Pith Number

pith:IYORSPW5

pith:2018:IYORSPW53BMNXZ5W2JQTUU2GFS

not attested not anchored not stored refs pending

Spectral Dimension for $\beta$-almost periodic singular Jacobi operators and the extended Harper's model

Fan Yang, Rui Han, Shiwen Zhang

arxiv:1804.04322 v2 · 2018-04-12 · 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{IYORSPW53BMNXZ5W2JQTUU2GFS}

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	2026-05-18T00:17:53.051923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

461d193eddd858dbe7b6d2613a53462c962fa084e305614d252a7d66a4d12fac

Aliases

arxiv: 1804.04322 · arxiv_version: 1804.04322v2 · doi: 10.48550/arxiv.1804.04322 · pith_short_12: IYORSPW53BMN · pith_short_16: IYORSPW53BMNXZ5W · pith_short_8: IYORSPW5

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/IYORSPW53BMNXZ5W2JQTUU2GFS \
  | 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: 461d193eddd858dbe7b6d2613a53462c962fa084e305614d252a7d66a4d12fac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "715fe9833a21c0383f958e8fbdedbe13e4dd4ea7f98b455578c8a0f3385bd746",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2018-04-12T05:22:34Z",
    "title_canon_sha256": "1ad7819355253581bbc76a9b09ffc290a8b700ce900aa7b417af5922454ad29c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.04322",
    "kind": "arxiv",
    "version": 2
  }
}