Pith Number

pith:W67QKR6N

pith:2018:W67QKR6N4LHPNAWSWBS4U3ZXU6

not attested not anchored not stored refs pending

Computable upper error bounds for Krylov approximations to matrix exponentials and associated $\varphi$-functions

Othmar Koch, Tobias Jawecki, Winfried Auzinger

arxiv:1809.03369 v2 · 2018-09-10 · math.NA · cs.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{W67QKR6N4LHPNAWSWBS4U3ZXU6}

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	2026-06-04T20:13:18.689748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7bf0547cde2cef682d2b065ca6f37a7ba04bcb9bedcf6186936741655c5ac8e

Aliases

arxiv: 1809.03369 · arxiv_version: 1809.03369v2 · doi: 10.48550/arxiv.1809.03369 · pith_short_12: W67QKR6N4LHP · pith_short_16: W67QKR6N4LHPNAWS · pith_short_8: W67QKR6N

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/W67QKR6N4LHPNAWSWBS4U3ZXU6 \
  | 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: b7bf0547cde2cef682d2b065ca6f37a7ba04bcb9bedcf6186936741655c5ac8e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d833a6d1f83832257b00d4b9e45b8076a06c0fe5d5ed17cd69f61031cb1f43b6",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2018-09-10T14:51:12Z",
    "title_canon_sha256": "32e59bd39ab43c53476964a39ade2f847a823dfc6e9decf55aba38e84412ab23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.03369",
    "kind": "arxiv",
    "version": 2
  }
}