Pith Number

pith:Y3F44FDD

pith:2010:Y3F44FDDK7YAMZTHXQVT2A5KL7

not attested not anchored not stored refs pending

Necessary conditions for the depth formula over Cohen-Macaulay local rings

Hailong Dao, Olgur Celikbas

arxiv:1008.2573 v2 · 2010-08-16 · 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{Y3F44FDDK7YAMZTHXQVT2A5KL7}

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	2026-05-18T04:23:34.283335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6cbce146357f0066667bc2b3d03aa5fe30866bfc42e122d699f347d2b496edc

Aliases

arxiv: 1008.2573 · arxiv_version: 1008.2573v2 · doi: 10.48550/arxiv.1008.2573 · pith_short_12: Y3F44FDDK7YA · pith_short_16: Y3F44FDDK7YAMZTH · pith_short_8: Y3F44FDD

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/Y3F44FDDK7YAMZTHXQVT2A5KL7 \
  | 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: c6cbce146357f0066667bc2b3d03aa5fe30866bfc42e122d699f347d2b496edc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f70b3e93f381c7cb217b56318a3bbe2ec5fe1d10e9dcb088cad1a168b2ef7575",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-08-16T05:11:59Z",
    "title_canon_sha256": "0599df8f9b5351e38219eb6eee673d022d3fd231b600046ef627f525ac368871"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.2573",
    "kind": "arxiv",
    "version": 2
  }
}