Pith Number

pith:3VXOEBPO

pith:2009:3VXOEBPOLI2CWKYBA6LRMGDZCQ

not attested not anchored not stored refs pending

Bethe-Sommerfeld conjecture for periodic operators with strong perturbations

A.V. Sobolev, L. Parnovski

arxiv:0907.0887 v1 · 2009-07-05 · 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{3VXOEBPOLI2CWKYBA6LRMGDZCQ}

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	2026-05-18T02:13:05.178803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd6ee205ee5a342b2b010797161879143149f8061a26364169eb3566a36b2b75

Aliases

arxiv: 0907.0887 · arxiv_version: 0907.0887v1 · doi: 10.48550/arxiv.0907.0887 · pith_short_12: 3VXOEBPOLI2C · pith_short_16: 3VXOEBPOLI2CWKYB · pith_short_8: 3VXOEBPO

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/3VXOEBPOLI2CWKYBA6LRMGDZCQ \
  | 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: dd6ee205ee5a342b2b010797161879143149f8061a26364169eb3566a36b2b75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "273bbc79b0a0b475932c2f39c325cd18a35ed385e407f2dd0340f79622d98ed0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2009-07-05T20:27:09Z",
    "title_canon_sha256": "3d5459c896eb7812f47d21b29f8ee755fb43e7dd60d172adb24d55141a8fda6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.0887",
    "kind": "arxiv",
    "version": 1
  }
}