Pith Number

pith:MR7C7K6H

pith:2026:MR7C7K6HBZUB7IIDVIM4NUVLBX

not attested not anchored not stored refs pending

$\mathbb{Z}^2$ is flexibly stable in the operator norm

Alexander Lubotzky, Guy Salomon

arxiv:2607.17578 v1 · 2026-07-20 · math.OA · 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{MR7C7K6HBZUB7IIDVIM4NUVLBX}

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	2026-07-21T01:21:53.272507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

647e2fabc70e681fa103aa19c6d2ab0dc217f12b02018eeb33794694b6a0f1d2

Aliases

arxiv: 2607.17578 · arxiv_version: 2607.17578v1 · doi: 10.48550/arxiv.2607.17578 · pith_short_12: MR7C7K6HBZUB · pith_short_16: MR7C7K6HBZUB7IID · pith_short_8: MR7C7K6H

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/MR7C7K6HBZUB7IIDVIM4NUVLBX \
  | 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: 647e2fabc70e681fa103aa19c6d2ab0dc217f12b02018eeb33794694b6a0f1d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e272236c968f854d0122a80999c1043604772589566578cba2614d9f26d04a29",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-07-20T05:47:04Z",
    "title_canon_sha256": "6e7d7b289ec56e3460c42ed42f35762b9ed5ca931bc9cd23bf06df30bbfe38c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17578",
    "kind": "arxiv",
    "version": 1
  }
}