Pith Number

pith:USOXRRFE

pith:2024:USOXRRFEHURE7FILJOX4OQGDIP

not attested not anchored not stored refs pending

Lower bounds on Loewy lengths of modules of finite projective dimension

Josh Pollitz, Nawaj KC

arxiv:2404.18368 v3 · 2024-04-29 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{USOXRRFEHURE7FILJOX4OQGDIP}

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	2026-07-05T10:52:11.830205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a49d78c4a43d224f950b4bafc740c343fa55c34b6116fb75666918a413191d46

Aliases

arxiv: 2404.18368 · arxiv_version: 2404.18368v3 · doi: 10.48550/arxiv.2404.18368 · pith_short_12: USOXRRFEHURE · pith_short_16: USOXRRFEHURE7FIL · pith_short_8: USOXRRFE

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/USOXRRFEHURE7FILJOX4OQGDIP \
  | 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: a49d78c4a43d224f950b4bafc740c343fa55c34b6116fb75666918a413191d46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06de2a3b9fcbd3290135be06a6884141eb43a4f872e60f23fdcc10bb52a67955",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2024-04-29T02:13:37Z",
    "title_canon_sha256": "3e73911a68cec37d6b00e9d09f61ea02fc96e18721f06aebc599ac38f5d2f657"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.18368",
    "kind": "arxiv",
    "version": 3
  }
}