Pith Number

pith:ARINCFD4

pith:2016:ARINCFD4UZ7UKLBVQ3XVSS2B4A

not attested not anchored not stored refs pending

Refined Bounds on the Number of Distinct Eigenvalues of a Matrix After Perturbation

Gang Wu, Yunjie Wang

arxiv:1612.08369 v2 · 2016-12-26 · 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{ARINCFD4UZ7UKLBVQ3XVSS2B4A}

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	2026-05-18T00:38:13.772270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0450d1147ca67f452c3586ef594b41e002f458fed8d7d53bb7c901c9dd37ec31

Aliases

arxiv: 1612.08369 · arxiv_version: 1612.08369v2 · doi: 10.48550/arxiv.1612.08369 · pith_short_12: ARINCFD4UZ7U · pith_short_16: ARINCFD4UZ7UKLBV · pith_short_8: ARINCFD4

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/ARINCFD4UZ7UKLBVQ3XVSS2B4A \
  | 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: 0450d1147ca67f452c3586ef594b41e002f458fed8d7d53bb7c901c9dd37ec31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0fc871dbd52d608f3e0cb64f1ea82e8c551fe43b111e0dc0609d4e0efde2307",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2016-12-26T12:18:15Z",
    "title_canon_sha256": "0acf1fa7dad2da2ba056d21871460c1894ee66fae298ddbd61016eee65d5a655"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08369",
    "kind": "arxiv",
    "version": 2
  }
}