Pith Number

pith:DZCG67DK

pith:2015:DZCG67DKDXQADW2SBTTZUDDFHG

not attested not anchored not stored refs pending

Measure contraction properties of Carnot groups

Luca Rizzi

arxiv:1510.05960 v4 · 2015-10-20 · math.MG · math.DG · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DZCG67DKDXQADW2SBTTZUDDFHG}

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	2026-05-18T00:44:39.024852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e446f7c6a1de001db520ce79a0c653999eae3c18b3c16b3875c050634ebf9d7

Aliases

arxiv: 1510.05960 · arxiv_version: 1510.05960v4 · doi: 10.48550/arxiv.1510.05960 · pith_short_12: DZCG67DKDXQA · pith_short_16: DZCG67DKDXQADW2S · pith_short_8: DZCG67DK

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/DZCG67DKDXQADW2SBTTZUDDFHG \
  | 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: 1e446f7c6a1de001db520ce79a0c653999eae3c18b3c16b3875c050634ebf9d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7ebfe60129671b14b6d669162d3d38c775f9ddc90a1227e60664bf2ddb58236",
    "cross_cats_sorted": [
      "math.DG",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-10-20T16:56:26Z",
    "title_canon_sha256": "1ca39642b060a5098a0d6038220e9d6fff1f02cdaf06c9dc8b2b827bb7097962"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05960",
    "kind": "arxiv",
    "version": 4
  }
}