Pith Number

pith:LOZO5YQK

pith:2000:LOZO5YQKMJUGWK7TDGE5XCHS2Y

not attested not anchored not stored refs pending

The invariants of the Clifford groups

E. M. Rains, Gabriele Nebe, N. J. A. Sloane

arxiv:math/0001038 v2 · 2000-01-06 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LOZO5YQKMJUGWK7TDGE5XCHS2Y}

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

2 papers in Pith

Maximally Sensitive Sets of States

Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates

Receipt and verification

First computed	2026-07-04T14:34:13.408826Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bb2eee20a62686b2bf31989db88f2d60995f7a366dfffd586cbb15508ec2c67

Aliases

arxiv: math/0001038 · arxiv_version: math/0001038v2 · doi: 10.48550/arxiv.math/0001038 · pith_short_12: LOZO5YQKMJUG · pith_short_16: LOZO5YQKMJUGWK7T · pith_short_8: LOZO5YQK

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/LOZO5YQKMJUGWK7TDGE5XCHS2Y \
  | 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: 5bb2eee20a62686b2bf31989db88f2d60995f7a366dfffd586cbb15508ec2c67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a63587b0e9eb4a583a48a85ead645a542842e3e48fbc1f61ca0fe292b55d8a0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2000-01-06T21:03:21Z",
    "title_canon_sha256": "1bd0385eb5f69cc394c622fae2e0bac4a7329b61e8830da177fa88770a04e633"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0001038",
    "kind": "arxiv",
    "version": 2
  }
}