Pith Number

pith:46AI4KEN

pith:2016:46AI4KENDZG4JJ36TRWMA2NFOJ

not attested not anchored not stored refs pending

Betti categories of graded modules and applications to monomial ideals and toric rings

Alexandre Tchernev, Marco Varisco

arxiv:1605.09748 v1 · 2016-05-31 · math.AC · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{46AI4KENDZG4JJ36TRWMA2NFOJ}

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	2026-05-18T01:13:10.228883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7808e288d1e4dc4a77e9c6cc069a5727ae87f2e95a426eed14e9f219bb34558

Aliases

arxiv: 1605.09748 · arxiv_version: 1605.09748v1 · doi: 10.48550/arxiv.1605.09748 · pith_short_12: 46AI4KENDZG4 · pith_short_16: 46AI4KENDZG4JJ36 · pith_short_8: 46AI4KEN

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/46AI4KENDZG4JJ36TRWMA2NFOJ \
  | 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: e7808e288d1e4dc4a77e9c6cc069a5727ae87f2e95a426eed14e9f219bb34558

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "389d1bf7dfaead1bea69ecfdb852c8cea336908bcadd9eaa38fcd478cc8e6dea",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-05-31T18:09:17Z",
    "title_canon_sha256": "a587c3bb19db586496175160f3c549b66bd38063e75b9ccb037df6701fec01db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.09748",
    "kind": "arxiv",
    "version": 1
  }
}