Pith Number

pith:7AZEYROI

pith:2018:7AZEYROIQQLTWPJF6V3ZSI3VFV

not attested not anchored not stored refs pending

Geometric properties of extremal sets for the dimension comparison in Carnot groups of step 2

Laura Venieri

arxiv:1808.10233 v1 · 2018-08-30 · math.CA · 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{7AZEYROIQQLTWPJF6V3ZSI3VFV}

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	2026-05-18T00:06:49.445356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8324c45c884173b3d25f5779923752d5a093f49ff130252a7981669dffa9dd0

Aliases

arxiv: 1808.10233 · arxiv_version: 1808.10233v1 · doi: 10.48550/arxiv.1808.10233 · pith_short_12: 7AZEYROIQQLT · pith_short_16: 7AZEYROIQQLTWPJF · pith_short_8: 7AZEYROI

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/7AZEYROIQQLTWPJF6V3ZSI3VFV \
  | 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: f8324c45c884173b3d25f5779923752d5a093f49ff130252a7981669dffa9dd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aeb2ce0487c7189cc4f58b8c74a530100797c86495c7daa21b530e3c3507b156",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-08-30T11:38:52Z",
    "title_canon_sha256": "b01849bea54c8c80e6e6797ecf3f7a047d3c3cde25f7068577b571d021cb6b11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.10233",
    "kind": "arxiv",
    "version": 1
  }
}