Pith Number

pith:MQ2PRNXA

pith:2006:MQ2PRNXARYLSH3FTV2FGVKLMIP

not attested not anchored not stored refs pending

Graded Betti numbers and $h$-vectors of level modules

Jonas S\"oderberg

arxiv:math/0612047 v2 · 2006-12-04 · 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{MQ2PRNXARYLSH3FTV2FGVKLMIP}

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	2026-07-04T14:57:58.746385Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6434f8b6e08e1723ecb3ae8a6aa96c43ec4a3593c82bc9e7a66015b2928e6e1d

Aliases

arxiv: math/0612047 · arxiv_version: math/0612047v2 · doi: 10.48550/arxiv.math/0612047 · pith_short_12: MQ2PRNXARYLS · pith_short_16: MQ2PRNXARYLSH3FT · pith_short_8: MQ2PRNXA

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/MQ2PRNXARYLSH3FTV2FGVKLMIP \
  | 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: 6434f8b6e08e1723ecb3ae8a6aa96c43ec4a3593c82bc9e7a66015b2928e6e1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6be34847dab60791b2e719ca70157ae657fdac3716af1b41d68f9c9bd2773807",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AC",
    "submitted_at": "2006-12-04T20:54:02Z",
    "title_canon_sha256": "9ff77818adba5cf5186a693f89518d515b610135d0a3dd86e4c9e74d02926395"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612047",
    "kind": "arxiv",
    "version": 2
  }
}