Pith Number

pith:4PMKOWI4

pith:2010:4PMKOWI4SNAPQ6OIPE3BEJWTHV

not attested not anchored not stored refs pending

Absolute continuity of the spectrum of the periodic Schr\"odinger operator in a layer and in a smooth cylinder

Ilya Kachkovskiy, Nikolay Filonov

arxiv:1011.1394 v1 · 2010-11-05 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4PMKOWI4SNAPQ6OIPE3BEJWTHV}

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	2026-05-18T04:36:58.533683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3d8a7591c9340f879c879361226d33d492f975fffaa1c462f4f876cab129a4c

Aliases

arxiv: 1011.1394 · arxiv_version: 1011.1394v1 · doi: 10.48550/arxiv.1011.1394 · pith_short_12: 4PMKOWI4SNAP · pith_short_16: 4PMKOWI4SNAPQ6OI · pith_short_8: 4PMKOWI4

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/4PMKOWI4SNAPQ6OIPE3BEJWTHV \
  | 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: e3d8a7591c9340f879c879361226d33d492f975fffaa1c462f4f876cab129a4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "758de818d11351b280d019d8f9d9a2d8f270c66f8d2cc4a124f1aafc936791c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-11-05T13:29:57Z",
    "title_canon_sha256": "b8489f68fa6e702372da1506a1d3069fe041a07a857ce07b0997c8f04cca98fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1394",
    "kind": "arxiv",
    "version": 1
  }
}