Pith Number

pith:VVRJRKZI

pith:2026:VVRJRKZIKLJFI7QYGI4JORDC6H

not attested not anchored not stored refs pending

The non-ergodic Host-Kra-Ziegler structure theorem for $\mathbb{Z}^d$-actions via measurable selections

Asgar Jamneshan, Simon Machado

arxiv:2601.09553 v2 · 2026-01-14 · 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{VVRJRKZIKLJFI7QYGI4JORDC6H}

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	2026-05-28T01:04:35.302910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad6298ab2852d2547e183238974462f1c61b3a8e2f026a6fe0e1bc8ddd6474f8

Aliases

arxiv: 2601.09553 · arxiv_version: 2601.09553v2 · doi: 10.48550/arxiv.2601.09553 · pith_short_12: VVRJRKZIKLJF · pith_short_16: VVRJRKZIKLJFI7QY · pith_short_8: VVRJRKZI

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/VVRJRKZIKLJFI7QYGI4JORDC6H \
  | 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: ad6298ab2852d2547e183238974462f1c61b3a8e2f026a6fe0e1bc8ddd6474f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb384306adc9395aec8fefb629596db09861f7a5f00c486b87a68cbbf9f2d1ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-01-14T15:13:51Z",
    "title_canon_sha256": "0e3b3b4f9318ded152326a2aeedbe11465f1301f1c720b101fc9014e5ed0e5d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.09553",
    "kind": "arxiv",
    "version": 2
  }
}