Pith Number

pith:VJUAN34O

pith:2001:VJUAN34OAWSH7TEI3FDSWSXJNO

not attested not anchored not stored refs pending

Commutators, Spectral Trace Identities, and Universal Estimates for Eigenvalues

Leonid Parnovski, Michael Levitin

arxiv:math/0102144 v2 · 2001-02-19 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VJUAN34OAWSH7TEI3FDSWSXJNO}

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	2026-05-18T03:30:38.615138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa6806ef8e05a47fcc88d9472b4ae96ba672c9e88ad5f760429ebbb4f2787915

Aliases

arxiv: math/0102144 · arxiv_version: math/0102144v2 · doi: 10.48550/arxiv.math/0102144 · pith_short_12: VJUAN34OAWSH · pith_short_16: VJUAN34OAWSH7TEI · pith_short_8: VJUAN34O

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/VJUAN34OAWSH7TEI3FDSWSXJNO \
  | 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: aa6806ef8e05a47fcc88d9472b4ae96ba672c9e88ad5f760429ebbb4f2787915

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e35a7ace191139b7c836c65146b4209678b738c58597847dc3fb94cb8e652252",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2001-02-19T10:10:34Z",
    "title_canon_sha256": "a4fe0cdba301f07bb6879804ec36e7cfd63682cbd2bc8bc5c5867041e529c3b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0102144",
    "kind": "arxiv",
    "version": 2
  }
}