Pith Number

pith:VY6YIJSZ

pith:2013:VY6YIJSZLSFTLT6ZAELY2ZRZEX

not attested not anchored not stored refs pending

Algebraic actions of the discrete Heisenberg group: Expansiveness and homoclinic points

Evgeny Verbitskiy, Klaus Schmidt, Martin G\"oll

arxiv:1312.2469 v2 · 2013-12-09 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VY6YIJSZLSFTLT6ZAELY2ZRZEX}

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	2026-05-18T03:03:12.355102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae3d8426595c8b35cfd901178d663925c9535cf3b84721c59dd33790d1cd1ff6

Aliases

arxiv: 1312.2469 · arxiv_version: 1312.2469v2 · doi: 10.48550/arxiv.1312.2469 · pith_short_12: VY6YIJSZLSFT · pith_short_16: VY6YIJSZLSFTLT6Z · pith_short_8: VY6YIJSZ

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/VY6YIJSZLSFTLT6ZAELY2ZRZEX \
  | 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: ae3d8426595c8b35cfd901178d663925c9535cf3b84721c59dd33790d1cd1ff6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2833b14bc54cf7ee9fbc4e2af62ddc9cbb4d00c4a37872e25724cf378b4a9338",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-12-09T15:35:46Z",
    "title_canon_sha256": "5c9b54f97cadd8d6dfba3fb0b4a47fd16d320d4294aa144924eef3a8573f893c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2469",
    "kind": "arxiv",
    "version": 2
  }
}