Pith Number

pith:RT4HNOAR

pith:2010:RT4HNOARSRQZUNXWDY4GQTEL5X

not attested not anchored not stored refs pending

Dual Bass Numbers and Co-Cohen Macaulay Modules

Lingguang Li

arxiv:1009.2229 v5 · 2010-09-12 · 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{RT4HNOARSRQZUNXWDY4GQTEL5X}

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	2026-05-18T03:18:32.195027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8cf876b81194619a36f61e38684c8bedd34a328d982bb29b82ac66b7f2f7f780

Aliases

arxiv: 1009.2229 · arxiv_version: 1009.2229v5 · doi: 10.48550/arxiv.1009.2229 · pith_short_12: RT4HNOARSRQZ · pith_short_16: RT4HNOARSRQZUNXW · pith_short_8: RT4HNOAR

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/RT4HNOARSRQZUNXWDY4GQTEL5X \
  | 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: 8cf876b81194619a36f61e38684c8bedd34a328d982bb29b82ac66b7f2f7f780

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "789725b7dc171fea47548684916a5d166be02023efc759dee2c081ed5b707515",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-09-12T10:52:40Z",
    "title_canon_sha256": "797e2fc8492410b38a0153abf1691615b77668f435fae38324fe62e3940b3b1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2229",
    "kind": "arxiv",
    "version": 5
  }
}