Pith Number

pith:EBGV2TFY

pith:2025:EBGV2TFYE2HHEY2JIVQWOKEYV5

not attested not anchored not stored refs pending

Ergodic Average Dominance for Unimodular Amenable Groups

Joachim Zacharias, Runlian Xia, Ujan Chakraborty

arxiv:2512.12894 v2 · 2025-12-15 · math.DS · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EBGV2TFYE2HHEY2JIVQWOKEYV5}

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	2026-05-20T00:02:08.019436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

204d5d4cb8268e7263494561672898af5e5ded4862a65ca00aaf6f7dad8756d0

Aliases

arxiv: 2512.12894 · arxiv_version: 2512.12894v2 · doi: 10.48550/arxiv.2512.12894 · pith_short_12: EBGV2TFYE2HH · pith_short_16: EBGV2TFYE2HHEY2J · pith_short_8: EBGV2TFY

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/EBGV2TFYE2HHEY2JIVQWOKEYV5 \
  | 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: 204d5d4cb8268e7263494561672898af5e5ded4862a65ca00aaf6f7dad8756d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b1dd019cbfdcbe356d404075dbf9eabdab8d16a8830f22da5cc4a0044dcfbd9",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-12-15T00:43:03Z",
    "title_canon_sha256": "4a48c8228c698920309c9da12df55f68076508015830c63a0ef0dd0f396eba2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.12894",
    "kind": "arxiv",
    "version": 2
  }
}