Pith Number

pith:7QQNKJ3H

pith:2016:7QQNKJ3HELTYAW6JR6FXWU2CJP

not attested not anchored not stored refs pending

Finite dimensional Hopf algebras over Kac-Paljutkin algebra $H_8$

Yuxing Shi

arxiv:1612.03262 v4 · 2016-12-10 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7QQNKJ3HELTYAW6JR6FXWU2CJP}

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

Spontaneous breaking of non-invertible symmetries and duality to beyond-Landau transitions

Receipt and verification

First computed	2026-07-05T05:47:53.335092Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc20d5276722e7805bc98f8b7b53424bccdb68014d289032de631fd2f6806bc9

Aliases

arxiv: 1612.03262 · arxiv_version: 1612.03262v4 · doi: 10.48550/arxiv.1612.03262 · pith_short_12: 7QQNKJ3HELTY · pith_short_16: 7QQNKJ3HELTYAW6J · pith_short_8: 7QQNKJ3H

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/7QQNKJ3HELTYAW6JR6FXWU2CJP \
  | 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: fc20d5276722e7805bc98f8b7b53424bccdb68014d289032de631fd2f6806bc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08eb12ec66050faf49745d236f7a7ae438d2223a21775691b82e34bf545bf53b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2016-12-10T06:39:13Z",
    "title_canon_sha256": "608bcfdb87d0ac071b63df51b1fb50082ed0cfd9c245a568cee5f2a21d55d619"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03262",
    "kind": "arxiv",
    "version": 4
  }
}