Pith Number

pith:LY7I7EVY

pith:2024:LY7I7EVYLDJYYCFVG7WLPNAX7F

not attested not anchored not stored refs pending

Sharp decay rate for eigenfunctions of perturbed periodic Schr\"odinger operators

John N. Treuer, Rodrigo Matos, Wencai Liu

arxiv:2409.10387 v1 · 2024-09-16 · math.SP · math-ph · math.CV · 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{LY7I7EVYLDJYYCFVG7WLPNAX7F}

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	2026-07-05T09:07:39.381358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e3e8f92b858d38c08b537ecb7b417f95c2ae4497f9914ebb7b45f004682ee82

Aliases

arxiv: 2409.10387 · arxiv_version: 2409.10387v1 · doi: 10.48550/arxiv.2409.10387 · pith_short_12: LY7I7EVYLDJY · pith_short_16: LY7I7EVYLDJYYCFV · pith_short_8: LY7I7EVY

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/LY7I7EVYLDJYYCFVG7WLPNAX7F \
  | 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: 5e3e8f92b858d38c08b537ecb7b417f95c2ae4497f9914ebb7b45f004682ee82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57177d420bc838d3d7b44bc778c63325da0436dca712c8c064034cbc073a5d34",
    "cross_cats_sorted": [
      "math-ph",
      "math.CV",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2024-09-16T15:21:55Z",
    "title_canon_sha256": "31f9be8af292a4071e6693bdcde8f885836373578b02dc47b41977ce4e187e1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.10387",
    "kind": "arxiv",
    "version": 1
  }
}