Pith Number

pith:VBDXGUZ4

pith:2007:VBDXGUZ4JBMM63OTK3YZUEZPBS

not attested not anchored not stored refs pending

Number of Bound States of Schroedinger Operators with Matrix-Valued Potentials

Elliott H. Lieb, Robert Seiringer, Rupert L. Frank

arxiv:0710.1877 v1 · 2007-10-09 · 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{VBDXGUZ4JBMM63OTK3YZUEZPBS}

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	2026-07-04T17:06:05.644195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a84773533c4858cf6dd356f19a132f0c95c7077067b3cf904cbec7197b4b4c18

Aliases

arxiv: 0710.1877 · arxiv_version: 0710.1877v1 · doi: 10.48550/arxiv.0710.1877 · pith_short_12: VBDXGUZ4JBMM · pith_short_16: VBDXGUZ4JBMM63OT · pith_short_8: VBDXGUZ4

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/VBDXGUZ4JBMM63OTK3YZUEZPBS \
  | 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: a84773533c4858cf6dd356f19a132f0c95c7077067b3cf904cbec7197b4b4c18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42d42d44468153c07e65fc93ed774072914e15643d13f829a348d66064848ff9",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2007-10-09T21:05:31Z",
    "title_canon_sha256": "35e70d4e888c3551de9316ba315c1350c4f457d50ed3ac12d9431d652fcac08b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.1877",
    "kind": "arxiv",
    "version": 1
  }
}