Pith Number

pith:RHPJHBGD

pith:2012:RHPJHBGDT4OSFNWSECRR223CYJ

not attested not anchored not stored refs pending

Exponential Mixing of Nilmanifold Automorphisms

Alexander Gorodnik, Ralf Spatzier

arxiv:1210.2271 v1 · 2012-10-08 · 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{RHPJHBGDT4OSFNWSECRR223CYJ}

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	2026-05-18T03:43:50.627756Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89de9384c39f1d22b6d220a31d6b62c27b528c8a84ba1c9478956a4cead6ee6f

Aliases

arxiv: 1210.2271 · arxiv_version: 1210.2271v1 · doi: 10.48550/arxiv.1210.2271 · pith_short_12: RHPJHBGDT4OS · pith_short_16: RHPJHBGDT4OSFNWS · pith_short_8: RHPJHBGD

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/RHPJHBGDT4OSFNWSECRR223CYJ \
  | 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: 89de9384c39f1d22b6d220a31d6b62c27b528c8a84ba1c9478956a4cead6ee6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82735e2d20c8226249d982749191f860e7e89f6186dcc8f931e3019e69dfb1d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-08T13:24:16Z",
    "title_canon_sha256": "02122604f8f393fcd9932892b57288d0677434b4ffbb05d9dd173e8539318b8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2271",
    "kind": "arxiv",
    "version": 1
  }
}