Pith Number

pith:QGCTM5NL

pith:2026:QGCTM5NLZILOJAQUYTIJSXOAQV

not attested not anchored not stored refs pending

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole

Nicola A. Spaldin, Nora Taufertsh\"ofer, Vinzenz A. M\"uller

arxiv:2607.13053 v1 · 2026-07-03 · quant-ph · cond-mat.mtrl-sci · 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{QGCTM5NLZILOJAQUYTIJSXOAQV}

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	2026-07-16T00:21:53.719554Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81853675abca16e48214c4d0995dc085768a1512b4fea169838fe5ce8c27f839

Aliases

arxiv: 2607.13053 · arxiv_version: 2607.13053v1 · doi: 10.48550/arxiv.2607.13053 · pith_short_12: QGCTM5NLZILO · pith_short_16: QGCTM5NLZILOJAQU · pith_short_8: QGCTM5NL

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/QGCTM5NLZILOJAQUYTIJSXOAQV \
  | 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: 81853675abca16e48214c4d0995dc085768a1512b4fea169838fe5ce8c27f839

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0121a81482e626e20a5225d3064cb7e1c376b4b9ec95676a10acdc801183f923",
    "cross_cats_sorted": [
      "cond-mat.mtrl-sci",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-03T16:15:18Z",
    "title_canon_sha256": "79cc941783440a31db466a3b0be8ff0a8bef8ec7f620e667965a6ed737bc0fb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.13053",
    "kind": "arxiv",
    "version": 1
  }
}