Pith Number

pith:3CSXE6TN

pith:2025:3CSXE6TNWUVLDV5SH2GR2FVH77

not attested not anchored not stored refs pending

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group

Chiara Rigoni, Omar Zoghlami, Samu\"el Borza

arxiv:2509.06563 v1 · 2025-09-08 · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3CSXE6TNWUVLDV5SH2GR2FVH77}

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	2026-07-05T12:06:38.330410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8a5727a6db52ab1d7b23e8d1d16a7ffdf3ace7a481ad8ffc4477106d5d97e22

Aliases

arxiv: 2509.06563 · arxiv_version: 2509.06563v1 · doi: 10.48550/arxiv.2509.06563 · pith_short_12: 3CSXE6TNWUVL · pith_short_16: 3CSXE6TNWUVLDV5S · pith_short_8: 3CSXE6TN

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/3CSXE6TNWUVLDV5SH2GR2FVH77 \
  | 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: d8a5727a6db52ab1d7b23e8d1d16a7ffdf3ace7a481ad8ffc4477106d5d97e22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f1c301af987c60cd787acefa0a6a5296ccc163e270e2408b3693e969677bd2d",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-09-08T11:24:20Z",
    "title_canon_sha256": "ee47343684128e2e788f16af1e97a871dce2a1e30eded483b035fa9aafc5b7d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.06563",
    "kind": "arxiv",
    "version": 1
  }
}