Pith Number

pith:NHG36D6R

pith:2011:NHG36D6RSKEUFA7IEBX242JPRH

not attested not anchored not stored refs pending

Ringel duality and derivatives of non-additive functors

Antoine Touz\'e

arxiv:1103.4580 v4 · 2011-03-23 · math.RT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NHG36D6RSKEUFA7IEBX242JPRH}

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	2026-05-18T03:33:26.727153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69cdbf0fd192894283e8206fae692f89e127e34145ff30194eb2c2a7e91258a1

Aliases

arxiv: 1103.4580 · arxiv_version: 1103.4580v4 · doi: 10.48550/arxiv.1103.4580 · pith_short_12: NHG36D6RSKEU · pith_short_16: NHG36D6RSKEUFA7I · pith_short_8: NHG36D6R

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/NHG36D6RSKEUFA7IEBX242JPRH \
  | 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: 69cdbf0fd192894283e8206fae692f89e127e34145ff30194eb2c2a7e91258a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c0eb3e89fc4977fc928fd1787b9a1114fe0891ef964b427653b97011ff0f967",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-03-23T17:38:47Z",
    "title_canon_sha256": "72c78994ca306b49ed035985f3508d4a3d715a88c6001f816466ddbba8e1420c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4580",
    "kind": "arxiv",
    "version": 4
  }
}