Pith Number

pith:6HJX3WZY

pith:2009:6HJX3WZYSBBHXNHTOKIMT6C2EB

not attested not anchored not stored refs pending

Multi-parameter Carnot-Caratheodory balls and the theorem of Frobenius

Brian Street

arxiv:0901.2910 v4 · 2009-01-19 · math.CA · 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{6HJX3WZYSBBHXNHTOKIMT6C2EB}

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	2026-05-18T04:31:41.589624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1d37ddb3890427bb4f37290c9f85a206a5356634fad7b827b6b12cdb922cd68

Aliases

arxiv: 0901.2910 · arxiv_version: 0901.2910v4 · doi: 10.48550/arxiv.0901.2910 · pith_short_12: 6HJX3WZYSBBH · pith_short_16: 6HJX3WZYSBBHXNHT · pith_short_8: 6HJX3WZY

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/6HJX3WZYSBBHXNHTOKIMT6C2EB \
  | 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: f1d37ddb3890427bb4f37290c9f85a206a5356634fad7b827b6b12cdb922cd68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c16180b4ad9166132af67150663fbb56d0dd09f918c7e56e00bf692369f8d451",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-01-19T18:19:25Z",
    "title_canon_sha256": "0206f6fd33537e99a7cf06b00a829eca87c4f2b2360a4540c19d2fefc52b07b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.2910",
    "kind": "arxiv",
    "version": 4
  }
}