Pith Number

pith:NTR2DDSY

pith:2024:NTR2DDSY4TEB7KOBDG6THFCG6V

not attested not anchored not stored refs pending

On gaps in the spectra of quasiperiodic Schr\"odinger operators with discontinuous monotone potentials

Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg

arxiv:2407.00705 v3 · 2024-06-30 · math.SP · 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{NTR2DDSY4TEB7KOBDG6THFCG6V}

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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.

Cited by

1 paper in Pith

On a Question of Poltoratski

Receipt and verification

First computed	2026-07-05T12:02:34.886307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ce3a18e58e4c81fa9c119bd339446f563c1d6d5ef679540c53c8fa76ba29fda

Aliases

arxiv: 2407.00705 · arxiv_version: 2407.00705v3 · doi: 10.48550/arxiv.2407.00705 · pith_short_12: NTR2DDSY4TEB · pith_short_16: NTR2DDSY4TEB7KOB · pith_short_8: NTR2DDSY

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/NTR2DDSY4TEB7KOBDG6THFCG6V \
  | 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: 6ce3a18e58e4c81fa9c119bd339446f563c1d6d5ef679540c53c8fa76ba29fda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df61e7100cee0b870c50652613c0fc15ac77710cd14c7eaf38e080c99a556306",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2024-06-30T14:12:23Z",
    "title_canon_sha256": "bcdac8c90b43d1d60990c714ffa889d045ecd0c3b3bd060c31153673b668bb52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.00705",
    "kind": "arxiv",
    "version": 3
  }
}