Pith Number

pith:ZNZXCMWX

pith:2025:ZNZXCMWX5ZENSDUZVBPR2Z4KP4

not attested not anchored not stored refs pending

Schr\"odinger Symmetry in Spherically-symmetric Static Mini-superspaces with Matter Fields

Taishi Sano, Yuki Yokokura

arxiv:2512.13651 v3 · 2025-12-15 · gr-qc · hep-th · 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{ZNZXCMWX5ZENSDUZVBPR2Z4KP4}

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	2026-06-12T01:09:17.815170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb737132d7ee48d90e99a85f1d678a7f1f37ed880161fed10591da293c41b8fc

Aliases

arxiv: 2512.13651 · arxiv_version: 2512.13651v3 · doi: 10.48550/arxiv.2512.13651 · pith_short_12: ZNZXCMWX5ZEN · pith_short_16: ZNZXCMWX5ZENSDUZ · pith_short_8: ZNZXCMWX

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/ZNZXCMWX5ZENSDUZVBPR2Z4KP4 \
  | 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: cb737132d7ee48d90e99a85f1d678a7f1f37ed880161fed10591da293c41b8fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ece4d3193975efe85f5c0eddc025ad834025822230e70b43632ec3c4a9b6a7f9",
    "cross_cats_sorted": [
      "hep-th",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-12-15T18:43:54Z",
    "title_canon_sha256": "e5483716bffe2843ffbf8cd2f6df4b6e268af7a9095db00f95d9098e4158bd1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.13651",
    "kind": "arxiv",
    "version": 3
  }
}