Pith Number

pith:QYEVQSZL

pith:2006:QYEVQSZLNIV267WVW5HCXN5ABC

not attested not anchored not stored refs pending

On the Superrigidity of Malleable Actions with Spectral Gap

Sorin Popa

arxiv:math/0608429 v6 · 2006-08-16 · 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{QYEVQSZLNIV267WVW5HCXN5ABC}

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	2026-07-04T15:06:27.257118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8609584b2b6a2baf7ed5b74e2bb7a008b727aa838c30111e7993523aa9a56c8d

Aliases

arxiv: math/0608429 · arxiv_version: math/0608429v6 · doi: 10.48550/arxiv.math/0608429 · pith_short_12: QYEVQSZLNIV2 · pith_short_16: QYEVQSZLNIV267WV · pith_short_8: QYEVQSZL

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/QYEVQSZLNIV267WVW5HCXN5ABC \
  | 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: 8609584b2b6a2baf7ed5b74e2bb7a008b727aa838c30111e7993523aa9a56c8d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "477657741fb8072321f2aabb4071f6c31b1569b8dcdf4e307def7ec0a79eff65",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2006-08-16T20:04:51Z",
    "title_canon_sha256": "243150d0cb705c57486e5158caf3e3d87e1c84692a2c8701e522faba7bc3e3c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0608429",
    "kind": "arxiv",
    "version": 6
  }
}