Pith Number

pith:FBG2XD7E

pith:2007:FBG2XD7EUAI772WM4X2TDGYXZU

not attested not anchored not stored refs pending

On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

Lyonell Boulton, Michael Levitin

arxiv:math/0702420 v1 · 2007-02-14 · math.SP · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FBG2XD7EUAI772WM4X2TDGYXZU}

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	2026-06-03T22:06:22.088184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

284dab8fe4a011ffeacce5f5319b17cd3a472f1ace7a449900085794619140a8

Aliases

arxiv: math/0702420 · arxiv_version: math/0702420v1 · doi: 10.48550/arxiv.math/0702420 · pith_short_12: FBG2XD7EUAI7 · pith_short_16: FBG2XD7EUAI772WM · pith_short_8: FBG2XD7E

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/FBG2XD7EUAI772WM4X2TDGYXZU \
  | 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: 284dab8fe4a011ffeacce5f5319b17cd3a472f1ace7a449900085794619140a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb57a8c8d55646f546e06132aadd88c55a6e2f5f04258db5912c8176540a0743",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2007-02-14T14:43:59Z",
    "title_canon_sha256": "e5aa21d73ed3f11475894739d4bdbf47f23d76b2a145e01f9a5a7e71dab92f26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0702420",
    "kind": "arxiv",
    "version": 1
  }
}