Pith Number

pith:PQTUN2ZZ

pith:2000:PQTUN2ZZJIMTWQTSQIZ4LHLX3N

not attested not anchored not stored refs pending

An Elementary Introduction to Groups and Representations

Brian C. Hall

arxiv:math-ph/0005032 v1 · 2000-05-31 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PQTUN2ZZJIMTWQTSQIZ4LHLX3N}

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

HoPE: Hyperbolic Rotary Positional Encoding for Stable Long-Range Dependency Modeling in Large Language Models

Receipt and verification

First computed	2026-07-04T14:33:35.608380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c2746eb394a193b42728233c59d77db6f212c96ff7396961aef6b1ba5ad4e93

Aliases

arxiv: math-ph/0005032 · arxiv_version: math-ph/0005032v1 · doi: 10.48550/arxiv.math-ph/0005032 · pith_short_12: PQTUN2ZZJIMT · pith_short_16: PQTUN2ZZJIMTWQTS · pith_short_8: PQTUN2ZZ

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/PQTUN2ZZJIMTWQTSQIZ4LHLX3N \
  | 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: 7c2746eb394a193b42728233c59d77db6f212c96ff7396961aef6b1ba5ad4e93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8314516be6f294cb2729b07b3dfd9c26710207bc23f170acef6e671365302cc",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2000-05-31T16:44:12Z",
    "title_canon_sha256": "ea6ae9f7a4e6946bfa5ce52612189093d23da125f3c16bc3ee49fd68a2094e1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0005032",
    "kind": "arxiv",
    "version": 1
  }
}