Pith Number

pith:4XDJUV5R

pith:2002:4XDJUV5RSRRMBPVSEIL3IQLZ2P

not attested not anchored not stored refs pending

Essential self-adjointness of Schroedinger type operators on manifolds

Maxim Braverman, Mikhail Shubin, Ognjen Milatovic

arxiv:math/0201231 v3 · 2002-01-24 · math.SP · math-ph · math.DG · 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{4XDJUV5RSRRMBPVSEIL3IQLZ2P}

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	2026-05-18T01:38:29.715687Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5c69a57b19462c0beb22217b44179d3ea40b406c83b0744490760cd887f122c

Aliases

arxiv: math/0201231 · arxiv_version: math/0201231v3 · doi: 10.48550/arxiv.math/0201231 · pith_short_12: 4XDJUV5RSRRM · pith_short_16: 4XDJUV5RSRRMBPVS · pith_short_8: 4XDJUV5R

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/4XDJUV5RSRRMBPVSEIL3IQLZ2P \
  | 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: e5c69a57b19462c0beb22217b44179d3ea40b406c83b0744490760cd887f122c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0da32fad9da3a3bfb993c49c7be21320cfa32597616275291172e39afe7f7a2",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2002-01-24T17:43:17Z",
    "title_canon_sha256": "91147cb9b5cb1a18dfd5e32e1d97068c5cd1e5fb13ed397d44e6bf77f4e277e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0201231",
    "kind": "arxiv",
    "version": 3
  }
}