Pith Number

pith:XCIW6LFY

pith:2012:XCIW6LFYQ2HM3KZADALTLD7OYK

not attested not anchored not stored refs pending

Closed subgroups generated by generic measure automorphisms

Slawomir Solecki

arxiv:1210.0833 v3 · 2012-10-02 · math.DS · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XCIW6LFYQ2HM3KZADALTLD7OYK}

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	2026-05-17T23:53:18.424355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8916f2cb8868ecdab201817358feec28425d1bc49291afd12df38256757b12e

Aliases

arxiv: 1210.0833 · arxiv_version: 1210.0833v3 · doi: 10.48550/arxiv.1210.0833 · pith_short_12: XCIW6LFYQ2HM · pith_short_16: XCIW6LFYQ2HM3KZA · pith_short_8: XCIW6LFY

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/XCIW6LFYQ2HM3KZADALTLD7OYK \
  | 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: b8916f2cb8868ecdab201817358feec28425d1bc49291afd12df38256757b12e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a1b25a8c1a8b001e67a3ca660e097339d581e9dd3b827fe56c4a5b9a022c074",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-02T16:32:20Z",
    "title_canon_sha256": "5ff402123d6460731b75e333b4198de54db2994d9fb3b17b45e0a23f4ef3c40b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0833",
    "kind": "arxiv",
    "version": 3
  }
}