Pith Number

pith:TY7MZCL5

pith:2005:TY7MZCL5NS7WMQDBTC77WL3ART

not attested not anchored not stored refs pending

Cocycle and Orbit Equivalence Superrigidity for Malleable Actions of w-Rigid Groups

Sorin Popa

arxiv:math/0512646 v8 · 2005-12-30 · math.GR · 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{TY7MZCL5NS7WMQDBTC77WL3ART}

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	2026-07-04T15:06:27.244290Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e3ecc897d6cbf66406198bffb2f608cf3d31346c319bc78bd14028ce5d54605

Aliases

arxiv: math/0512646 · arxiv_version: math/0512646v8 · doi: 10.48550/arxiv.math/0512646 · pith_short_12: TY7MZCL5NS7W · pith_short_16: TY7MZCL5NS7WMQDB · pith_short_8: TY7MZCL5

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/TY7MZCL5NS7WMQDBTC77WL3ART \
  | 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: 9e3ecc897d6cbf66406198bffb2f608cf3d31346c319bc78bd14028ce5d54605

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf2044f79352d81c6945d5cf7c11bf79f8804fb21ccf84ef8b90b3a9618e230a",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2005-12-30T08:45:37Z",
    "title_canon_sha256": "2105fd9172184390b1a59df8c821fe3e75bb37868e7d9145fc5492cc793ac08f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512646",
    "kind": "arxiv",
    "version": 8
  }
}