Pith Number

pith:YKENMSF2

pith:2020:YKENMSF2OEJVEFKHIKYAR6I7KO

not attested not anchored not stored refs pending

A bivariate extension of the Crouzeix-Palencia result with an application to Fr\'echet derivatives of matrix functions

Daniel Kressner, Michel Crouzeix

arxiv:2007.09784 v1 · 2020-07-19 · math.FA · cs.NA · 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{YKENMSF2OEJVEFKHIKYAR6I7KO}

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

Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions

Receipt and verification

First computed	2026-07-05T01:20:29.105502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c288d648ba711352154742b008f91f53a97ff7a31f0eeb9f4176e06185e2c53c

Aliases

arxiv: 2007.09784 · arxiv_version: 2007.09784v1 · doi: 10.48550/arxiv.2007.09784 · pith_short_12: YKENMSF2OEJV · pith_short_16: YKENMSF2OEJVEFKH · pith_short_8: YKENMSF2

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/YKENMSF2OEJVEFKHIKYAR6I7KO \
  | 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: c288d648ba711352154742b008f91f53a97ff7a31f0eeb9f4176e06185e2c53c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2d048094b5b1bf61e1dcbde04b0f16ca1b80f6a64b7f341caca0529a85c9b17",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2020-07-19T21:12:12Z",
    "title_canon_sha256": "b39b8225a7dbe6cd7cb76f6f9dfb64a28162aa5c9eda79c40341cb77529a6485"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.09784",
    "kind": "arxiv",
    "version": 1
  }
}