Pith Number

pith:XHJLFNGS

pith:2016:XHJLFNGSKSVXHXEGK4DFUO72O7

not attested not anchored not stored refs pending

When almost Cohen-Macaulay algebras map into big Cohen-Macaulay modules

Rajsekhar Bhattacharyya

arxiv:1609.03133 v2 · 2016-09-11 · 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{XHJLFNGSKSVXHXEGK4DFUO72O7}

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	2026-05-18T00:18:57.184073Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9d2b2b4d254ab73dc8657065a3bfa77d64da790768ab7db6309f7e6d6b0444d

Aliases

arxiv: 1609.03133 · arxiv_version: 1609.03133v2 · doi: 10.48550/arxiv.1609.03133 · pith_short_12: XHJLFNGSKSVX · pith_short_16: XHJLFNGSKSVXHXEG · pith_short_8: XHJLFNGS

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/XHJLFNGSKSVXHXEGK4DFUO72O7 \
  | 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: b9d2b2b4d254ab73dc8657065a3bfa77d64da790768ab7db6309f7e6d6b0444d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e744f7757c39a611201e376643cdf7ba9c9d453188ef2f5899896929391aee7c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-09-11T08:07:43Z",
    "title_canon_sha256": "008a3bfc28af7c92f63a264ede07866279aec9f4787ff7e6af18cbd0c8a514c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03133",
    "kind": "arxiv",
    "version": 2
  }
}