwarz-Jack lemma, circularly symmetric domains and numerical ranges

Receipt and verification

First computed	2026-05-18T00:29:51.436879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c983216305e6c5ae9708cffa0bc1bd5989984ff5466fe3df4ab8e787ee88d2a9

Aliases

arxiv: 1707.08603 · arxiv_version: 1707.08603v2 · doi: 10.48550/arxiv.1707.08603 · pith_short_12: ZGBSCYYF43C2 · pith_short_16: ZGBSCYYF43C25FYI · pith_short_8: ZGBSCYYF

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/ZGBSCYYF43C25FYIZ75AXQN5LG \
  | 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: c983216305e6c5ae9708cffa0bc1bd5989984ff5466fe3df4ab8e787ee88d2a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa75e0c1b1bf6c566826a06388cb60b288105e559aef330c8e5a541a268650cb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2017-07-26T18:36:17Z",
    "title_canon_sha256": "0728aa6bcd251d0f2caf38e4dbdd940f625ef75e809c3d75d33561c7ce714134"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.08603",
    "kind": "arxiv",
    "version": 2
  }
}