Pith Number

pith:TPSKWBFF

pith:2019:TPSKWBFFF2C7QTI2FYCUUYLV7T

not attested not anchored not stored refs pending

On the spectrum of the Schr\"odinger operator on $\mathbb{T}^d$: a normal form approach

Beatrice Langella, Dario Bambusi, Riccardo Montalto

arxiv:1903.09449 v1 · 2019-03-22 · 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{TPSKWBFFF2C7QTI2FYCUUYLV7T}

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	2026-05-17T23:50:39.598232Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9be4ab04a52e85f84d1a2e054a6175fce89b4b373e9c6740c828af3f6896955f

Aliases

arxiv: 1903.09449 · arxiv_version: 1903.09449v1 · doi: 10.48550/arxiv.1903.09449 · pith_short_12: TPSKWBFFF2C7 · pith_short_16: TPSKWBFFF2C7QTI2 · pith_short_8: TPSKWBFF

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/TPSKWBFFF2C7QTI2FYCUUYLV7T \
  | 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: 9be4ab04a52e85f84d1a2e054a6175fce89b4b373e9c6740c828af3f6896955f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "645079925e06af7099ee2ce760a28eee56e7fa38710ee1b2c55a8dacf481bcb9",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-03-22T11:27:40Z",
    "title_canon_sha256": "e8e68a1483819d6a992045b6fa1163a30604714eb63210f526bf2677abf02545"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.09449",
    "kind": "arxiv",
    "version": 1
  }
}