Pith Number

pith:WFGTRRPL

pith:2013:WFGTRRPL2IR36Y2GP77UYU22P7

not attested not anchored not stored refs pending

Spectra of Discrete Schr\"odinger Operators with Primitive Invertible Substitution Potentials

May Mei

arxiv:1311.0954 v2 · 2013-11-05 · 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{WFGTRRPL2IR36Y2GP77UYU22P7}

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	2026-05-18T00:50:52.649876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b14d38c5ebd223bf63467fff4c535a7ff86544fffabc91a3676ed2cb07a7941e

Aliases

arxiv: 1311.0954 · arxiv_version: 1311.0954v2 · doi: 10.48550/arxiv.1311.0954 · pith_short_12: WFGTRRPL2IR3 · pith_short_16: WFGTRRPL2IR36Y2G · pith_short_8: WFGTRRPL

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/WFGTRRPL2IR36Y2GP77UYU22P7 \
  | 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: b14d38c5ebd223bf63467fff4c535a7ff86544fffabc91a3676ed2cb07a7941e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b9afcdd72fe54802e3050b4586d31e4c1e7f2a7a4e00559ef16e7e5f7d3c542",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-11-05T03:24:28Z",
    "title_canon_sha256": "dfa2b936f59f09ab093714568ff9f4c2b92fad31537645279fb430288b2aa24b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0954",
    "kind": "arxiv",
    "version": 2
  }
}