Pith Number

pith:6IQW5STW

pith:2016:6IQW5STWUGTXF3YGL6VBNCSDMK

not attested not anchored not stored refs pending

Approximate invariance for ergodic actions of amenable groups

Alexander Fish, Michael Bj\"orklund

arxiv:1607.02575 v4 · 2016-07-09 · math.DS · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6IQW5STWUGTXF3YGL6VBNCSDMK}

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	2026-05-17T23:45:21.233628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2216eca76a1a772ef065faa168a43629417b707096e88285cfbad00cd9e737e

Aliases

arxiv: 1607.02575 · arxiv_version: 1607.02575v4 · doi: 10.48550/arxiv.1607.02575 · pith_short_12: 6IQW5STWUGTX · pith_short_16: 6IQW5STWUGTXF3YG · pith_short_8: 6IQW5STW

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/6IQW5STWUGTXF3YGL6VBNCSDMK \
  | 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: f2216eca76a1a772ef065faa168a43629417b707096e88285cfbad00cd9e737e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a474a86d0d135a1b9360ae38fdbf248085db5d036c57f9fe37926ff4e4994d9f",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-07-09T07:05:56Z",
    "title_canon_sha256": "d08b113b8288d32f4fa090b477106854cd5b02111667433dc31efcb5614be3a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.02575",
    "kind": "arxiv",
    "version": 4
  }
}