Pith Number

pith:M4FE3K5A

pith:2025:M4FE3K5AEMODAQSNNQTI3YR3LM

not attested not anchored not stored refs pending

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians

Andrew James Bruce

arxiv:2507.21906 v2 · 2025-07-29 · math.DG · gr-qc · 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{M4FE3K5AEMODAQSNNQTI3YR3LM}

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.

Cited by

1 paper in Pith

Carrollian $\mathbb{R}^\times$-bundles: Connections and Beyond

Receipt and verification

First computed	2026-06-10T01:10:56.764981Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

670a4daba0231c30424d6c268de23b5b27938f2e8de2b2619890efc8efe2093f

Aliases

arxiv: 2507.21906 · arxiv_version: 2507.21906v2 · doi: 10.48550/arxiv.2507.21906 · pith_short_12: M4FE3K5AEMOD · pith_short_16: M4FE3K5AEMODAQSN · pith_short_8: M4FE3K5A

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/M4FE3K5AEMODAQSNNQTI3YR3LM \
  | 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: 670a4daba0231c30424d6c268de23b5b27938f2e8de2b2619890efc8efe2093f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a73240d57646e04e9a4a962bda58bb77bcb33f5b772dff6acd651437f014ec0f",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-07-29T15:18:25Z",
    "title_canon_sha256": "76d06dc5bbb9edc208e5ce572dd3373453e79e81d4147b0a838774395f240438"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.21906",
    "kind": "arxiv",
    "version": 2
  }
}