Pith Number

pith:CTBBU3EP

pith:2011:CTBBU3EPMRWBFGEDY3F4HK3JPK

not attested not anchored not stored refs pending

Completions of Grothendieck groups

Catharina Stroppel, Pramod N. Achar

arxiv:1105.2715 v2 · 2011-05-13 · math.CT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CTBBU3EPMRWBFGEDY3F4HK3JPK}

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	2026-05-18T02:58:00.903239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14c21a6c8f646c129883c6cbc3ab697a838253d8ae122577405f5df2f8451d71

Aliases

arxiv: 1105.2715 · arxiv_version: 1105.2715v2 · doi: 10.48550/arxiv.1105.2715 · pith_short_12: CTBBU3EPMRWB · pith_short_16: CTBBU3EPMRWBFGED · pith_short_8: CTBBU3EP

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/CTBBU3EPMRWBFGEDY3F4HK3JPK \
  | 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: 14c21a6c8f646c129883c6cbc3ab697a838253d8ae122577405f5df2f8451d71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d88d26c7d9b043ffa94696e5c604a84d1c8aca5fa0bb32eede1b5726e2293c2",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2011-05-13T12:51:35Z",
    "title_canon_sha256": "85a94e06f73fc136e0db53c0a32ac2a9ac658a4567877b109c6a62728f670315"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2715",
    "kind": "arxiv",
    "version": 2
  }
}