Pith Number

pith:VNYWYANV

pith:2010:VNYWYANVP7NYCXXTBH7WWTBUA4

not attested not anchored not stored refs pending

Singular continuous spectrum of half-line Schr\"odinger operators with point interactions on a sparse set

Vladimir Lotoreichik

arxiv:1011.2459 v3 · 2010-11-10 · 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{VNYWYANVP7NYCXXTBH7WWTBUA4}

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	2026-05-18T04:15:36.844910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab716c01b57fdb815ef309ff6b4c34070d5625edd3ccf5bcca70663b08ae172e

Aliases

arxiv: 1011.2459 · arxiv_version: 1011.2459v3 · doi: 10.48550/arxiv.1011.2459 · pith_short_12: VNYWYANVP7NY · pith_short_16: VNYWYANVP7NYCXXT · pith_short_8: VNYWYANV

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/VNYWYANVP7NYCXXTBH7WWTBUA4 \
  | 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: ab716c01b57fdb815ef309ff6b4c34070d5625edd3ccf5bcca70663b08ae172e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2db73de84f76efff43b17251c466edf34745128fb06b6915a1cb619bf687feb",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-11-10T19:12:22Z",
    "title_canon_sha256": "901494c427b7b80c1d8c57f91a3ed7daeedde72e5b68074fe1cc874c02b70d85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2459",
    "kind": "arxiv",
    "version": 3
  }
}