Pith Number

pith:4GV6DRJR

pith:2006:4GV6DRJRNS3F63AO7P4BQNC6Z3

not attested not anchored not stored refs pending

Indefinite Sturm-Liouville operators $ (\sgn x) (- \frac{d^2}{dx^2} +q(x))$ with finite-zone potentials

I. M. Karabash, M. M. Malamud

arxiv:math/0610087 v3 · 2006-10-02 · 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{4GV6DRJRNS3F63AO7P4BQNC6Z3}

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	2026-05-18T04:34:10.307743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1abe1c5316cb65f6c0efbf818345ecee020b12da2efcd78b9fc5ef46bafab2e

Aliases

arxiv: math/0610087 · arxiv_version: math/0610087v3 · doi: 10.48550/arxiv.math/0610087 · pith_short_12: 4GV6DRJRNS3F · pith_short_16: 4GV6DRJRNS3F63AO · pith_short_8: 4GV6DRJR

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/4GV6DRJRNS3F63AO7P4BQNC6Z3 \
  | 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: e1abe1c5316cb65f6c0efbf818345ecee020b12da2efcd78b9fc5ef46bafab2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06932c72edbf04ee7676b1d2a08d0c88598de9df610b07937d4acac9b34d7d3a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2006-10-02T19:23:26Z",
    "title_canon_sha256": "acf42fbdf1678523a5a9879fbfe7cff3ab976260c8c77cb2ff579e2766b46029"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0610087",
    "kind": "arxiv",
    "version": 3
  }
}