Pith Number

pith:4MN5VNGA

pith:2010:4MN5VNGAKPLX56BN55TN6LXYVZ

not attested not anchored not stored refs pending

Commutation Methods for Schroedinger Operators with Strongly Singular Potentials

Aleksey Kostenko, Alexander Sakhnovich, Gerald Teschl

arxiv:1010.4902 v2 · 2010-10-23 · math.SP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4MN5VNGAKPLX56BN55TN6LXYVZ}

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	2026-05-18T04:01:51.219648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e31bdab4c053d77ef82def66df2ef8ae6c7543d673cea54f5c8f11131f169369

Aliases

arxiv: 1010.4902 · arxiv_version: 1010.4902v2 · doi: 10.48550/arxiv.1010.4902 · pith_short_12: 4MN5VNGAKPLX · pith_short_16: 4MN5VNGAKPLX56BN · pith_short_8: 4MN5VNGA

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/4MN5VNGAKPLX56BN55TN6LXYVZ \
  | 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: e31bdab4c053d77ef82def66df2ef8ae6c7543d673cea54f5c8f11131f169369

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb9ea239f9f2469cf59e366dc6aa125c41b5a38ec92bc15e0b2bd3be1bc6322e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-10-23T19:18:42Z",
    "title_canon_sha256": "dec3ace46eb9cb043cd4908cffe68e3461eaabc598b9145dec7a7cb65ea5ae48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4902",
    "kind": "arxiv",
    "version": 2
  }
}