Pith Number

pith:ANKYNXZS

pith:2016:ANKYNXZSPC2KYNKBYYG2KW366O

not attested not anchored not stored refs pending

On the growth of L2-invariants of locally symmetric spaces, II: exotic invariant random subgroups in rank one

Ian Biringer, Iddo Samet, Jean Raimbault, Miklos Abert, Nicolas Bergeron, Nikolay Nikolov, Tsachik Gelander

arxiv:1612.09510 v1 · 2016-12-30 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ANKYNXZSPC2KYNKBYYG2KW366O}

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	2026-05-18T00:53:41.336506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

035586df3278b4ac3541c60da55b7ef38f7d7f1867a6fec4c52772518f27a63f

Aliases

arxiv: 1612.09510 · arxiv_version: 1612.09510v1 · doi: 10.48550/arxiv.1612.09510 · pith_short_12: ANKYNXZSPC2K · pith_short_16: ANKYNXZSPC2KYNKB · pith_short_8: ANKYNXZS

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/ANKYNXZSPC2KYNKBYYG2KW366O \
  | 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: 035586df3278b4ac3541c60da55b7ef38f7d7f1867a6fec4c52772518f27a63f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0529f12556ab308c89484a29a650d7ed86cf76cf0d178750fdd22c4df5e619c",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-12-30T15:40:40Z",
    "title_canon_sha256": "4c01c40605fb9dc7e1d6ade2bf0a4eed0c2125257db66bbede9ce205f99cb4da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.09510",
    "kind": "arxiv",
    "version": 1
  }
}