Pith Number

pith:SUGC6KHY

pith:2012:SUGC6KHYEUOYCMABYKIAQQNDQU

not attested not anchored not stored refs pending

Mixing Properties of Commuting Nilmanifold Automorphisms

Alexander Gorodnik, Ralf Spatzier

arxiv:1211.0987 v2 · 2012-11-05 · 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{SUGC6KHYEUOYCMABYKIAQQNDQU}

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	2026-05-18T03:26:10.189900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

950c2f28f8251d813001c2900841a3850e6d6c9fc7595a575533852f52b5e9f7

Aliases

arxiv: 1211.0987 · arxiv_version: 1211.0987v2 · doi: 10.48550/arxiv.1211.0987 · pith_short_12: SUGC6KHYEUOY · pith_short_16: SUGC6KHYEUOYCMAB · pith_short_8: SUGC6KHY

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/SUGC6KHYEUOYCMABYKIAQQNDQU \
  | 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: 950c2f28f8251d813001c2900841a3850e6d6c9fc7595a575533852f52b5e9f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d412dcc96a7676d2d100acb630a1689310153baf389301760716e95e28b04233",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-11-05T19:59:55Z",
    "title_canon_sha256": "492ac13c6b9cff033c94af43e63079c325f3eca55af2181d81927b6f7a193a6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0987",
    "kind": "arxiv",
    "version": 2
  }
}