Pith Number

pith:D2FXP74Q

pith:2012:D2FXP74QYATLZWS6FGKDNLPAPS

not attested not anchored not stored refs pending

The Sturm--Liouville problem with singular potential and the extrema of the first eigenvalue

A. A. Vladimirov, E. S. Karulina

arxiv:1206.5081 v2 · 2012-06-22 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D2FXP74QYATLZWS6FGKDNLPAPS}

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	2026-05-18T03:26:32.469717Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e8b77ff90c026bcda5e299436ade07ca18ffff178dddc5597a6aa973ec55558

Aliases

arxiv: 1206.5081 · arxiv_version: 1206.5081v2 · doi: 10.48550/arxiv.1206.5081 · pith_short_12: D2FXP74QYATL · pith_short_16: D2FXP74QYATLZWS6 · pith_short_8: D2FXP74Q

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/D2FXP74QYATLZWS6FGKDNLPAPS \
  | 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: 1e8b77ff90c026bcda5e299436ade07ca18ffff178dddc5597a6aa973ec55558

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a41a50d0da694428b43402ed8a27b2538c620dd115c73ab41bcfd60a766847d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-06-22T08:27:54Z",
    "title_canon_sha256": "e3299a78cd0302fc465f3f60fe72a13e98a54f5a8c76515cafda8195d748f1f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.5081",
    "kind": "arxiv",
    "version": 2
  }
}