Pith Number

pith:ES7ES6WB

pith:2026:ES7ES6WB4DQMQUXUWM2WWP55M2

not attested not anchored not stored refs pending

An $\ell^2$ Obstruction for Elementary Embeddings of Hyperbolic Groups

Connor MacMahon

arxiv:2605.20397 v1 · 2026-05-19 · math.GR · math.LO · 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{ES7ES6WB4DQMQUXUWM2WWP55M2}

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	2026-05-21T01:04:36.489114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24be497ac1e0e0c852f4b3356b3fbd668a93468da2ed9cef1974f8f510c098c9

Aliases

arxiv: 2605.20397 · arxiv_version: 2605.20397v1 · doi: 10.48550/arxiv.2605.20397 · pith_short_12: ES7ES6WB4DQM · pith_short_16: ES7ES6WB4DQMQUXU · pith_short_8: ES7ES6WB

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/ES7ES6WB4DQMQUXUWM2WWP55M2 \
  | 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: 24be497ac1e0e0c852f4b3356b3fbd668a93468da2ed9cef1974f8f510c098c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90c576b5c76e6ea87eb6e4878e3157d0cd8c5bcecdf4b27f43241aaf8c3a694c",
    "cross_cats_sorted": [
      "math.LO",
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-19T18:52:16Z",
    "title_canon_sha256": "9a91a33b625d289a8faf3c4096830e608c1eb5b681f0b26ada1f2d77329c90bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20397",
    "kind": "arxiv",
    "version": 1
  }
}