Pith Number

pith:PPTO3SWU

pith:2022:PPTO3SWUWE46LSAYF3SOMKL5RQ

not attested not anchored not stored refs pending

Invariants and Gorenstein projective modules

Chi-Heng Zhang, Nan Gao

arxiv:2209.03191 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{PPTO3SWUWE46LSAYF3SOMKL5RQ}

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	2026-07-05T04:55:32.622960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7be6edcad4b139e5c8182ee4e6297d8c1a8636cabc4c7fb612a002bbed0d83af

Aliases

arxiv: 2209.03191 · arxiv_version: 2209.03191v1 · doi: 10.48550/arxiv.2209.03191 · pith_short_12: PPTO3SWUWE46 · pith_short_16: PPTO3SWUWE46LSAY · pith_short_8: PPTO3SWU

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/PPTO3SWUWE46LSAYF3SOMKL5RQ \
  | 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: 7be6edcad4b139e5c8182ee4e6297d8c1a8636cabc4c7fb612a002bbed0d83af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "644a353c5efc33d041a33bf418f8fa9039d1221321160c528521ccd07dff364d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2022-09-01T15:35:31Z",
    "title_canon_sha256": "9d43fd49aa5ec6a040a8603104f5706908525b20bf8916e6871dc76db9bc3f15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.03191",
    "kind": "arxiv",
    "version": 1
  }
}