Pith Number

pith:YJUPTEJ4

pith:2012:YJUPTEJ4EW23UJLADB4QINMCHO

not attested not anchored not stored refs pending

Uniqueness of solutions to Schr\"odinger equations on 2-step nilpotent Lie groups

Detlef M\"uller, Jean Ludwig

arxiv:1207.4652 v1 · 2012-07-19 · math.AP · 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{YJUPTEJ4EW23UJLADB4QINMCHO}

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	2026-05-18T03:50:36.290197Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c268f9913c25b5ba256018790435823bb350c7aaa1da73ecf1ad59fd3edff832

Aliases

arxiv: 1207.4652 · arxiv_version: 1207.4652v1 · doi: 10.48550/arxiv.1207.4652 · pith_short_12: YJUPTEJ4EW23 · pith_short_16: YJUPTEJ4EW23UJLA · pith_short_8: YJUPTEJ4

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/YJUPTEJ4EW23UJLADB4QINMCHO \
  | 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: c268f9913c25b5ba256018790435823bb350c7aaa1da73ecf1ad59fd3edff832

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1af6a08626fa84fd7d1191433a745cc4ed6029083d9f02bf05f71bd3f6cba22",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-07-19T13:09:43Z",
    "title_canon_sha256": "1665ffd8c3bbc94fe4e6e46b8ca6cbd04f8482789989086cb6ff51d35e5b36cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4652",
    "kind": "arxiv",
    "version": 1
  }
}