Pith Number

pith:LA36QIYM

pith:2025:LA36QIYM65RJLZ3VBHG5PG5C2T

not attested not anchored not stored refs pending

Four-dimensional operator systems without the lifting property

Samuel J. Harris

arxiv:2508.00113 v2 · 2025-07-31 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LA36QIYM65RJLZ3VBHG5PG5C2T}

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	2026-06-19T16:09:50.499000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5837e8230cf76295e77509cdd79ba2d4f3ce9d4f97880b7e11cfaa2c74a6e3dd

Aliases

arxiv: 2508.00113 · arxiv_version: 2508.00113v2 · doi: 10.48550/arxiv.2508.00113 · pith_short_12: LA36QIYM65RJ · pith_short_16: LA36QIYM65RJLZ3V · pith_short_8: LA36QIYM

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/LA36QIYM65RJLZ3VBHG5PG5C2T \
  | 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: 5837e8230cf76295e77509cdd79ba2d4f3ce9d4f97880b7e11cfaa2c74a6e3dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccd075a72ffc53a841989f3d3df4bb71ca965655fb0eb7bbea3a1a2bc50c4d27",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2025-07-31T19:06:43Z",
    "title_canon_sha256": "7fa20875c7ecd9568aa6bcdd7902758029736baa109b92c902ebdddf14384387"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.00113",
    "kind": "arxiv",
    "version": 2
  }
}