Pith Number

pith:CZTPGJ25

pith:2018:CZTPGJ25QSZ5J767O4BLZGV7BY

not attested not anchored not stored refs pending

Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality

Omar Mustafa, Zeinab Algadhi

arxiv:1806.02983 v3 · 2018-06-08 · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CZTPGJ25QSZ5J767O4BLZGV7BY}

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	2026-05-17T23:43:09.451235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1666f3275d84b3d4ffdf7702bc9abf0e07352052a2a98586f7c2290d21addaa2

Aliases

arxiv: 1806.02983 · arxiv_version: 1806.02983v3 · doi: 10.48550/arxiv.1806.02983 · pith_short_12: CZTPGJ25QSZ5 · pith_short_16: CZTPGJ25QSZ5J767 · pith_short_8: CZTPGJ25

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/CZTPGJ25QSZ5J767O4BLZGV7BY \
  | 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: 1666f3275d84b3d4ffdf7702bc9abf0e07352052a2a98586f7c2290d21addaa2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a57d9d00e065a6043639ae118c4b9d130e00600435adc392bd2a545c3a32662",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2018-06-08T06:43:49Z",
    "title_canon_sha256": "3ed6ec75e8beb163d1300d38db801a9c66290799620e88316c834258b7305698"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.02983",
    "kind": "arxiv",
    "version": 3
  }
}