Pith Number

pith:2DKU5X2X

pith:2015:2DKU5X2XEZUZHJDIG3437ZUISA

not attested not anchored not stored refs pending

Intrinsic Diophantine approximation in Carnot groups and in the Siegel model of the Heisenberg group

Anton Lukyanenko, Joseph Vandehey

arxiv:1510.06033 v1 · 2015-10-20 · math.NT · 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{2DKU5X2XEZUZHJDIG3437ZUISA}

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	2026-05-18T01:29:38.856081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0d54edf57266993a46836f9bfe68890010a749dd32e2ab6cfcecfa2f08f87c4

Aliases

arxiv: 1510.06033 · arxiv_version: 1510.06033v1 · doi: 10.48550/arxiv.1510.06033 · pith_short_12: 2DKU5X2XEZUZ · pith_short_16: 2DKU5X2XEZUZHJDI · pith_short_8: 2DKU5X2X

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/2DKU5X2XEZUZHJDIG3437ZUISA \
  | 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: d0d54edf57266993a46836f9bfe68890010a749dd32e2ab6cfcecfa2f08f87c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7375ebfcd84f674f0e392ecab2630d7d5dc314679686d55d79b0d981c000b2d",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-10-20T20:06:12Z",
    "title_canon_sha256": "0c58e3cf095b0443e3e546ea4c95bda428b11dcca5c5b2943e3d10831a996ae2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.06033",
    "kind": "arxiv",
    "version": 1
  }
}