Pith Number

pith:LWDC72II

pith:2011:LWDC72IIXUN5RLXKJSCPUF3CT3

not attested not anchored not stored refs pending

Direct and inverse spectral theory of singular left-definite Sturm-Liouville operators

Jonathan Eckhardt

arxiv:1110.5195 v3 · 2011-10-24 · math.SP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LWDC72IIXUN5RLXKJSCPUF3CT3}

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	2026-05-18T03:55:00.342600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d862fe908bd1bd8aeea4c84fa17629ef863f1883e8386761f77c1414ea268cc

Aliases

arxiv: 1110.5195 · arxiv_version: 1110.5195v3 · doi: 10.48550/arxiv.1110.5195 · pith_short_12: LWDC72IIXUN5 · pith_short_16: LWDC72IIXUN5RLXK · pith_short_8: LWDC72II

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/LWDC72IIXUN5RLXKJSCPUF3CT3 \
  | 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: 5d862fe908bd1bd8aeea4c84fa17629ef863f1883e8386761f77c1414ea268cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18a5dcff23fe514647d9cc2d73b5ad006037b1946953902b5bc8eac05f3d9261",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-10-24T11:00:05Z",
    "title_canon_sha256": "07ddec42676ed69d9c07a5514c5d8b0e9a7f06895ffe59aa5d03c50bd4be3d42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5195",
    "kind": "arxiv",
    "version": 3
  }
}