Pith Number

pith:U6TU2TKQ

pith:1997:U6TU2TKQGAL3SV5I5VXSBRH4UP

not attested not anchored not stored refs pending

Gauge Transformations in Quantum Mechanics and the Unification of Nonlinear Schr\"odinger Equations

G.A. Goldin, H.-D. Doebner, P. Nattermann

arxiv:quant-ph/9709036 v1 · 1997-09-17 · 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{U6TU2TKQGAL3SV5I5VXSBRH4UP}

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	2026-07-04T16:06:31.359373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7a74d4d503017b957a8ed6f20c4fca3de01696a172b2d041b1d853319523d24

Aliases

arxiv: quant-ph/9709036 · arxiv_version: quant-ph/9709036v1 · doi: 10.48550/arxiv.quant-ph/9709036 · pith_short_12: U6TU2TKQGAL3 · pith_short_16: U6TU2TKQGAL3SV5I · pith_short_8: U6TU2TKQ

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/U6TU2TKQGAL3SV5I5VXSBRH4UP \
  | 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: a7a74d4d503017b957a8ed6f20c4fca3de01696a172b2d041b1d853319523d24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db72e5f42cb0b102f60296bf9a62db480378d136a8023cb4aa5d778a8bf685bf",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "1997-09-17T13:13:10Z",
    "title_canon_sha256": "5069109f2b5e3228a6b814adcc49bfbb51f3d325e8d131ab3a5efe50507c4de7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/9709036",
    "kind": "arxiv",
    "version": 1
  }
}