Pith Number

pith:OM4KKYGO

pith:2014:OM4KKYGOP3QDBBZQ6WU2S4WERY

not attested not anchored not stored refs pending

The Isospectral Torus of Quasi-Periodic Schr\"odinger Operators via Periodic Approximations

David Damanik (Rice University), Michael Goldstein (University of Toronto), Milivoje Lukic (University of Toronto, Rice University)

arxiv:1409.2434 v3 · 2014-09-08 · math.SP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OM4KKYGOP3QDBBZQ6WU2S4WERY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-17T23:52:44.864460Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7338a560ce7ee0308730f5a9a972c48e06de2a167820ad2964e8b0b97b22828a

Aliases

arxiv: 1409.2434 · arxiv_version: 1409.2434v3 · doi: 10.48550/arxiv.1409.2434 · pith_short_12: OM4KKYGOP3QD · pith_short_16: OM4KKYGOP3QDBBZQ · pith_short_8: OM4KKYGO

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/OM4KKYGOP3QDBBZQ6WU2S4WERY \
  | 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: 7338a560ce7ee0308730f5a9a972c48e06de2a167820ad2964e8b0b97b22828a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c1726ede1f7fce9b4f84079e4351f6a31e82b8c8659cb15bc4c7b5d2cbb15d7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2014-09-08T17:23:08Z",
    "title_canon_sha256": "30ebfdae8366642f413ecebeb6a55a40f275ec0f95060616f9ca342e768d8d04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.2434",
    "kind": "arxiv",
    "version": 3
  }
}