Pith Number

pith:WDRDHHZP

pith:2010:WDRDHHZP5KG7GH5P7GQUZM5UTY

not attested not anchored not stored refs pending

Defect Modes and Homogenization of Periodic Schr\"odinger Operators

M. A. Hoefer, M. I. Weinstein

arxiv:1009.0922 v2 · 2010-09-05 · math-ph · math.AP · 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{WDRDHHZP5KG7GH5P7GQUZM5UTY}

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	2026-05-18T04:08:44.799428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0e2339f2fea8df31faff9a14cb3b49e01bfc4cbfd2a78818de543332f240be5

Aliases

arxiv: 1009.0922 · arxiv_version: 1009.0922v2 · doi: 10.48550/arxiv.1009.0922 · pith_short_12: WDRDHHZP5KG7 · pith_short_16: WDRDHHZP5KG7GH5P · pith_short_8: WDRDHHZP

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/WDRDHHZP5KG7GH5P7GQUZM5UTY \
  | 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: b0e2339f2fea8df31faff9a14cb3b49e01bfc4cbfd2a78818de543332f240be5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3af0611c8b622e40cfda2ddc965b5a466e745d3f5f43dd39b4a3664a3e7fd4a2",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-09-05T14:22:30Z",
    "title_canon_sha256": "7b4adc27200145f42c747734bc732fb9c7f35285d31cbbf00d3a679708f0c767"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0922",
    "kind": "arxiv",
    "version": 2
  }
}