Pith Number

pith:PIK5ZDKW

pith:2011:PIK5ZDKW6GANPGFXMOHDPVONZ7

not attested not anchored not stored refs pending

More counterexamples to Happel's question and Snashall-Solberg's conjecture

Chao Zhang, Yunge Xu

arxiv:1109.3956 v1 · 2011-09-19 · math.RT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PIK5ZDKW6GANPGFXMOHDPVONZ7}

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	2026-05-18T04:12:45.489767Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a15dc8d56f180d798b7638e37d5cdcfc662eb043eec3878315e63a6228c6a11

Aliases

arxiv: 1109.3956 · arxiv_version: 1109.3956v1 · doi: 10.48550/arxiv.1109.3956 · pith_short_12: PIK5ZDKW6GAN · pith_short_16: PIK5ZDKW6GANPGFX · pith_short_8: PIK5ZDKW

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/PIK5ZDKW6GANPGFXMOHDPVONZ7 \
  | 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: 7a15dc8d56f180d798b7638e37d5cdcfc662eb043eec3878315e63a6228c6a11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0fcbed61d87c78aca9c7d2417694a1143c3d5074d7c3fd15614256be1e72c80e",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-09-19T07:32:26Z",
    "title_canon_sha256": "e09c9c37a8ea234dabd1b2a1d94f7441636df5346abd3df1fbcbdecbf96311c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3956",
    "kind": "arxiv",
    "version": 1
  }
}