Pith Number

pith:7VVERFDR

pith:2011:7VVERFDR5B5QBFBLM6VDUXTGPD

not attested not anchored not stored refs pending

Quantitative uniqueness for Schr\"odinger operator

Laurent Bakri

arxiv:1105.5247 v1 · 2011-05-26 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7VVERFDR5B5QBFBLM6VDUXTGPD}

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	2026-05-18T04:07:06.641242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd6a489471e87b00942b67aa3a5e6678c71f7c36f1227604bd2b5dd2a13a147b

Aliases

arxiv: 1105.5247 · arxiv_version: 1105.5247v1 · doi: 10.48550/arxiv.1105.5247 · pith_short_12: 7VVERFDR5B5Q · pith_short_16: 7VVERFDR5B5QBFBL · pith_short_8: 7VVERFDR

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/7VVERFDR5B5QBFBLM6VDUXTGPD \
  | 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: fd6a489471e87b00942b67aa3a5e6678c71f7c36f1227604bd2b5dd2a13a147b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de919b69aa412094f3e7a81f15fc6127546f60fd0894c93a5c8ebac59bf271d2",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-05-26T10:15:12Z",
    "title_canon_sha256": "363bf6bf3ac4725e1bf0ecb5d63c9f4f5179b73d5d66c90adcbc3c1aa4dca833"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5247",
    "kind": "arxiv",
    "version": 1
  }
}