Pith Number

pith:SFP3OOA4

pith:2012:SFP3OOA42V4WYRKR72X2QRVGPZ

not attested not anchored not stored refs pending

Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones

Denis Borisov, Konstantin Pankrashkin

arxiv:1211.5786 v2 · 2012-11-25 · 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{SFP3OOA42V4WYRKR72X2QRVGPZ}

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	2026-05-18T03:24:41.664398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

915fb7381cd5796c4551feafa846a67e6338e326e6d1683d54832b3561a538c5

Aliases

arxiv: 1211.5786 · arxiv_version: 1211.5786v2 · doi: 10.48550/arxiv.1211.5786 · pith_short_12: SFP3OOA42V4W · pith_short_16: SFP3OOA42V4WYRKR · pith_short_8: SFP3OOA4

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/SFP3OOA42V4WYRKR72X2QRVGPZ \
  | 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: 915fb7381cd5796c4551feafa846a67e6338e326e6d1683d54832b3561a538c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77822d5a4d4fb4ca8fda1cb4694b6523bb4e41f6f0c91ab3d9983f8bccb3d6c6",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-11-25T17:40:32Z",
    "title_canon_sha256": "2e3e6ca5d870e4ae0a9407cf96c4c44799ea870cff38454191db2b057447873e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5786",
    "kind": "arxiv",
    "version": 2
  }
}