Pith Number

pith:FZMO3PKC

pith:2019:FZMO3PKCTCLQVX6UZCLAKI32FC

not attested not anchored not stored refs pending

A criterion of Cohen Macaulayness of the form module

M. Azeem Khadam

arxiv:1908.07317 v1 · 2019-08-20 · 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{FZMO3PKCTCLQVX6UZCLAKI32FC}

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	2026-07-04T23:58:33.197584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e58edbd4298970adfd4c89605237a28b336aa0195887a0ff03457e3e1282fb1

Aliases

arxiv: 1908.07317 · arxiv_version: 1908.07317v1 · doi: 10.48550/arxiv.1908.07317 · pith_short_12: FZMO3PKCTCLQ · pith_short_16: FZMO3PKCTCLQVX6U · pith_short_8: FZMO3PKC

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/FZMO3PKCTCLQVX6UZCLAKI32FC \
  | 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: 2e58edbd4298970adfd4c89605237a28b336aa0195887a0ff03457e3e1282fb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73c6a338cab8426cf5dae238393441e2ecd6d20890b05647c5b2fcb67b80cf43",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2019-08-20T13:00:56Z",
    "title_canon_sha256": "c7276357a856158f50d503191097d753c4be28b1a0d9e78c9969adf9e6e6ee8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07317",
    "kind": "arxiv",
    "version": 1
  }
}