Pith Number

pith:ZWRLSZDO

pith:2014:ZWRLSZDOEVELZNUXIZDCQUA3BD

not attested not anchored not stored refs pending

Marstrand's density theorem in the Heisenberg group

Jeremy T. Tyson, Vasilis Chousionis

arxiv:1407.6636 v1 · 2014-07-24 · math.MG · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZWRLSZDOEVELZNUXIZDCQUA3BD}

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	2026-05-18T01:02:21.407529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cda2b9646e2548bcb697464628501b08e5f41e3fa5df21ba465de2a5e53ab6c9

Aliases

arxiv: 1407.6636 · arxiv_version: 1407.6636v1 · doi: 10.48550/arxiv.1407.6636 · pith_short_12: ZWRLSZDOEVEL · pith_short_16: ZWRLSZDOEVELZNUX · pith_short_8: ZWRLSZDO

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/ZWRLSZDOEVELZNUXIZDCQUA3BD \
  | 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: cda2b9646e2548bcb697464628501b08e5f41e3fa5df21ba465de2a5e53ab6c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "202c75af12292856f57393d3d3e086531f49932a3db3666ba754a7a0c9e8120e",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2014-07-24T16:13:03Z",
    "title_canon_sha256": "59be5b701e102924e42230e375111ec8bc7f698531a0ccd91d7a5d889bfaa041"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.6636",
    "kind": "arxiv",
    "version": 1
  }
}