Pith Number

pith:PXENN3EK

pith:2022:PXENN3EKPBLESBGUTLFREI3XQX

not attested not anchored not stored refs pending

Cotorsion pairs and model structures on Morita rings

Jian Cui, Pu Zhang, Shi Rong

arxiv:2208.05684 v3 · 2022-08-11 · 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{PXENN3EKPBLESBGUTLFREI3XQX}

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	2026-07-05T07:22:13.131646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7dc8d6ec8a78564904d49acb12237785d163f5df6ee9fe4076e75d958db2395b

Aliases

arxiv: 2208.05684 · arxiv_version: 2208.05684v3 · doi: 10.48550/arxiv.2208.05684 · pith_short_12: PXENN3EKPBLE · pith_short_16: PXENN3EKPBLESBGU · pith_short_8: PXENN3EK

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/PXENN3EKPBLESBGUTLFREI3XQX \
  | 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: 7dc8d6ec8a78564904d49acb12237785d163f5df6ee9fe4076e75d958db2395b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3a78b0c4863bb0034a2bb6e55117f82b3b62ae227781199bc986ee6eaa7957c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2022-08-11T08:01:11Z",
    "title_canon_sha256": "bafa46d8ec798882c69a53af61662f24926caa504262348540ebcc34dde5c7e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2208.05684",
    "kind": "arxiv",
    "version": 3
  }
}