Pith Number

pith:BJ2ALS6A

pith:2006:BJ2ALS6AR7HNO7BHWKQBJUTEYC

not attested not anchored not stored refs pending

Graded Betti numbers of Cohen-Macaulay modules and the Multiplicity conjecture

Jonas S\"oderberg, Mats Boij

arxiv:math/0611081 v2 · 2006-11-03 · 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{BJ2ALS6AR7HNO7BHWKQBJUTEYC}

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	2026-05-18T02:57:45.417947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a7405cbc08fced77c27b2a014d264c080d4773ab8f6e9bc4d6d6e3d61e0c2e9

Aliases

arxiv: math/0611081 · arxiv_version: math/0611081v2 · doi: 10.48550/arxiv.math/0611081 · pith_short_12: BJ2ALS6AR7HN · pith_short_16: BJ2ALS6AR7HNO7BH · pith_short_8: BJ2ALS6A

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/BJ2ALS6AR7HNO7BHWKQBJUTEYC \
  | 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: 0a7405cbc08fced77c27b2a014d264c080d4773ab8f6e9bc4d6d6e3d61e0c2e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2bd1a30dc8623b41eae4e2231c54de75b04a6ecce39571193e2fdb4d7e45400",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AC",
    "submitted_at": "2006-11-03T15:45:43Z",
    "title_canon_sha256": "3ee83c133cdbe43a3856c3691a2305b8f1873e33d28dd8be3c970c165c4d7594"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0611081",
    "kind": "arxiv",
    "version": 2
  }
}