Pith Number

pith:TMHU4MK6

pith:2025:TMHU4MK6LU3465FVWRNRQHPJMO

not attested not anchored not stored refs pending

Hyperlinearity, stability and asymptotic spectral gap of higher rank lattices

Alon Dogon, Itamar Vigdorovich

arxiv:2506.20843 v2 · 2025-06-25 · 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{TMHU4MK6LU3465FVWRNRQHPJMO}

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.

Cited by

1 paper in Pith

Characters of surface groups

Receipt and verification

First computed	2026-06-24T01:14:57.651556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b0f4e315e5d37cf74b5b45b181de963982af92a66cef6fdf854e9681005da22

Aliases

arxiv: 2506.20843 · arxiv_version: 2506.20843v2 · doi: 10.48550/arxiv.2506.20843 · pith_short_12: TMHU4MK6LU34 · pith_short_16: TMHU4MK6LU3465FV · pith_short_8: TMHU4MK6

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/TMHU4MK6LU3465FVWRNRQHPJMO \
  | 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: 9b0f4e315e5d37cf74b5b45b181de963982af92a66cef6fdf854e9681005da22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef36e595c6cf2f775f730d0b60ce8e57ea07dea9604f0d8b4e8aec131919852c",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-06-25T21:27:27Z",
    "title_canon_sha256": "4892bfd9d878b8512ed95f67287a53d45e69f9ba90e7bdc9453d5194a4f30912"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.20843",
    "kind": "arxiv",
    "version": 2
  }
}