Pith Number

pith:RE2VCOFZ

pith:2011:RE2VCOFZHHGWUZZJ34CKC47MVD

not attested not anchored not stored refs pending

Symbolic approach and induction in the Heisenberg group

Jean-Fran\c{c}ois Bertazzon

arxiv:1112.2945 v1 · 2011-12-13 · 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{RE2VCOFZHHGWUZZJ34CKC47MVD}

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	2026-05-18T04:01:50.730582Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89355138b939cd6a6729df04a173eca8eee6a6605d41ce184b2a5813ff6f6f5d

Aliases

arxiv: 1112.2945 · arxiv_version: 1112.2945v1 · doi: 10.48550/arxiv.1112.2945 · pith_short_12: RE2VCOFZHHGW · pith_short_16: RE2VCOFZHHGWUZZJ · pith_short_8: RE2VCOFZ

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/RE2VCOFZHHGWUZZJ34CKC47MVD \
  | 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: 89355138b939cd6a6729df04a173eca8eee6a6605d41ce184b2a5813ff6f6f5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "811ac1296d2de499af45e6dbd9f725de7ad6f9af811f824654d2b231e745fa7c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-12-13T16:33:32Z",
    "title_canon_sha256": "bb3613c71161a7980cd4ffc4b3d7213170aa61f323c6c143c19a4ef43c8ebae6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2945",
    "kind": "arxiv",
    "version": 1
  }
}