Pith Number

pith:TMOTZH4N

pith:2022:TMOTZH4NF2SJRJFPJG5VNDVETZ

not attested not anchored not stored refs pending

Lifting of recollements and Gorenstein projective modules

Jing Ma, Nan Gao

arxiv:2209.03192 v1 · 2022-09-01 · 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{TMOTZH4NF2SJRJFPJG5VNDVETZ}

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	2026-07-05T04:55:32.639828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b1d3c9f8d2ea498a4af49bb568ea49e780fad5c84f8e6cd5f9de693b0317efe

Aliases

arxiv: 2209.03192 · arxiv_version: 2209.03192v1 · doi: 10.48550/arxiv.2209.03192 · pith_short_12: TMOTZH4NF2SJ · pith_short_16: TMOTZH4NF2SJRJFP · pith_short_8: TMOTZH4N

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/TMOTZH4NF2SJRJFPJG5VNDVETZ \
  | 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: 9b1d3c9f8d2ea498a4af49bb568ea49e780fad5c84f8e6cd5f9de693b0317efe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bedd69eb72ad4945332e6eadfff56d727c8865c02e71586d30ae6f3b074976f7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2022-09-01T15:39:02Z",
    "title_canon_sha256": "996cb23b67222b52fa3cd0a72c0440a3d90aa0d76a5227f706848d46577a35b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.03192",
    "kind": "arxiv",
    "version": 1
  }
}